Stock-Flow Model for Forecasting Labor Supply

Stock-Flow Model for Forecasting Labor Supply

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Chun-pong Sing1; P. E. D. Love2; and C. M. Tam3

Abstract: Forecasting the supply of labor in the construction industry is pivotal to long-term economic growth. A labor supply model using a stock-flow approach was developed in this research for use in the construction industry. The model was tested using Hong Kong census statistics and data derived from interviews with 3,000 randomly selected construction workers. The findings were determined using a stockflow model, which enabled the determination of future aging distribution trends and workforce supply for specific trade types. The developed stock-flow model can be effectively used in countries in which registration schemes for construction workers are in use. DOI: 10.1061/ (ASCE)CO.1943-7862.0000485. © 2012 American Society of Civil Engineers. CE Database subject headings: Forecasting; Labor; Construction industry; Hong Kong. Author keywords: Forecasting; Labor supply; Stock-flow model; Hong Kong.

Introduction Human resources are needed to construct critical social and economic infrastructure. Such infrastructure provides the basic physical and organizational structures needed for the operation of society and enterprises, and the services and facilities necessary for an economy to function (Agapiou et al. 1995; Schmidt et al. 2003; Wong et al. 2005). Specialist and non skilled labor is required to construct buildings, roads, bridges, schools, and housing. Construction is crafted in a way that is heavily reliant on an adequate supply of construction workers (Mackenzie et al. 2000). In many developed economies such as Australia, Hong Kong, Singapore, and the United Kingdom (UK), skill shortages have and continue to prevail in many sectors, particularly construction. In Hong Kong, for example, during the 1990s the construction industry experienced significant growth resulting from the initiation of several large-scale infrastructure projects. The demand for skilledtrade personnel exceeded the available supply, which resulted in a significant increase in wages. Briscoe and Wilson (1991) revealed that in the UK in the late 1980s, when skills shortages were being experienced, the industry’s strategy for tackling this problem was to also increase remuneration. In contrast, Singapore adopted a labor importation scheme (Briscoe and Wilson 1991; Borjas 2004). The adoption of short-term strategies of this nature can severely affect future labor supply. For example, the importation of labor can place a downward pressure on wage levels for local labor (Borjas 2004), which can lead to local labor seeking alternative employment and discouraging future people from entering the industry. Increasing remuneration can increase the costs of construction and influence 1

Senior Lecturer, Dept. of Construction Management, Curtin Univ., Perth WA 6845, Australia. E-mail: [email protected] 2 John Curtin Distinguished Professor, Dept. of Construction Management, Curtin Univ., Perth WA 6845 Australia (corresponding author). E-mail: [email protected] 3 Professor and Associate Dean, Dept. of Civil and Architectural Engineering, City Univ. of Hong Kong, Hong Kong SAR, China. E-mail: [email protected] Note. This manuscript was submitted on August 14, 2010; approved on September 2, 2011; published online on September 5, 2011. Discussion period open until November 1, 2012; separate discussions must be submitted for individual papers. This paper is part of the Journal of Construction Engineering and Management, Vol. 138, No. 6, June 1, 2012. ©ASCE, ISSN 0733-9364/2012/6-707–715/$25.00.

inflation within an economy. Therefore, imperative that labor supply forecasting be undertaken so the appropriate educational and training mechanisms are enacted to enable the labor supply to meet the demand side of workforce (Hillebrandt and Meikle 1985; Ofori 1988). Despite the importance of forecasting labor supply, there has been limited empirical research undertaken in the construction industry. Inadequate statistics pertaining to labor supply in the construction industry have been identified as a major barrier to formulating accurate forecasting (Bassett 1973; Rosenfeld and Warszawski 1993; Agapiou et al. 1995). According to Harvey and Murthy (1998), the forecasting of labor supply for an industry sector is an arduous and complicated task as many factors need to be considered. Notwithstanding this concern, attempts have been made to forecast the supply side of labor using an array of different models (e.g., Agapiou et al. 1995; Bell et al. 2003; Rizza et al. 2003). Against this contextual backdrop, the research presented in this paper builds on the work of Briscoe and Wilson (1993) and Rizza et al. (2003) by developing a stock-flow model to forecast labor supply within the Hong Kong construction industry. It has been constructed by incorporating the key factors that affect the inflow/outflow of the workforce and information derived from a questionnaire survey.

Labor Supply Models Policy makers and managers need to determine the supply of labor currently within the Hong Kong construction industry and estimate those who are preparing to enter the workforce to ensure construction projects can be built efficiently and effectively. Labor supply forecasting models that have been used to determine labor supply in construction can be categorized as inflow and outflow (stock-flow), multiple regression, autoregressive integrated moving average (ARIMA), and econometric. Inflow and Outflow Modeling The inflow of labor is typically based on the concept of transition such as new entrants, promotion, or transfers (Purkiss 1981). A “pull” flow is often generated by a need to fill vacancies, for example, a promotion to a specific organizational or managerial need. The probability of transition from one position to another can be defined using the Markov Chain

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xðt þ 1Þ ¼ xðtÞP þ NðT þ 1Þp

ð1Þ

where xðtÞ ¼ stock vector that is observed at time t; nðt þ 1Þ ¼ number of new entrants at time (t þ 1); p = indicates entrants who are distributed among the states of categories; P = is the matrix of transition proportions among the categories, and the expected stocks vector at time ðt þ 1Þ is xðt þ 1Þ. Although this model initially provided invaluable insights to labor supply, it neglects the complexities of labor supply within the industry and is thus limited in scope and application. For example, it only assesses existing labor stock and recruitment, wastage, working conditions, promotion policies, and labor market trends (Edwards 1983). In addressing the limitations of this model, Briscoe and Wilson (1993) developed a stock-flow model that included factors such as the existing stock of labor (which included employed and unemployed persons) and labor actively searching for work net of any unfilled vacancies. Essentially, the stock of labor is subject to constant change because of retirement and new entrants to the industry. Briscoe and Wilson’s (1993) supply model is expressed as TS ¼ CS þ U RD W RM þ NS

ð2Þ

where TS = total supply of occupational skill; CS = current supply; i = forecast year, t; U = number of unemployed persons; RD = number of workers lost because of retirements and death; W = number of workers transfered to other occupations and industries (“wastage”); RM = number of workers moved between the regions at the regional level; and NS = number of new entrants. There is a proclivity for stock-flow models to eschew the complexity associated with more than one trade. This is particularly the case in Hong Kong, where a person may register as being competent in one or more trade areas with the Hong Kong Construction Worker Registration Authority (HKCWRA) or as general labor. Moreover, the changing age distribution of the workforce is another factor that has not been previously taken into account in forecasting labor supply models developed within construction. Multiple Regression Techniques Agapiou et al. (1995) utilized multiple regression techniques to model the flow of the new entrants to the construction industry. Agapiou et al. (1995) sought to examine how relative weekly earnings and output influenced the future supply of labor within the construction industry. An aggregated labor supply model was developed and is expressed as tct ¼ a þ bðrywt Þ þ cðryawt Þ þ dðrawt Þ þ eðcot Þ þ f ðdyt Þ þ gðtct1 Þ þ hðslt Þ

regression models can be misleading for policy makers, especially when small effects come into question (Wilkinson 1999). The forecast of supply, i.e., new entrants, is usually dependent on selected economical variables, such as employment rate and real wage rate. Most economical variables are influenced by social issues therefore, insufficient understanding of past conditions can corrupt future forecasts. Autoregressive Integrated Moving Average Autoregressive Integrated Moving Average (ARIMA) is used to identify the characteristics of a time series and to determine the “best” model through a process of iteration. It decomposes timeseries data into an autoregressive process [ARðpÞ], in which there is a memory of past parameters; an integrating process [IðdÞ], which accounts for stabilizing or making the data stationary and noncorrelated, making it easier to forecast; and a moving average [MAðqÞ] of the forecast error, such that the longer the historical data, the more accurate the forecast. The ARIMA has been used widely for forecasting in construction (e.g., Goh and Teo 2000; Lu and AbouRizk 2009; Fan et al. 2010). In forecasting labor supply, Wong et al. (2005) used the ARIMA approach and used the following variables: employment level, productivity, unemployment rate, underemployment rate, and real wages. Wong et al. (2005) modeled each indicator using quarterly time-series statistics from 1983 to 2002 using Augmented Dickey-Fuller and the correlegram of autocorrelations. The Wong et al. (2005) MAðqÞ model for estimation is expressed as Z t ¼ ϕ4 Z t4 þ at

where Z t = Y t Y t1 ; Y t = itime series of the indicator being studied; ϕ = MA coefficients; and a = random error term. The model developed by Wong et al. provides the foundation to determine labor shortages or surpluses and therefore can be used to adjust policies with regard to construction activity. The model, however, is not able to forecast the actual supply of labor that is needed to meet demand. Akin to regression models, the moving average approach is based on the notion that past data will prescribe future changing patterns, which again can be misleading for policy makers. Econometric Modeling Beenstock and Warburton (1982) examined the association between the “supply of labor” and “real wage rate”. They developed the following labor supply empirical equation on the basis of established employment data

ð3Þ

where tct = intake of craft trainees; ryw = the average weekly earnings of youth in construction relative to earnings of youth in all industries and services; ryaw = average weekly earnings of youth in construction relative to adults in construction; raw = average weekly earnings of adults in construction relative to earnings of adults in all industries and services; dy = national population between the ages of 15 and 24; and sl = total number of school leavers entering employment. The results found in Eq. (3) are consistent with the human capital view of labor supply proposed by Green (1990), who revealed that wages and relative earnings have a strong influence on the supply of new entrants. Regression models developed to date have been based on the premise that historical data will be replicated in the future. Yet, shifting trends and the changing demands and needs of industry clients and demographics of the population are difficult, and perhaps impossible, to predict in the long term. A reliance on

ð4Þ

S ¼ f ðw; rÞ

ð5Þ

where w = willingness of the workforce, that is, hours that average people wish to work; and r = real wage rate. The model is based on the concept of an indifference curve: any point on the curve represents a combination of income (or real wage rate) and a willingness to work. As wages rise, people are confronted with the decision to either increase income by working longer hours or maintain current income levels by working less and having more leisure time. Grossberg (1989) developed a mathematical model to quantify the willingness of people toward different wage levels by simulating how they choose to work under “wage rate uncertainty”. The proposed economic model was heavily dependent on an individual’s perception. This was also observed and confirmed by Ruby (1999), who revealed that the labor supply curve tended to slope upward when people preferred to work. Conversely, the labor supply curve was reversed when people wanted to enjoy more leisure time and work fewer hours as wage levels rose. To date, limited

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studies in the normative literature that have been able to successfully demonstrate the relationship between the supply of labor and real wage rate.


Proposed Supply-Side Model Building on the work of Briscoe and Wilson (1993) and Rizza et al. (2003), a modified stock-flow labor supply model is developed. The model incorporates the in/out flow of labor and information derived from a questionnaire telephone survey that can provide a more reliable output than regression-based approaches. The creation of this stock flow commences with determining the existing workforce. Labor inventory is then subjected to “new entrants,” “retired labor,” and other key variables such as “labor mobility.” The key parameters that are included in the developed supply model are shown in Table 1: age; current stock of labor; attitude rate (or retention rate); potential new entrants; promotion procedure; recruitment rule; retirement rate; time lag between entry and completion of job training; and skill mix of the workforce. The parameters identified are incorporated into the following equation for forecasting the supply of construction workers in Hong Kong and the model function is expressed as For each work trade, i Nt ¼

70 X

fN a;t1 · ð1 r a;t1 Þ þ E t · ð1 wi Þ þ ðI in I out Þ O

a¼20

þ GSR · N gw g þ ε

ð6Þ

where N t = total number of construction workers in year t; N a;t1 = number of construction workers who were a years old in year t 1; r a;t1 = retirement rates for construction workers who were age a in

Table 1. Key Model Parameters Parameter Age Current stock of labor

Attitude rate

Potential new entrants

Promotion procedure

Recruitment rule

Retirement rate

Time lag between entry and completion of job training Skill mix of the workforce

Authors Purkiss (1981); Green (1990) Purkiss (1981); McClean (1991); Harvey and Murthy (1988); Agapiou et al. (1995); Edwards (1983); Martin (1990); Green (1990); Purkiss (1981); Edwards (1983); Harvey and Murthy (1988); Martin (1990) Edwards (1983); Harvey and Murthy (1988); Martin (1990); Agapiou et al. (1995); Green (1990) Purkiss (1981); Silverman et al. (1988); McClean (1991); Edwards (1983); Green (1990) Purkiss (1981); Edwards (1983); Martin (1990); McClean (1991); Green (1990) Purkiss (1981); Edwards (1983); Harvey and Murthy (1988); Martin (1990) Harvey and Murthy (1988); Green (1990) Harvey and Murthy (1988); Martin (1990)

period t 1; E t = number of new entrants in the year t; wi = ratio of attrition for trade i; I in = number of construction workers entering this trade from internal promotion; I out = number of construction workers leaving this trade because of internal promotion; O = number of construction workers working in cities of the vicinity; GSR = ratio of registered general workers who are actually engaged in the trade I; N gw = number of registered general workers; i = trade number, for i ∈ ð1; nÞ; ε = error term of the prediction. With the assistance of MatLab software, Eq. (6) was turned into a computer-based model to enable forecasts from a database of 260,000 workers and to produce visualizations of the output. The architecture of the database that was designed for forecasting is shown in Fig. 1. The developed architecture enables data to be readily updated and used to evaluate the characteristics of labor workforce, (i.e., aging workforce) and produce visualizations of the overall effect of the supply side from any change in training policies that may be implemented. The developed labor supply model was tested using data that was obtained from several publications provided by agencies such as the Construction Industry Council Training Academy (CICTA) and the HKCWRA. Types of data obtained from HKCWRA included the age of workers and the total number of workers registered as general workers and for specific trade types. From a population of 60,000 general workers, 3,000 were randomly contacted by telephone and invited to participate in the research and to provide data about their current and future work arrangements (e.g., training acquired, specialist trade type, and expected retirement age). All 3,000 agreed to participate in the research. The data that was obtained from participants was entered into the developed database and subsequently analyzed using the MatLab software. A total of 40% of respondents had registered as a “general worker” and “skilled tradesperson.” Therefore, an adjustment process within the developed model was needed to transfer nongenuine general workers into their respective skilled trades. Most respondents stated that they would continue to work until they physically could not do so any longer or until employers ceased their employment. Trade Classification List, i The trade classification list that is used for the supply model is compiled by examining the popular categories of subcontract trades used to construct a building in Hong Kong (see Table 2). A similar approach was adopted by Rosenfeld and Warszawski (1993). References are also made to published materials from the governmental departments (e.g., labor deployment records) to determine those specific trades that require attention. Estimated Number of New Entrants, E t The percentage of new entrants for each trade is derived from data that projects the total intake of different courses provided by the Hong Kong local training authorities and the percentage distribution of graduates available to work, which is derived from published annual reports (e.g., Annual Report 2009, Hong Kong Construction Industry Council). The data that is obtained is then entered into the model (Fig. 2) through the database (s2.1). The time lag in training for different courses (e.g., in the case of a 2-year, full-time course for a craftsperson, the number of new entrants is based on the intake number from the previous 2 years) is also simulated in the supply model. Eq. (7) is used to estimate the new entrants. Attrition Ratio, w An attrition ratio can be defined as the percentage of graduates who do not engage in the construction industry. In this model, the profile




Fig. 1. Architecture for labor supply model

Table 2. Types of Construction Workers Trade number, i

Trade name

Trade number, i

Trade name

1 2 3 4 5 6

Bar bender Drainlayer Concretor Scaffolder Electrician Plumber

7 8 9 10 11 12

General welder Equipment operator Painter and decorator Bricklayer Building services mechanic General workers (low-skilled workers)

of attrition is established through figures commonly found in the annual reports provided by the Hong Kong training authority. Thus, for any trade, i, the following equation combining the estimated number of new entrants and attrition ratio is developed: For year t and trade i E0i;t ¼ ðN 2i;t2 þ N 0i;t Þ · ð1 wi Þ

ð7Þ

where E 0t;i = new entrants of workers in trade i and year t after consideration of the attrition ratio; N 2t2 = number of intakes of the 2-year basic craft course for trade i in year t 2; N 0t = number

of intakes of the 1-year basic short course for trade i in current year t; and wi = attrition ratio of work trade i. Retirement Rate, r The retirement ratio can be defined as the percentage of workers retiring from their current position at the age of 60. The retirement age of 60 is commonly adopted by Hong Kong government agencies. According to Purkiss (1981) and McClean (1991), the probability of retirement should be described as a function of age, rather than length of service. As construction is labor intensive, general workers and trades personnel need to be physically fit and in good health, particularly bar benders and concreters. A retirement ratio is assigned to each trade using a range of 0.6 to 1, on the basis of the degree of physical activity required for each trade. A retirement ratio of 0.9, for example, indicates that over 90% of labor would retire or be unable to continue their work in the age range of 60 to 65. A worker over age 65 would be assumed to be retired or unfit for work and therefore would be assigned a value of 1. Career Progression/Promotion of Construction Workers, I in and I out

Fig. 2. Example of graphic output from proposed stock-flow model

To acquire an ameliorated understanding of the number of skilled workers required for particular positions, promotion or career advancement should also be considered in the supply pool. In Hong Kong, construction workers are required to register with HKCWRA under a number of classifications that are identified in Table 3. A registered skilled/semiskilled worker who is classified as provisional, for example, is required to complete a specified training course or pass a relevant trade test within 3 years to obtain full status. If a registered worker (Provisional) fails to complete a relevant trade test and specified training course within the 3-year period, then he or she has the option of applying for registration



Table 3. Categories of Workers under Construction Workers Registration Ordinance Categories


(1) Registered Skilled Worker (for a designated trade)

(2) Registered Skilled Worker (Provisional) (for designated trade)

(3) Registered Semiskilled Worker (for designated trade)

(4) Registered Semiskilled Worker (Provisional) (for designated trade)

(5) Registered General Worker

Qualification for Registration Holds a trade test certificate issued by the local training authorities or as specified by the Registration Ordinance (e.g., other recognized registration, certificates, or licenses). For those not holding qualifications listed in item (1), possesses no less than 6 years of experience to personally carry out construction work of a particular trade with documentary proof. Holds an intermediate trade test certificate issued by local training authorities, or other qualifications as specified by the Registration Ordinance. For those not holding qualifications listed in item (3), possesses no less than 2 years of experience to personally carry out construction work of a particular trade with documentary proof. Holds a construction industry safety training certificate.a

Source: Construction Workers Registration Authority (HKCWRA), Hong Kong. a This is a one-day training course for any person intending to work on construction sites. The objective of safety training is to introduce the basic safety requirements on construction sites, such as use of personal protective equipment. After attending the lesson and passing the test, a green card will be awarded.

as a general worker. According to the 2009 HKCIC annual report, the trade test is the most common way for provisional construction workers to acquire promotion to the skilled/semiskilled labor status. Thus, in the proposed model, the number of provisional workers promoted to skilled/semiskilled as a result of passing this trade test is used. Number of Construction Labor Working Overseas, O The mobility of labor in Hong Kong is dependent on its domestic economic climate and that of neighboring cities such as Macau. Financial remuneration is a key driver that influences labor mobility. The Hong Kong construction industry has experienced a considerable decline in construction activity since 2000 and as a result of the global economic crisis (GEC). A number of planned economic infrastructure projects have been placed on hold. Before the GEC, Hong Kong workers were attracted to Macau as it was

experiencing considerable growth and better job opportunities. However, many of the major construction projects that were undertaken in Macau have been completed, and workers are returning to Hong Kong for employment (VTC 2009). Number of General Workers Who Are Actually Engaged in a Skilled Trade, GSR As shown in Table 3, labor in Hong Kong is classified as being (a) skilled or semiskilled; and (b) low-skilled and without any formal qualifications. The HKCWRA estimates that there are 170,000 general workers, which accounts for 63% of the total number of registrations. Therefore, a certain proportion of general workers are assumed to be working within a specific trade. Findings from the telephone survey revealed that approximately 40% of the sample registered as being both skilled and a general worker. Taking into account the potential for double counting, the misregistered workers need to be reassigned back to their original trades using an assignment model. Thus, the General-Skill ratio (GSR) for each skilled trade is introduced, which is defined as the percentage of the general workers who are actually working in specific skilled trades. This ratio was obtained from the information provided by the general workers who were interviewed using the telephone survey. The GSR for each trade, the number of workers available in each trade i in year t can then be re-estimated using Eqs. (8) and (9). This is also defined as the process of the adjustment on general workers in the supply model. N ti;adj ¼ ðGSRi ÞN tgw þ N ti

for i ∈ ð1; nÞ

ð8Þ

where N ti;adj = Adjusted number of available skilled workers in trade number i in year t (i.e., declaration of skilled workers from the pool of general workers); N tgw = projected general workers in year t; N ti = forecasting number of genuine skilled workers in trade number i in year t; GSRi = General-Skill Ratio for trade i; and n = number of skilled trades in the trade classification list. n X N tgw;adj ¼ 1 GSRi N tgw ð9Þ i¼1

where N tgw;adj = projected number of genuine general workers in year t after adjustment on general workers (i.e., declaration of skilled workers from the pool of general workers); and GSRi = General-Skill Ratio for trade i. To simulate the inflow and outflow of general workers, an aging index is developed. This is understood as general workers who do not need to attend a training course before registration. Trades sharing similar working conditions with general workers, such as bar benders and concreters, were selected for the purposes of simulating future supply requirements. The formula for the Aging Index (AIt for general workers) is Xn N ti · β i AIt ¼ Xni¼1 1 i ð10Þ N · β ii i¼1 i where N ti = number of skilled workers in trade i in year number t; t = year number; β i ¼ 1 if the trade i has a similar working nature as general worker; s ¼ 0 if the trade i does not have a similar working nature as general workers. A regression model that is formulated to fit the aging index is developed and expressed as N tgw ¼ ðaxt þ bÞ • N 1gw

ð11Þ

where N tgw = projected supply of general workers in year t; gw = general workers; xt = year number t = (1, 2, 3…)



Table 4. Summary of the Definition of Aging Workforce Rule 1 2


3

4

5

Description Defined as a working individual who is 40 years of age or older Defined as those workers who are beyond the age of 45 Higher percentage net increase in the working age population will occur in the 55 to 64 age category in the forthcoming years Higher percentage increase in working population in the 45 to 64 age category in the forthcoming years Older workers (between the ages of 45 and 65 years) will account for a large share of the working-age population

Author Bockman et al. (2008) Streb et al. (2009) Purcell (2000)

Lende (2005)

Human Resources Development Canada (2002)

Fig. 5. Concreters: Aging workforce

Fig. 6. Age distribution of painters in forthcoming 10 years Fig. 3. Age distribution of concreters in forthcoming 10 years

The developed model can provide a control interface for converting the existing census figures that have been obtained (i.e., in the format of numbers and all key variables) into a graphical format

(Fig. 2). The age distribution for each category of skilled workers before adjusting the GSR ratio within the model can then be used to provide insights about the characteristics of the workforce within the industry. Outputs generated from the model can also be used to make comparisons with a demand-side model to ensure that labor supply and demand correspond.

Fig. 4. Concreters: Aging workforce

Fig. 7. Painter: Without aging workforce

Empirical Estimation and Supply Model Application




Identification of Aging Workforce

Fig. 8. Painters: Without aging workforce

Fig. 9. Projected age distribution of bar benders in forthcoming 10 years, varying the number of intakes

The aging workforce has long been recognized as one of the significant factors affecting organizational productivity in many industrialized countries (Streb et al. 2009). The construction industry, for example, could face both a labor shortage and skills shortage once an aging workforce is formed. Definitions of what constitutes an aging workforce are presented in Table 4. An examination of the literature revealed that a number of determinants of an aging workforce exist (see Table 4). As shown in Table 4, rules 1 and 2 are similar and therefore can be combined. As a result, the following rules are formulated and incorporated into the supply model. If the following rules are fulfilled, then trades can be identified as having an aging problem in the future. Rule (1): The percentage of workers in the 45–65 age categories has accounted for more than α ¼ 50% of the total working population in the forthcoming years.

Fig. 10. Projected age distribution of bar benders in forthcoming 10 years, varying the attrition ratio




Rule (2): The percentage net increase of workers in the 25–45 age category is less than the 45–65 age category in the forthcoming years. Rule (3): The mean age is located on the age category of β ¼ 45 or higher in the forthcoming years. The values of parameters α and β are determined by policy makers or the training policies that may be developed by a local training authority (in this case, α and β are set to be 50 and 45%, respectively). On the basis of the above three criteria and selected numerical values for each of the parameters, the model reveals that the trades subjected to an aging workforce are (1) bar bender, (2) drain layer, (3) concreter, and (4) general welder. An example of the age distribution for the concrete and painting trades are provided in Figs. 3–5 and Figs. 6–8, respectively. Fig. 11. Effect on varying the number of intakes (E) or attrition ratio (w) in the mean age of bar benders in forthcoming 10 years

Fig. 12. Effect on varying the number of intakes (E) or attrition ratio (w) in bar benders under age 45 in forthcoming 10 years

Scenario Analysis for the Supply Model A number of strategies may be adopted to address the aging workforce of the supply pool, such as the local training authority increasing its intake of trainees (Ei ) and reducing their attrition ratio (wi ). The effectiveness of such strategies can be examined using a scenario analysis. For example, in the case of the bar bender, where Ei ¼ 60, wi ¼ 0:2, ri ¼ 0:9, O ¼ 0, and I in ¼ 64%, Figs. 4 and 5 show that this trade will be subjected to an undersupply resulting from the increasing age of workers in the future. The CICTA could attract new entrants by providing financial allowances and subsidies. With regard to the inflow of intakes, various estimates for the future supply of bar benders are projected on the basis of the number of intake ranges of E i þ 10%, Ei þ 20%, and Ei þ 30%, respectively, with other key variables held constant. Fig. 9 identifies the age distribution of the bar bender on the basis of various specific ranges of new entrants. Another set of estimates of future labor supply is projected on the basis of the attrition rate of 30, 20, and 10% with other key variables being held constant. The age distribution of the bar bender under various attrition rates of graduates is shown in Fig. 10. By comparing the mean age and percentage distribution for each trade in the age categories (Figs. 11 and 12), the effectiveness of the respective reformulation strategies can be evaluated. For example, in case of the bar bender, an increase in the number of intakes (e.g., E i þ 10%, Ei þ 20%, Ei þ 30%) demonstrates positive results in reducing the mean age and percentage of age categories over age 45 in the projected scenario.

Fig. 13. Procedures for applying the stock-flow model 714 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / JUNE 2012



The use of the supply model for forecasting and scenario analyses could enable the training authority to better understand the characteristics of the workforce such as the age distribution of specific trades. Using this information, the training authority could then reformulate their strategies to address the changing demographics of the workforce. This situation is prevalent in many Western economies, so the stock-flow model could potentially be used to address this situation. An overview of the process for applying the developed stock-flow model to forecast the supply of construction workers is presented in Fig. 13. The model can be applied only in countries where a registration scheme exists for construction workers.

Conclusion A plethora of techniques have been developed to forecast the supply of labor for different industries. No specific technique has succeeded in fully utilizing real-life databases and information obtained directly from the workforce pertaining to their future aspirations and employment. To address this shortfall, this paper developed a pragmatic labor supply model using a stock-flow approach that can be used to forecast labor for the next 10 years in the construction industry. The obtained data enabled the model not only to determine the aging distribution trends but also to identify the availability of the workforce using various scenarios and over the predefined period. The accuracy of the model, however, is dependent the quality and availability of data for the analysis. Data from the supply model is derived from databases that contain the number of registered skilled and nonskilled workers (general workers) who are registered, and information on the new entrants. An examination of the databases revealed some general workers were also registered as skilled workers, which may have distorted the accuracy of the databases. To address this problem, a telephone survey was conducted to determine the extent to which general workers had also registered as a skilled worker for a specific trade. Thus, the concept of the General-Skill ratio was introduced into the modeling process. It is acknowledged, however, that a better understanding of the characteristics of general workers is required to improve the proposed model’s accuracy. The identification of new entrants was also found to be problematic as some skilled workers were trained from the traditional master-apprenticeship, which tends to be informal. Therefore, they had to be discounted from the number of new entrants, thus reducing the model’s ability to accurately forecast the number of incoming workers. Future research will attempt to capture and include the aforementioned issues that limit the model’s forecasting ability.

References Agapiou, A., Price, A. D. F., and Maccaffer, R. (1995). “Forecasting the supply of construction skills in the UK.” Constr. Manage. Econ., 13(4), 353–364. Bassett, G. A. (1973). “Elements of manpower forecasting and scheduling.” Hum. Resour. Manage., 3, 35–40. Beenstock, M., and Warburton, P. (1982). “An aggregative model of the UK labour market.” Oxford Econ. Pap. New Series, 34(2), 253–275. Bell, L. C., and Brandenburg, S. G. (2003). “Forecasting construction staffing for transportation agencies.” J. Manage. Eng., 19(3), 116–120. Bockman, S., and Sirotnik, B. (2008). “The aging workforce: An expanded definition.” Bus. Renaissance Q., 3(3), 129–135. Borjas, G. J. (2004). “Increasing the supply of labor through immigration: Measuring the impact on native-born workers.” CIS Backgrounder, Centre for Immigration Studies, Washington, DC. Briscoe, G., and Wilson, R. (1991). “Explanations of the demand for labour in

the United Kingdom engineering sector.” Appl. Econ., 23(5), 913–926. Briscoe, G., and Wilson, R. (1993). Employment forecasting in the construction industry, Avebury, Surrey, UK. Edwards, J. S. (1983). “A survey of manpower planning models and their application.” J. Oper. Res. Soc., 34(11), 1031–1040. Fan, R. Y. C., Ng, S. T., and Wong, J. M. W. (2010). “Reliability of the Box-Jenkins model for forecasting construction demand covering times of economic austerity.” Constr. Manage. Econ., 28(3), 241–254. Goh, B. H., and Teo, H. P. (2000). “Forecasting construction industry demand, price and productivity in Singapore: The Box-Jenkins approach.” Constr. Manage. Econ., 18(5), 607–618. Green, A. E. (1990). “Craft and technician skill shortages in engineering.” Int. J. Manpower, 11(2), 18–22. Grossberg, A. J. (1989). “Labor supply under real wage uncertainty: A new look at the intertemporal substitution hypothesis.” South. Econ. J., 55(4), 974–986. Harvey, E. B., and Murthy, K. S. R. (1988). “Forecasting manpower demand and supply: A model for the accounting professionals in Canada.” Int. J. Forecast., 4(4), 551–562. Hillebrandt, P. M., and Meikle, J. L. (1985). “Resource planning for construction.” Constr. Manage. Econ., 3(3), 249–263. Hong Kong Construction Industry Council (HKCIC). “Annual report 2009.” 〈http://www.hkcic.org〉 (July 10, 2010). Hong Kong Construction Workers Registration Authority (HKCWRA). “Total number of valid registered construction workers.” 〈http://www .cwra.org.hk〉 (July 10, 2010). Human Resources Development Canada. (2000). “Challenges of an aging workforce.” Dept. of Human Resources and Skills Development Canada, 〈http://www.hrsdc.gc.ca〉 (July 20, 2010). Lende, T. (2005). “Older workers: Opportunity or challenge?” Canadian Manager, 30(1), 20–30. Lu, Y., and AbouRizk, S. M. (2009). “Automated Box—Jenkins forecasting modelling.” Autom. Constr., 18(5), 547–558. Mackenzie, S., Kilpatrick, A. R., and Akintoye, A. (2000). “UK construction skills shortage response strategies and an analysis of industry perceptions.” Constr. Manage. Econ., 18(7), 853–862. Martin, L. (1990). “Nursing skills: Is there a shortage?” Int. J. Manpower, 11(2), 37–43. McClean, S. (1991). “Manpower planning models and their estimation.” Eur. J. Oper. Res., 51(2), 179–187. Ofori, G. (1988). “Construction industry and economic growth in Singapore.” Constr. Manage. Econ., 6(1), 57–70. Purcell, P. (2000). “Older workers: Employment and retirement trends.” CRS Rep. for Congress, Congressional Research Service, Washington, DC. Purkiss, C. (1981). “Corporate manpower planning: A review of models.” Eur. J. Oper. Res., 8(4), 315–323. Rizza, R. A. et al. (2003). “A model to determine workforce needs for endocrinologists in the United States until 2020.” Diabetes Care, 26(5), 1545–1552. Rosenfeld, Y., and Warszawski, A. (1993). “Forecasting methodology of national demand for construction labour.” Constr. Manage. Econ., 11(1), 18–29. Ruby, D. A. (1999). “Labour supply decisions and labour market equilibrim.” 〈http://digitaleconomist.org〉 (August 3, 2010). Schmidt, S. L., Schomann, K., and Terssaring, M. (2003). “Early identification of skill need in Europe.” In Cedefop reference series, Luxembourg. Silverman, J., Steuer, R. E., and Whisman, A. W. (1988). “A multi-period, multiple criteria optimization system for manpower planning.” Eur. J. Oper. Res., 34(2), 160–170. Streb, C., Voelpel, S., and Leibold, M. (2009). “Aging workforce management in the automobile industry: Defining the concept and its constituting elements.” Ger. J. Res. Hum. Res. Manage., 23(1), 8–27. The Vocational Training Council (VTC). (2009). Manpower survey report of the building and civil engineering industry, Hong Kong. Wilkinson, L. (1999). “Statistical methods in psychology journals: Guidelines and explanations.” Am. Psychol., 54(8), 594–604. Wong, M. W., Chan, P. C., and Chiang, Y. H. (2005). “Time series forecasts of the construction labour market in Hong Kong: The Box-Jenkins approach.” Constr. Manage. Econ., 23(9), 979–991.



Multiplier Model for Forecasting Manpower Demand


Chun-pong Sing1; Peter E. D. Love2; and C. M. Tam3

Abstract: To better manage and forecast the demand for labor in the construction industry, a mathematical model is developed using a distributed lag model and labor multiplier approach. The model is tested using economic statistics and manpower data derived from Hong Kong construction projects. The model can be used by public and private sectors to forecast future labor demand so that an optimal workforce can be attained. DOI: 10.1061/(ASCE)CO.1943-7862.0000529. © 2012 American Society of Civil Engineers. CE Database subject headings: Forecasting; Labor; Construction management; Hong Kong. Author keywords: Forecasting; Manpower demand; Labor multiplier; Distributed lag model.

Introduction Manpower forecasting is an essential and important strategic managerial practice for government and business organizations (Barnes 1975; Park et al. 2007). It is a technique that can be used to ensure organizations have the appropriate personnel to achieve the demands and requirements for their services (Khoong et al. 1996; Diebold 2007). Additionally, a well-defined manpower forecasting plan can be used to respond to changing demands that exist within dynamic labor markets such as construction (Smith 1997). A question that many organizations in construction are often confronted with is “what manpower will be required in the future?”. The changing demographics of the workforce, and in some countries prevailing skills shortages, have resulted in a plethora of approaches for forecasting the future demand requirements of construction labor to be propagated (e.g., Uwakweh and Maloney 1991; Hua 2000; Wong et al. 2010). Forecasting accurate manpower demand is a challenging task for the construction industry because it is often subjected to vast fluctuations in output (Rosenfeld and Warszawski 1993; Hua 2000; Wong et al. 2010). In addressing the need for accurate manpower demand forecasting models, several have been propagated (Briscoe and Wilson 1993; Rosenfeld and Warszawski 1993; Wong et al. 2005, 2007, 2010); Yet, the models developed to date are complicated and contain many explanatory variables such as labor productivity and wage level that are not able to be predicted with any degree of accuracy. Meanwhile, because the building industry is composed of different trade workers, it remains a challenging task to assign precise values for each variable. Instead, building on previous research, this paper develops a manpower forecasting model that utilizes linkages between major economic variables such as 1

Postgraduate Student, Dept. of Construction Management, Curtin Univ., GPO Box U1987, Perth WA 6845, Australia. 2 John Curtin Distinguished Professor, School of Built Environment, Curtin Univ., GPO Box U1987, Perth WA 6845, Australia (corresponding author). E-mail: [email protected] 3 Chair Professor, Dept. of Building and Construction, City Univ. of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong SAR. E-mail: [email protected] Note. This manuscript was submitted on November 22, 2010; approved on January 12, 2012; published online on January 14, 2012. Discussion period open until March 1, 2013; separate discussions must be submitted for individual papers. This paper is part of the Journal of Construction Engineering and Management, Vol. 138, No. 10, October 1, 2012. © ASCE, ISSN 0733-9364/2012/10-1161-1168/$25.00.

construction output and labor that can be used to forecast labor demand in changing economic conditions. The presented model focuses on the relationship between construction output and economic conditions, and therefore its accuracy is not dependent on a spate of explanatory variables. The model is demonstrated using data derived from private sector construction projects in Hong Kong.

Manpower Demand Types of manpower forecasting techniques that have been developed and empirically tested in construction include univariate time series, multiple regression, and econometric modeling (Wong et al. 2010). Multiple regression and econometric techniques that have been used to predict manpower demand are reliant on a number of key variables such as employment and wage rates. Such models are complicated and comprise multiple processes for estimating key variables that can change dramatically and thus suppress their accuracy. An alternative to the aforementioned approaches is the labor multiplier technique, which enables the relationship between construction output and labor demand to be determined. Similar approaches have been developed by Uwakweh and Maloney (1991) and Rosenfeld and Warszawski (1993), which can cater for dynamics changes in manpower based on various economic conditions. A detailed review of manpower demand forecasting in construction can be found in Wong et al. (2005, 2007). Econometric Model Using Multiple Regression Techniques Econometric models make use of the multiple regression technique. They have been used by economists to analyze correlation relationships of economic indicators. Briscoe and Wilson (1993) developed an econometric model and examined total employment within the construction industry using a number of explanatory variables such as output and real wages. Similarly, Ncube and Heshmati (1998) examined manpower demand using capital inputs, wages, time trend, and production technology, but in the context of manufacturing. The models proposed by Wong et al. (2007), however, used market determinants that included wage level, material price, interest rate, construction output, bank rate, and labor productivity (a proxy for technological change). Manpower demand modeling is generally expressed using the following equation:

JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / OCTOBER 2012 / 1161



MDt ¼ β 0 þ β 1 Qt þ β 2 RWt þ β 3 MPt þ β 4 BRt þ β 5 LPt

(1)

where at time t, MDt = manpower demand; Qt = construction output; RWt = real wage in construction industry; MPt = material price; BRt = interest rate; and LPt = labor productivity. Wong et al. (2007) have demonstrated that the multiple regression technique can provide a platform for linking economics and social variables to manpower demand. This model is effective if all variables on the right side of Eq. (1) are accurately estimated. The collection of historical data is, however, an onerous task (Campbell 1997). Considering the political, economic, environmental, technological, and social changes that have and continue to occur, the use of such data for predicting the accuracy of the future is questionable (Meehan and Ahmed 1990). Irrespective of the problems with historical data, attempts to address the issue of missing data have been addressed using mathematical integration whereby yearly annualized data have been converted into quarterly (Chan 1993). Labor Multiplier Approach In its simplest form, the labor multiplier approach assumes a relationship exists between construction output and manpower demand per construction unit. It is further assumed that the demand for manpower resource per unit of the construction output remains constant in the short term (Lemessany and Clapp 1978). Fundamentally, the labor multiplier makes use of the correlation between construction output and manpower demand (Uwakweh and Maloney 1991). If a fixed labor multiplier is assigned to a specific work trade, then the expected construction output and subsequent manpower demand can be determined (Persad et al. 1995). The use of this modeling approach is deemed to be reasonably reliable (Proverbs et al. 1999). While the approach is straightforward, its application requires a detailed analysis of parameters such as construction output (Rumberger and Levin 1985). Another issue is the difficulty associated with formulating a database of labor multipliers to cover the array of trades required to deliver a construction project. Because of the scarcity of data, some simplified assumptions have been traditionally made (Uwakweh and Maloney 1991), particularly with regard to (1) economic planning of private and public projects in forthcoming years, (2) demand for construction, and (3) labor demand by skill type. In the case of construction, labor records can be obtained through site daily deployment reports and the expenditure incurred within completed projects from private contractors. By dividing the manpower demand (of each trade) with the expenditure of the construction project, the multipliers of each trade could be developed [Eq. (2)]. The projected workload of each trade can be projected by applying the corresponding labor multipliers calculated from Eq. (2) with the projected expenditure of construction works. The following equations demonstrate the concept of this forecasting model. Data for the labor multiplier (per unit construction cost) can be derived using the following equation:

M ij ¼

Dij Cij

For the manpower demand of the construction projects Dij ¼ M ij Ej

(3)

where, Ej = projected expenditure (HK$ million) of project j; and Dij = projected labor demand (unit: man-days) of trade i for a type j construction project. The generic features of the labor multiplier approach have also been demonstrated by Rosenfeld and Warszawski (1993). They have suggested formulating a forecasting demand model by linking the physical yearly quantity of construction works (e.g., in m2 ) to the number of man-hours required to produce a unit of work. Hence, for each construction type j, the manpower demand (in man-hours) is expressed as Li ¼

n X i¼1

Qj sij

(4)

where, Li = required manpower demand for each skill, i (unit: in man-hours); Qj = physical yearly quantity of construction type j; and sij = typical man-hours of skill i required to produce one unit of construction type j. In the next section of this paper a labor multiplier manpower model is proposed as it is deemed to be an effective technique to use for forecasting. The underlying concept of this approach is to make use of the relationship between (1) construction output and economic conditions and (2) fixed labor multiplier, which as derived from the collected labor deployment record. Unlike the traditional regression model, it does not involve the minute and complicated process of assessing volatile parameters such as real wages, material prices as propagated in econometric, and multiple regression models.

Model Development The proposed model is based on a detailed review of the normative literature (Rumberger and Levin 1985; Uwakweh and Maloney 1991; Rosenfeld and Warszawski 1993; Ghost and Cruz 2005). Fig. 1 identifies the model’s structure and the key stages that are used to develop a labor demand forecast. Secondary data sources provide inputs into the model. Databases 1 and 2 are used to derive quarterly time series of gross domestic product (GDP) and construction output from the Hong Kong government’s published statistical yearbooks, such as the Report on the Quarterly Survey of Construction Output published by Census and Statistics Department of Hong Kong, from the first quarter of 1988 to the first quarter of 2008. This time period was chosen because it provided sufficient data points for examining the trend of the GDP movement as well as the relationship between the economic development and the construction sector (Bon 1992). Database 3 is derived from the number of workers required to deliver the product and the composition of workers in terms of their discipline/ trade and competency/skill level. To obtain such data, information from recently completed projects was collected from private contractors.

(2) Stage One: Synthesis of Forthcoming Economic Conditions

where, M ij = labor multiplier of trade i of the selected project type j; Cij = project expenditure of the selected project type j; and Dij = labor deployment (man-days) of trade i of the selected project type j.

The construction industry makes a significant contribution to an economy in terms of its contribution to GDP, total output, the number of people it directly employees, and its multiplier effect on other industries (Ofori 1988; Tan 1989; Hillebrandt 1985). When an

1162 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / OCTOBER 2012


Stage Two: Mathematical Model Linking Economic Scenario with Construction Output

economy experiences economic growth, spending and investment in private housing typically occurs and as a result stimulates construction activity (Bon 1992; Akintoye and Skitmore 1994; Hua 1996; Tse and Ganesan 1997; Chan 2001). With this in mind, these trends can be extrapolated and used within the model to examine labor demand patterns. Visualization of future GDP patterns is therefore a key attribute of the proposed model to study future manpower demand. For example, in Fig. 2, the GDP for Hong Kong from 1986 to 2008 is presented. A recessionary period was experienced in 1989 and is denoted by point A in Fig. 2. As a result of government policies designed to stimulate the economy, such as the construction of Chek Lap Kok Airport (Hong Kong International Airport). This scenario is illustrated by a number of V-shapes for the time period noted because of various economic and political instabilities that occurred. In Fig. 2, points A to E are used to divide GDP into different segments representing different economic conditions encountered. By making reference to these segments, and reconstructing different scenarios, a forecast on GDP pattern can be developed. Figs. 3(a and b) are used to demonstrate the combination of scenarios that represent varying GDP projections.

GDP can be viewed as a macroeconomic indicator of an economy’s overall well-being. Unlike investment in financial assets, the design and construction sequence most often begins after the need for the buildings is realized (Hua 2000). Therefore, construction projects are always characterized by time elapse between the decision to initialize the projects and the completion of design, bidding, and construction (Killingsworth 1990). A ‘lag’ is experienced, and as such a modified distributed lag model is introduced. In the traditional distributed lag model, the value of the dependent variables at a given point in time should depend not only on the value of the explanatory variable at that time period, but also on value of the explanatory variables in the past. In its basic form a distributed lag model can be expressed as Y t ¼ α þ β 0 X t þ β 1 X t−1 þ : : : þ β q X t−q þ e

(5)

where, Y = dependent variable at the time t (e.g., change of construction output at the time t); X = explanatory variable at the time t (e.g., change of GDP at time t); q = lagged order; and e = error.

20

15

A Year-on year % change


Fig. 1. Proposed labor demand multiplier model

B

C

D

E

10

5

0 1986

1991

1996

2001

2006 Year

-5

-10

Fig. 2. Trend of GDP in Hong Kong for 1987–2008 JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / OCTOBER 2012 / 1163



Fig. 4. Scatter plot of yearly percentage change on construction output/ yearly percentage change on GDP relationship

Fig. 3. GDP projections: (a) Scenario A, high growth and high productivity after the global economic crisis (GEC) of 2009; (b) Scenario B, assumed economic growth recovery from GEC but followed by further economic decline

Unlike the traditional lagged model, the relationship between the dependent variable, Y, and explanatory variables, X, at the time period from t to t − q are tested individually. A polynomial equation is generated together with an R-squared value for each selected value of q, showing the strength of the relationship between (1) dependent variable—yearly change in construction output of the private sector, ΔCOt;q and (2) independent variable—yearly change of the GDP with lag year q, ΔGDPt−q . Fig. 4 is a scatter plot of ΔCOt;q and ΔGDPt−q . The estimated polynomial equation for each time lag is ΔCOt;q ¼ α þ β 0 ΔGDPt−q þ β 1 ΔGDP 2t−q þ e

(6)

According to Chan (1999), the duration of private construction projects in Hong Kong can be modeled using Eq. 7. Chan (1999) proposes that construction periods of 0.7 to 2.3 years have contract values ranging from HK$10 to HK$300 million. The value of lagged order is q = 4, which allows a maximum of one year for a feasibility study stage of a project. T ¼ 120 · C0.34

(7)

where, T = construction period of the private construction project (unit: year); and C = contract value (HK$ million) In Table 1, the results of the regression analysis are presented for the Hong Kong data (C&SD 1982–2008; C&SD 1998–2008). The R2 value provides a measure of how well the quadratic regression line fits the data. The significance F is used to test whether the value of R2 is significantly different from zero. If the significance F is larger than 0.1, it could concluded that the value of R is nearly zero and there are no direct relationships between the independent and dependent variables. As the value of F is insignificant, the consideration of a lagged year with q ¼ 3 is ignored in the forthcoming model. The relationship between private work and GDP with lagged years, q ¼ 1 and q ¼ 2 were significant. The findings presented in Table 1 are included in the modified distributed lagged model as it is assumed that a change in the forecast of construction output for private work is a function of GDP. The mathematical model is shown as ΔFCOprivate;t ¼ kð0.474 · ΔCOt;1 þ 0.189 · ΔCOt;2 Þ

(8)

The forecast of construction output for the private sector at a year, FCOprivate;t can then be estimated using the following equation: FCOprivate;t ¼ COprivate;t−1 · ΔFCOprivate;t

(9)

To examine whether the proposed model can capture the trend in construction output under changing economic conditions, the yearly percentage of GDP at year 1998 as a base was selected. The mathematical modeling for calculating the theoretical yearly percentage change of the construction output was then executed. Table 1. Relationship between Construction Output and GDP Lagged year, q 1 2 3

β0

β1

2.529 0.076 1.425 −0.036 0.515 0.012



α

R2

Significance F

−6.831 −2.851 −1.564

0.474 0.189 0.139

0.001 0.090 0.180

of the manpower forecast) using Eqs. 10 and 11. Table 3 shows the adjusted factor calculated for the labor multiplier. A constant price level at year 2008 is assumed 0 LI2008 ¼1


0 LI2008 ¼

(10)

LI2007 LI2008

(11)

Using the collected daily reports as stated in Table 4, the labor multipliers of each trade can be developed by dividing the labor deployment record (of each trade) with the project expenditure. For each type of daily report collected at year t, the labor multiplier is derived as LMi ¼ Fig. 5. Yearly percentage change of construction output in private sector

A visual representation of the pattern of construction output generated by the mathematical model is presented in Fig. 5. Eqs. 8 and 9 are able to capture changing construction outputs under specific levels of economic activity. As a result, they can be applied to a labor multiplier approach to forecast the forward manpower demand for the construction industry. Stage Three: Labor Multiplier Approach The labor multiplier approach assumes the demand for manpower is a function of workload, which can be measured in dollar terms. For each work trade, their workload was collected from labor deployment records that are used as the basis for assessing and aggregating the global manpower demand for the industry. The total workload is then summarized by sector at any given time period. To determine the number of workers required, particularly for specific trades, information from recently completed projects is required. A list of the most popular subcontract trades, as identified in Table 2, was compiled with reference to published materials from governmental departments (HKCWRA 2010). A similar approach has been advocated by Rosenfeld and Warszawski (1993) who recommended applying the International Labor Organization (ILO) classification into occupations. Information from specific projects can be used to obtain contract values. Such data, however, provide only a nominal price value. However, it only refers to project expenditure expressed in the form of cost per project day neglecting the effect of inflation. In addressing this shortcoming, an adjusted factor using a construction labor index is introduced to take into account inflation (i.e., the first year

Table 2. Types of Subcontract Trades Trade number, i

Trade name

Trade number, i

1 2 3 4 5 6

Bar bender Drainlayer Concretor Scaffolder Electrician Plumber

7 8 9 10 11 12

Di · LIt0 C

(12)

where, LMi = labor multiplier of trade, i of the project; C = project expenditure (unit: $ million) of the project; Di = labor deployment (unit: man-days) of the trade, i of the project. Projected Workload The workload (in man-days) can then be projected by applying the corresponding labor multipliers with the projected construction output and is expressed as PWt;i ¼

n X ðFCOprivate;t · αp Þ · LMi;αp

(13)

p¼1

where, PWt;i = forecast workload of the trade, i (unit: man-days); FCOprivate;t = forecast construction output of private sector at year t; LMi;αp = labor multiplier for the trade, i at the type, p of the construction project; αp = percentage on type of construction projects, p, over the whole private sector; and t = year Stage Four: Forecast Manpower Demand Stages Ones to Three have focused on projecting workload according to the project type, p, and trade, i. By considering the number

Table 3. Original Construction Labor Index and Adjusted Labor Price Index, LIt Year, t

Construction labor index, LIt

Adjusted factor (year 2008 based) for existing labor multiplier, LIt0

151.7 149.4 145.5 140.2 134.6 133.5 133.1 128.8

1.18 1.16 1.13 1.09 1.05 1.04 1.03 1.00

2001 2002 2003 2004 2005 2006 2007 2008

Note: Figures above are yearly average of monthly indices. Source: Census and Statistics Department (C&SD 2001-2008a), Hong Kong. Trade name General workers Equipment operator Painter and decorator Bricklayer Building services mechanic General workers (low-skilled workers)

Table 4. Number of Construction Projects Studied for Establishing Database of Labor Multipliers Types of building/development Private residential buildings Private commercial buildings

Number of projects studied 10 15



of working days per year available, the demand for each trade and project type in terms of the “number of workers required” can be derived. Their relationship is expressed as


MDt;i ¼ PWt;i ÷ W

(14)

where, MDt;i = forecast manpower demand for the trade i at year t; PWt;i = projected workload of the trade i at year t; and W = number of the working days per year. By summing up the manpower demand in each trade, i, of each type of project, p, the total manpower demand for private construction projects can be obtained. Determining the number of working days per year, however, is an issue that needs to be addressed. In the case of Hong Kong, specific factors affecting the value of W [Eq. (15)] includes the number of public holidays (H), inclement weather (IW), for which the construction projects should be stopped, and the unemployment/underemployment rate of the industry (UER). The implicit function is expressed as W ¼ fðH; IW; UERÞ

(15)

In considering holidays and inclement weather, past data regarding rainfall and typhoons were examined. Table 5 provides details about holidays in Hong Kong. Table 6 provides time rainfall and typhoon records, with the total number of days subjected to inclement weather being 29 days. The unemployment rate is defined as the percentage of workers within the industry who are currently unemployed. In the Hong Kong construction industry, the unemployment rate and underemployment rate have been approximately 15 and 7.2%, respectively C&SD 2001–2008b, c).

Projections on Manpower Demand of Construction Workers for 2009–2013 Selection of Economic Scenarios To demonstrate how the proposed demand model can be applied, two economic scenarios have been selected. Scenario A, the most optimistic, envisages high growth and high productivity after the global economic crisis of 2009 [Fig. 3(a)]. Second, Scenario B, a less optimistic scenario, where economic growth is assumed to have recovered from GEC, but is then followed by further economic decline [Fig. 3(b)]. The selection of the economic scenario is entered into the preset programming of the demand model so that the corresponding forecast construction output can be generated. Figs. 6(a and b) illustrate the forecast construction output based on selected Scenario A and Scenario B, respectively. Ratio of Different Types of Construction Works over Whole Private Sector In Hong Kong, private sector projects are generally divided into the following types: 1. Residential; 2. Commercial development (office and shopping facilities); and 3. Industrial (e.g., factories)

Forecasting Manpower Demand A quantitative approach based on examining historical economic data has been developed. The model was programmed into MATLAB. The raw data is stored in an MS Excel spreadsheet format for ease of updating. The preset variables, parameters, and data sets stored in MS Excel can be read by MATLAB. Forecasts can be computed according to a preset program. An end-user can define the economic scenario using their preferences. The forecast results can then be plotted and all numerical values stored in the buffer of memory for detailed analysis. Table 5. Total Number of Holidays Number of holidays (n ¼ 69)

Holidays (a) Number of general holidays established by local government (b) Number of holidays per week construction works should be stopped (c) Number of holidays after Chinese lunar years

12 48 9

Table 6. Total Number of Days Subjected to Heavy Rainfall Year Number of days subjected to heavy rainfall, a Number of days subjected to tropical cyclone warning signal, b Total number of days subjected to inclement days, a þ b

2005 2006 2007 2008 2009 32

24

18

36

23

0

0

1

4

5

32

24

19

40

28

Fig. 6. Construction output: (a) Scenario A; (b) Scenario B



Table 7. Predicted Forecast Output for Private Construction Projects by Types Based on Scenario A and Scenario B (Unit: HK$ million)


Scenario A—most optimistic

Scenario B—least optimistic

Year

Residential buildings

Commercial development

Total

Residential buildings

Commercial development

Total

2009 2010 2011 2012 2013

23,400 20,480 21,020 22,970 25,170

10,030 8,780 9,010 9,840 10,790

33,430 29,250 30,030 32,810 35,960

23,400 19,030 19,440 19,650 19,650

10,030 8,160 8,330 8,420 8,420

33,430 27,190 27,770 28,070 28,070

Table 8. Aggregate Demand Forecasting of Construction Workers for Private Construction Projects (Unit: Number of Workers Required) Year

Scenario A—most optimistic

Scenario B—least optimistic

2009 2010 2011 2012 2013

26,950 23,590 24,210 26,460 29,000

26,950 21,920 22,390 22,630 22,630

No raw data on the ratios of above project types exist in Hong Kong. Data of completed property was compiled by the Hong Kong Property Review (Rating and Valuation Dept., 1990–2008) and the Construction Cost Handbook China and Hong Kong 2008 (Davis Langdon & Seah Hong Kong Limited, 2008) to determine the total value of projects undertaken in each area. Approximate ratios were (1) residential building 70% and (2) commercial development 30%. Industrial buildings have been ignored in the model as no evidence for future demand could be found. Table 7 identifies the forecasted output for private construction projects for Scenarios A and B. Projected Workload Using Eq. (13), the projected workload for the residential buildings and commercial development based on Scenarios A and B can be estimated. Forecast of Manpower Demand on Construction Workers The primary aim of a manpower policy is to provide sufficient working opportunities to all construction workers. The number of working days per year should be considered. Besides fixed

variables such as number of holidays and days of inclement weather, if a target is set to allow labor to work more than 80% of the year, then the number of working days can be set at W ¼ ð365 − 69 − 29Þ · 0.8 ¼ 214 days. Using Eq. (14), the aggregate forecast of the manpower demand for construction workers is identified in Table 8 and illustrated in Fig. 7. The effect of the economic situation could be visualized in the Fig. 7. For Scenario A, it can be seen that manpower demand declines because of the lagged effect of the GEC in 2009. This was followed by an increase in demand as economic conditions began to improve. Scenario B is a less optimistic because manpower demand remains low after the GEC. Policymakers and managers can use the model to forecast manpower requirements, but will also need to examine the supply side in congruence to determine surpluses or shortages that may prevail. Early identification of an imbalance in manpower can be useful for strategic planning and policy development.

Conclusion In contrast to traditional forecasting approaches, the multiplier model developed in this paper is integrated and adaptable to changing economic conditions, specifically the way in which it examines the relationship between economic conditions and manpower demand. The model provides an invaluable insight for decision makers about how the impact of changing economic conditions can influence the demand for manpower. Several limitations of the model should be acknowledged, which include: • User input variables and past economic scenarios. The selection of an appropriate scenario is a critical point to generating an accurate and reliable forecasting of manpower requirements; and • Model’s global view on manpower demand based on the selected economic scenarios. In particular, the issue of unbalanced manpower demand throughout the duration of individual projects has not been considered in this model. Instead, it is assumed that labor multipliers are constant. The proposed demand model provides a means to forecast the labor demand for construction workers in the next 5 to 10 years. The accuracy of the model is dependent upon the quality of the labor daily records collected. Future research needs to focus on developing a database of labor multipliers, which can be used to forecast accurate and reliable labor demand.

References

Fig. 7. Demand forecast of construction workers for private construction projects

Akintoye, A., and Skitmore, M. (1994). “Models of UK private sector quarterly construction demand.” Constr. Manage. Econ., 12(1), 3–13. Barnes, D. (1975). “Manpower planning.” Educ. Train., 17(8), 190–191. Bon, R. (1992). “The future of international construction.” Habitat Int., 16(3), 119–128. Briscoe, G., and Wilson, R. (1993). Employment forecasting in the construction industry, Aldershot, Avebury, England.




Campbell, C. P. (1997). “Workforce requirements: The basis for relevant occupational training.” J. Euro. Ind. Train., 21(8), 279–297. Census and Statistics Dept. (C&SD). (1982–2008). Gross domestic product (GDP) and its man expenditure components in chained (2008), Census and Statistics Dept., Hong Kong. Census and Statistics Dept. (C&SD). (1998–2008). Report on the quarterly survey of construction output, Census and Statistics Dept., Hong Kong. Census and Statistics Dept. (C&SD). (2001–2008a). Index numbers of the costs of labour and material used in public sector construction projects, Census and Statistics Dept., Hong Kong. Census and Statistics Dept. (C&SD). (2001–2008b). Underemployment rate by industry, Census and Statistics Dept., Hong Kong. Census and Statistics Dept. (C&SD). (2001–2008c). Unemployment rate by previous industry, Census and Statistics Dept., Hong Kong. Chan, A. P. C. (1999). “Modelling building durations in Hong Kong.” Constr. Manage. Econ., 17(2), 189–196. Chan, S. L. (2001). “Empirical tests to discern linkages between construction and other economic sectors in Singapore.” Constr. Manage. Econ., 19(4), 355–363. Chan, W. S. (1993). “Disaggregation of annual time-series data to quarterly figures: A comparative study.” J. Forecasting, 12(8), 677–688. Davis Langdon & Seah Hong Kong Limited. (2008). Construction cost handbook-China and Hong Kong, Davis Langdon & Seah Hong Kong Limited, Hong Kong. Diebold, F. X. (2007). Elements of forecasting, Thomson Learning, London. Ghost, B., and Cruz, G. (2005). “Nurse requirement planning: A computerbased model.” J. Nurs. Manage., 13(4), 363–371. Heshmati, A., and Ncube, M. (1998). “An econometric model of employment in Zimbabwe’s manufacturing industries.” J. Dev. Econ., 17(3), 527–551, 〈http://swopec.hhs.se/hastef/abs/hastef0277.htm〉. Hillebrandt, P. M., and Meikle, J. L. (1985). “Resource planning for construction.” Constr. Manage. Econ., 3(3), 249–263. Hong Kong Construction Workers Registration Authority (HKCWRA). (2010). “Designation trades for registration.” 〈http://www.cwra.org .hk/registration/DesignTrades.asp〉 (Aug. 14, 2010). Hua, G. B. (1996). “Residential construction demand forecasting using economic indicators: A comparative study of artificial neural networks and multiple regression.” Constr. Manage. Econ., 14(1), 25–34. Hua, G. B. (2000). “Evaluating the performance of combining neural networks and genetic algorithms to forecast construction demand: The case of the Singapore residential sector.” Constr. Manage. Econ., 18(2), 209–217. Khoong, C. M. (1996). “An integrated system framework and analysis methodology for manpower planning.” Int. J. Manpower, 17(1), 26–46. Killingsworth, R. A. (1990). “A preliminary investigation into formulating a demand forecasting model for industrial construction.” Cost Eng., 32(8), 11–15.

Lemessany, J., and Clapp, M. A. (1978). “Resource inputs to construction: The requirements of house building.” Building Research Establishment, Current paper 76/78, Watford, U.K. Meehan, R. H., and Ahmed, S. B. (1990). “Forecasting human resources requirements: A demand model.” Human Resource Plann., 13(4), 297–307. Ofori, G. (1988). “Construction industry and economic growth in Singapore.” Constr. Manage. Econ., 6(1), 57–70. Park, S. H., Lee, S. M., Yoon, S. N., and Yeon, S. J. (2008). “A dynamic manpower forecasting model for the information security industry.” Ind. Manage. Data Syst., 108(3), 368–384. Persad, K. R., O’Connor, J. T., and Varghese, K. (1995). “Forecasting engineering manpower requirements for highway preconstruction activities.” J. Manage. Eng., 11(3), 41–47. Proverbs, D. G., Holt, G. D., and Olomolaiye, P. O. (1999). “A method for estimating labour requirements and costs for international construction projects at inception.” Build. Environ., 34(1), 43–48. Rating and Valuation Dept. (1990–2008). Hong Kong property review, Rating and Valuation Dept., Hong Kong. Rosenfeld, Y., and Warszawski, A. (1993). “Forecasting methodology of national demand for construction labour.” Constr. Manage. Econ., 11(1), 18–29. Rumberger, R. W., and Levin, H. M. (1985). “Forecasting the impact of new technologies on the future job market.” Technol. Forecasting Soc. Change, 27(4), 399–417. Smith, A. R. (1977). “Developments in manpower planning.” Pers. Rev., 1(1), 44–54. Tan, W. (1989). “Subsector fluctuations in construction.” Constr. Manage. Econ., 7(1), 41–51. Tse, R. Y. C., and Ganesan, S. (1997). “Causal relationship between construction flows and GDP: Evidence from Hong Kong.” Constr. Manage. Econ., 15(4), 371–376. Uwakweh, B. O., and Maloney, W. F. (1991). “Conceptual model for manpower planning for the construction industry in developing countries.” Constr. Manage. Econ., 9(5), 451–465. Wong, J. M. W., Chan, A. P. C., and Chiang, Y. H. (2005). “The quality of projections: Manpower demand for the Hong Kong Construction Industry.” The Queensland Univ. of Technology Res. Week Int. Conf., Queensland Univ. of Technology, Brisbane, Australia. Wong, J. M. W., Chan, A. P. C., and Chiang, Y. H. (2007). “Forecasting construction manpower demand: A vector error correction model.” Build. Environ., 42(8), 3030–3041. Wong, J. M. W., Chan, A. P. C., and Chiang, Y. H. (2010). “Modeling construction occupational demand: Case of Hong Kong.” J. Constr. Eng. Manage., 136(9), 991–1002.



Michael Sing From: Sent: To: Subject:

[email protected] on behalf of [email protected] Friday, 3 May 2013 8:56 PM Michael Sing; [email protected]; Peter Love; Peter Davis Structural Survey - Decision on Manuscript ID SS-02-2013-0017.R1

03‐May‐2013 Dear Dr. Sing, It is a pleasure to accept your manuscript entitled "Experimental Study on Condition Assessment of Reinforced Concrete Structure Using a Dynamics Response Approach" in its current form for publication in Structural Survey. By publishing in this journal, your work will benefit from Emerald EarlyCite. This is a pre‐publication service which allows your paper to be published online earlier, and so read by users and, potentially, cited earlier. Please note, EarlyCite is not a proofing service. Emerald operates a 'right first time' policy, which means that the final version of the article which has been accepted by the Editor will be the published version. We cannot allow further changes to the article once it has been accepted. Please go to your Author Centre on ScholarOne Manuscripts (Manuscripts with Decisions/Manuscripts I have co‐ authored) to complete the copyright assignment form. We cannot publish your paper without the copyright form. All authors are requested to complete the form and to input their full contact details, to ensure that a complimentary journal copy can be despatched upon publication. If you have provided full contact information in the completed copyright form your journal copy should arrive within 8 weeks of print publication. If any of the contact information is incorrect you can update it by logging onto your author account and go to Edit Details at the top right of the screen. You cannot edit the copyright form directly. If the information on the article title page is incorrect you must contact the journal Publisher immediately. If you would like more information about Emerald’s copyright policy please visit the Information & Forms section in the Resources section of your Author Centre. Please note that Emerald requires you to clear permission to re‐use any material not created by you. If there are permissions outstanding, please upload these when you submit your revision or send directly to Emerald if your paper is accepted immediately. Emerald is unable to publish your paper with permissions outstanding. Thank you for your contribution. On behalf of the Editors of Structural Survey, we look forward to your continued contributions to the Journal. Yours sincerely, Prof. David Proverbs Editor, Structural Survey [email protected] Referee(s)' Comments to Author: Referee: 1 Recommendation: Accept Comments: The revised manuscript has addressed all reviewer comments and is recommended for publication in Structural Survey.

[Article title] Experimental Study on Condition Assessment of Reinforced Concrete Structures Using a Dynamics Response Approach Author Details: [1st Author] Chun Pong Sing Department of Construction Management, School of Built Environment, Curtin University, Perth, Western Australia [2nd Author] P.E.D. Love School of Built Environment, Curtin University, Perth, Western Australia [3rd Author] P.R. Davis School of Built Environment, Curtin University, Perth, Western Australia Corresponding author: Chun Pong Sing [Corresponding Author’s Email]: [email protected]

NOTE: affiliations should appear as the following: Department (if applicable); Institution; City; State (US only); Country. No further information or detail should be included Acknowledgments (if applicable): N/A

Biographical Details (if applicable): [1st Author] Senior Lecturer, PhD [2nd Author] Professor, PhD [3rd Author] Head of School, PhD

Structured Abstract: Purpose – Condition assessment on reinforced concrete (RC) structures is one of the critical issues as a result of structure degradation due to aging in many developed countries. This paper examines the sensitivity and reliability of the conventional dynamic response approaches, which are currently applied in the RC structures. The key indicators include: (a) natural frequency and (b) damping ratio. To deal with the non-linear characteristics of RC, the concept of random decrement is applied to analyze time domain data and a non-linear damping curve could be constructed to reflect the condition of RC structure.

Design/ methodology/ approach – A full scale RC structure was tested under ambient vibration and the impact from a rubber hammer. Time history data was collected to analyze dynamics parameters such as natural frequency and damping ratio.

Findings - The research demonstrated that the measured natural frequency is not a good indicator for integrity assessment. Similarly, it was revealed that the traditional theory of viscous damping performed poorly for the RC with non-linear characteristics. To address this problem, a non-linear curve is constructed using random decrement and it can be used to retrieve the condition of the RC structure in a scientific manner.

Originality/ value – The time domain analysis using random decrement can be used to construct a non-linear damping curve. The results from this study revealed that the damage of structure can be reflected from the changes in the damping curves. The nonlinear damping curve is a powerful tool for assessing the health condition of RC structures in terms of sensitivity and reliability. Keywords: Condition assessment, damping ratio, natural frequency, RC structure

Article Classification: Research Paper

For internal production use only Running Heads:

Introduction Condition assessment for reinforced concrete (RC) has attracted a considerable amount of attention from the research community, practicing engineers and surveyors, as a result of structural degradation due to aging (e.g., Xia and Hao, 2003; Concu et al., 2011). Traditional approaches to examine dynamic response parameters have been based upon visual or localized experimental procedures such as a rebounded hammer. With such approaches the location of the damage must be known a priori and the inspection area must be accessible (Xia and Hao, 2003). Moreover, such methods are largely based on the experience of the observer who may not be able to ascertain the level of degradation or safety of the structure (Concu et al., 2011).

Unlike traditional approaches, dynamics response provides an assessment of the condition for a structure with entire integrity rather than a single location. Every structure is considered to possess a series of modes of vibrations. Each mode is defined by three dynamic parameters: (1) natural frequency, (2) model shape and (3) damping (Lee and Shin, 2002). Different methods have been proposed for extracting the dynamic parameters such as the half-power bandwidth method for measuring damping. The natural frequency is often used to assess structural integrity, as it is cost effective and quick to implement (Wang et al., 1997; Kim and Stubbs, 2003; Carrion et al., 2006). In this paper, the dynamic response of a full-scale RC structure with induced damage is examined to evaluate the reliability of frequency and damping as condition assessment parameters. The application of a random decrement to assess the non-linear damping on the RC structure’s condition assessment is also introduced.

Theory of Dynamics Response Measurements Condition assessment using the dynamics approach is typically based on the structures response to vibration. The natural frequency and mode shapes are directly related to the stiffness and integrity of the structure. Any drop in natural frequency or change in the model’s shape will indicate a loss in stiffness (Curadelli et al., 2008). The damping ratio is considered to increase when damage has been induced into the structure. Both are indicators of structural physical integrity and therefore can be regarded as a sign of condition assessment.

Frequency The natural frequency in the ‘fundamental mode’ (i.e. the lowest frequency of a periodic waveform measured from the structure) is typically adopted in a dynamic response study (Breads, 1996). This is due to the fundamental mode dominating the response, while higher modes are dampened relatively quickly. In fact, research undertaken by Wong (2001) has revealed that 95% of energy dissipates in the ‘fundamental mode’ of vibration. The analysis of the fundamental mode significantly explains the condition of a structure. As a result, the natural frequency measurement in the ‘fundamental mode’ is commonly used in the field of condition assessment. If the mass and stiffness are M and K respectively, and the amplitude and acceleration at time t are x and  x respectively, the force, F will be equal to –kx. Based on Newton's second law, their relationship could be derived as follows:

Kx  M x

(1)

Since the motion of any points can closely resemble simple harmonic motion (SHM), Eq.[1] can be transformed as follows:

Hence,

Kx  Mx 2

(2)

  2 f

(3)

f

1 K M 2

(4)

From Eq.(4), the fundamental natural frequency is related to stiffness and mass of the concrete structure.

Damping Crandall (1970) defined damping as a measure of energy dissipation in a vibrating structure that can result in quiescent. Damping capacity is defined as a ratio of the energy dissipated in one cycle of oscillation to the maximum amount of energy accumulated in the structure in that cycle. As energy is dissipated, heat is generated in a number of ways, for example, the internal friction of an element. In such a case, less energy is provided for free vibration, which can lead to higher damping values

(Kareem and Gurley, 1996). Any change in the damping level indicates that a crack has developed within the concrete. Again, the measurement of damping is deemed to be one of the key indicators in the field of condition assessment.

Mode Shape The mode shape of a structure can be obtained by analyzing its vibration response at multiple locations. In theory changes in mode shape of a structure can provide evidence of damage assessment in localized areas (Pandey et al., 1991). However, modal shape data invariably contains accumulative errors (Wang et al., 1997). According to Abdo (2012), variations with damage are difficult to detect by changes of mode shapes. Moreover, model shape measurement is an extremely timeconsuming process (Ge and Lui, 2005). The measurement time is proportional to the number of measurement points, as the accelerometers used to capture the local vibration have to be placed manually to cover the entire surface of the structure. Bearing in mind the complexity and time needed, mode shape techniques in condition assessment will not be considered in this study.

A number of approaches for assessing a buildings structural integrity exist as identified in Table 1. These approaches are also compared with the dynamics response approach. Dynamic response approaches are simple, direct and reliable for condition assessment. The application of dynamic approaches is increasingly attractive over other conventional inspection techniques (Curadelli et al., 2008; Yang

et al., 2009).

Table 1 Comparison between the traditional and dynamics responses approach Traditional approach Dynamics response (e.g. visual inspection) approach Number of sensors Numerous local inspection required point is required in large Few sensors are required structures How long does the Time consuming and costly, Time and money can be inspection take? for example, a large number much reduced with less of rebound hammer points is inspection point required for a scale structure Data quality Data is only collected from The data collected reflects part of the structure. This the integrity and stiffness of does not represent the health the whole structure. A global condition of whole structure assessment of the structure is

provided. Any laboratory testing is required?

Yes

No

Experimental Setup For this study, the fundamental frequency of a RC structure was first analyzed from the ambient vibration. To measure the damping ratio, the rubber hammer is used to give an impact force to the structure, as it is easy, direct and simple to excite the structure in order to obtain the acceleration-time history data for the damping measurements. To study the sensitivity of the dynamics parameter, damage was then introduced gradually to the structure. Figure 1 shows a schematic diagram of the RC structure and position of cracks that were induced to the structure.

Figure 1 RC structure and position of cracks created

Data acquisition and determining dynamics parameter To measure the dynamic response of the structure, an accelerometer was placed at its center to monitor its vertical motion. An impact force using a rubber hammer was applied at the center of structure to induce vibration. Better quality data can be obtained if the signal is amplified and filtered before recording as this increases the signal to noise ratio and ameliorates use of the digitization range of the recording device.

The signal from the accelerometer was initially amplified by signal

conditioners and filtered at 50Hz low pass and 150Hz high pass by an analog filter.

The connection between the vertical section and base structure was then cut using a dedicated cutting machine (Figure 3 and Table 2). Test procedures were repeated until a drop in the natural frequency was observed. To ensure the reliability of the data collected: (a) all the electronic devices were checked by multi-meter to ensure that all devices were earthed; and (b) the accelerometer was fixed securely to the center of the structure with no relative movement being allowed to occur between the accelerometer and structure.

Figure 2 Cutting machine was used to induce damage to the structure Table 2 Schedule of damage created to the structure Condition Crack in Position 1 Crack in Position 2 Intact 0mm 0mm st 1 damage created 10mm 0mm 2nd damage created 10mm 10mm 3rd damage created 30mm 10mm th 4 damage created 30mm 30mm 5th damage created 50mm 30mm th 6 damage created 50mm 50mm 7th damage created 70mm 50mm 8th damage created 70mm 70mm

Discussion Traditionally, the vibration response of a structure can be obtained through the measurement of its displacement against time. However, with small amplitudes and a lack of no reference points makes it difficult to measure for displacement. In

addressing this shortcoming, the measurement of acceleration is used (Jeary, 1987). A constant multiplier would be applied on the displacement value at a particular frequency and displacement, so as to form a new acceleration-time series. Figure 3 shows the acceleration-time history from the RC structure. The dynamic parameters (including the fundamental frequency and damping) can be extracted from this history.

Figure 3 Acceleration-time history

Fundamental frequency To obtain the natural frequency from the RC structure, the standard Fourier transform analysis is adopted. It allows the condition of the RC structure to be analyzed in the frequency domain from the time domain history. A periodic function f(t) of frequency,  rad/s can be written as a summation of an infinite trigonometric series as follows:

f (t ) 

a0    (an cos nt  bn sin nt ) 2 n 1

(5)

where an and bn are known as Fourier coefficient. The above aperiodic function is assumed to be repetitive over time. The frequency of repetition associated with the aperiodic function becomes negligibly small and the frequency

components

n

continuous.

Assuming

the

time

period

T  2 /  approaches to infinity. The frequency component, in Fourier series [Eq.5]

shall become: F ( )  





f (t )  e it dt

(6)

For the intact condition, the frequency spectrum from the ambient vibration of the RC structure is shown in Figure 4. From the experimental results, the fundamental frequency decreased when the depth of crack increased. This indicates that when the frequency decreases the stiffness of structure dropped due to the increase in the crack’s size. To a certain degree, the change of frequency could reflect the changes in stiffness of the RC structure. This finding is akin with the normative literature that frequency measurement could be used for condition assessment. However, it is found that the frequency decreased significantly until a crack depth of 50mm was reached, Noteworthy, there was no significant change in frequency in the crack depth of was 30mm. Hence, this diagnosis may not be sensitive enough to detect small cracks in structures. The change of frequency from intact condition for each damage scenario induced is identified in Table 3. It is discovered that the presence of small, visually undetectable cracks would also cause negligible variation in fundamental frequencies. The sensitivity of this parameter is dependent on the width and the length of crack. If a crack is particularly small; it is possible that the frequency does not vary and fail to reflect the condition of RC structure.

Figure 4 The frequency spectrum obtained by ambient vibration (intact condition)

Table 3 The percentage change of natural frequency for damage induced from intact condition Fundamental Natural Frequency Condition Intact st 1 damage 2nd damage 3rd damage 4th damage 5th damage 6th damage 7th damage 8th damage

Value (Hz) 100.105 100.007 100.006 99.766 99.263 98.667 98.546 98.545 98.348

% change from intact state --0.10% -0.10% -0.34% -0.84% -1.44% -1.56% -1.56% -1.76%

Damping The conventional theory of measuring damping assumes that it is of a viscous nature (Beards, 1983). Essentially damping is a constant, irrespective of amplitude. Under this theory, methods of logarithm decrement and half power bandwidth have been developed to measure damping using the time-history data. Unlike the natural frequency, external excitation has to apply to obtain a decay curve as shown in Figure 5. In this experiment, a rubber hammer was used to give such an impact to the structure.

Figure 5 Impact response from the rubber hammer measured with accelerometer

(a) Logarithmic decrement It is based on the relationship between the amplitude of motion at particular cycle and number of cycles later. Logarithm decrement could be defined as follows: X1 X X  ln 2  ...  ln n 1 X2 X3 Xn 1 X That is    ln 1 n Xn   ln

(7)

for a viscous damping, it is assumed that   2 ,



1 X ln 0 2n X n

(8)

In third column of Table 4, when the damage is inflicted to the RC structure, the increment of damping ratio was observed. The change in the damping ratio is due to the crack development within the structure. Once the original assumption is valid, the damping ratio is far more sensitive than the fundamental frequency related to the damage created. A 42% change in the damping ratio was accompanied by 1.6% change in natural frequency after the 8th damage scenario was created to the structure. This indicates that when the damping parameter is measured properly and the assumption of viscous characteristics is valid, it is more sensitive tool for evaluating the condition of a structure.

Table 4 The percentage change of damping ratio for damage induced from intact condition Damping Ratio Damping Ratio (through logarithm decrement) (through half-power bandwidth Condition method) Value

Intact 1 damage 2nd damage 3rd damage 4th damage 5th damage st

0.784 0.818 0.854 0.913 0.927 0.942

% change from intact state 4.34% 8.93% 16.45% 18.24% 20.15%

Value 1.157 0.800 0.599 0.752 0.917 0.942

% change from intact state -30.86% -48.23% -35.00% -20.74% -18.58%

6th damage 7th damage 8th damage

0.950 1.013 1.115

21.56% 29.21% 42.22%

0.953 1.013 1.115

-17.63% -12.45% -3.63%

(b) Half power band-width method This method is available in frequency spectrum analysis. It involves measuring the response at resonance, R and determining the frequency f1 and f2 at which the response is. The mathematical equation is presented as follows:



f 2  f1 f 2  f1

(9)

Where f1 and f2 are the frequencies at which the amplitude of response is equal to

1 / 2 times the maximum amplitude. Using the half power method, the results are unexpected. The fluctuation in the damping ratio is related to the damage that is created and is presented in the fourth column of Table 4. Based on conventional damping theory, the damping ratio should be increased as the damage has been induced to the structure. Ironically, this belief was not demonstrated in the results of half power method due to nonlinear characteristics, which are found in the RC structure.

Observations of non-linear characteristics in the damping ratio To confirm whether the RC structure has undergone any non-linear characteristics, it was tested at various degrees of excitation by applying different force levels using the rubber hammer. With the increased force on the structure, the damping ratio increased (Table 5). This finding confirmed that the RC structure has experienced high nonlinear damping characteristics at the fundamental mode.

Table 5 Damping ratio with different level of excitation (under the intact condition) Relative initial Damping, % amplitude (from logarithm decrement) 1 0.818% 0.8 0.699% The presence of non-linear characteristics in the RC structure demonstrates the weaknesses in applying the logarithm decrement and half-power bandwidth method in

damping measurement. For the logarithm decrement, it is used for the sake of simplicity as it tends to a linear motion. This theory is fully violated for RC. It is also a good practice that a single damping value is ascribed to a non-linear process. As the nonlinear characteristics of the damping ratio have been ignored, some useful information at lower initial amplitude would be disregarded.

Time domain analysis The technique of ‘random decrement is used to analyze the time domain data collected from the RC structure and to establish the non-linear damping curve. This concept was first introduced by Cole (1973) to monitor damage and cracks that appear on the wings of spacecraft. However, there has been limited research on its application to building condition assessment. In the random decrement, the time domain history is firstly collected under random excitation and at the fundamental natural frequency. The data would then pass into a threshold selection process in which they are selected based on the pre-determined amplitude of response. Taking a segment from the time domain history and storing the following parts of the segment then produce a signature. By averaging these segments, the parts of forced vibration responses such as random excitation from the environment and response due to initial velocity would tend to cancel. It will then yield a signature that represents free vibration of the structure at the selected amplitude. Damping estimations are then extracted from this free vibration signature by the logarithm decrement. By repeating this process at different thresholds, a non-linear damping curve can be constructed. By repeating this process at different amplitude, a general non-linear damping structural damping curve was constructed as shown in Figure 5.

Figure 6 General forms of non-linear structural damping curve obtained from RC structure The damping ratio is related to the energy dissipation of the structure. The most important thing to consider is material and friction damping (Kareem and Gruley, 1996). Under this mechanism, each section of the curve in Figure 6 can be interpreted as follows:

(a) Damping remains constant at a very low amplitude (zone A, friction damping) At very low amplitude, it was observed that the damping ratio was nearly zero as no molecules within the materials are capable of being mobilized at this stage. As no energy was entrapped, the RC structure in this study would oscillate quickly through this region until an energy balance was reached. The damping ratio would be nearly zero at this stage. Noteworthy, significantly different results are reported by Jeary (1996) and Wong (2001). In their study of a high-rise building, a lower constant damping is formulated due to the involvement of friction damping. Building components such as external walls and slabs in high-rise buildings would undergo differential movement at this low amplitude; the friction between them would generate a heat and less energy providing for free vibration. This leads to a low but constant damping ratio. In contrast, no large elements are available to undergo differential movement in the experimental specimen of this study, thus friction damping was not observed and zero damping was then resulted.

(b) Damping increases with increasing amplitude (zone B, Material damping) At this stage, the main energy dissipation mechanism is due to the imperfection of the materials. From the theory of fracture mechanism, the materials could not achieve their full strength, which assumes the presence of cracks (Anderson, 2005). The cracks could be interpreted as imperfections within material, which leads to a reduction in strength. In RC imperfections generally come from the voids between cement paste, aggregate and sand (Zaitsev and Wittmann, 1981; Kowk, 2003). This implies that there will be an increasing number of imperfections participating as amplitude increases. As more imperfections participate, considerable free energy will be entrapped within and leave less free energy for the vibration. Consequently, higher damping ratio would result.

From non-linear damping curve to condition assessment The true damping ratio in structures has been fully deciphered by using random decrement and constructing a non-linear structural damping curve. This damping curve also rises more sharply in zone B as the crack was created to the RC structure. From this observation, any changes in a non-linear curve would be able to reflect changes in condition of the structure. As the crack developed into the structure the implication is that the density of imperfection in the structure would be increased. More and more energy is entrapped and dissipated through the imperfections at the same amplitude, leaving less free energy for the vibration. This leads to an increase in damping ratio and an obvious change in zone after damage was induced. Thus monitoring the changes in non-linear damping curve could give an indicator of the state of health of the structure and act as an effective condition monitoring techniques as well. The results from this study have explored and further confirmed the applicability of dynamic response using a random decrement in assessing the condition of the structure. The location of the accelerometer to measure the dynamic response of the structure should be carefully selected based on the data from the fundamental mode. Using computer simulation techniques such as the finite element method may help identify the range of fundamental natural frequency (Hyynh and Tran, 2005).

If the natural frequency is calculated from the collected data is within the range identified through computer simulation, it can be used to construct the non-linear

damping curve. Noteworthy, the time history data should be collected from the structure and used to construct a non-linear damping curve. Working on this curve independently does not provide any insight on the condition of structure. Instead, the time history should be collected again at the same location after a specific period of time for constructing another non-linear curve. If there are no obvious changes between the two damping curves, then the energy dissipation pattern remains unchanged. As a result this indicates that there is no significant crack development within the structure. Conversely, when significant cracks within the RC structure occur, the cracks will invariably increase due to the existing and dead loads. As a result, the density of the imperfection within the RC will increase and lead to a variation in the damping ratio occurring. By examining the variations in the nonlinear damping curves, the condition of the structure can be assessed. Further research is recommended to study the percentage changes in damping curve in related to the severity of crack development in RC structure.

Conclusions

This paper presents the results of dynamics response measurement for a RC structure. Conventional theory using natural frequency and viscous damping ratio for a building’s condition assessment has been tested.

In theory, the changes in the

fundamental frequency should reflect a certain degree of change in the stiffness of RC structure but no significant reduction in frequency was observed while cracks were induced in the RC structure. For 42% change in damping ratio detecting from logarithm decrement method, only 2% of changes in frequency are recorded. The damping ratio, when measured precisely, provides a more desirable analysis for condition assessment. Unfortunately, due to the observance of non-linear characteristics in RC, the reliance on viscous damping theory becomes invalid. To deal with this, an effective method using random decrement has been presented for generating a non-linear damping curve and capturing crack development. From these findings, the non-linear damping curve is considered to be a powerful tool in the field of condition assessment.

References

Abdo, M. A. B. (2012), "Parametric study of using only static response in structural damage detection", Engineering Structures, Vol. 34, pp.124-131. Anderson, T.L. (2005), Fracture Mechanics: Fundamentals and Applications (3rd ed.), Boca Raton, CRC Press. Breads, C.F. (1983), Structural vibration analysis: modeling, analysis, and damping of vibrating structures, Chichester, Ellis Horwood. Breads, C.F. (1996), Structural vibration: analysis and damping, Amold, London. Carrion, F.J., Lozano, A. and Castano, V.M. (2006), "Condition monitoring of vibrating steel-reinforced concrete beams through wavelet transforms", Structural Survey, Vol. 24 No.2, pp.154-162. Cole, H.A. (1973), On-line failure detection and damping measurement of aerospace structures by random decrement signature, Washington, D.C., National Aeronautics and Space Administration. Concu, G., Nicolo, B.D. and Pani, L. (2011), "Non-destructive testing as a tool in reinforced concrete buildings refurbishments", Structural Survey, Vol. 29 No. 2, pp.147-161. Crandall, S. H. (1970), "The role of damping in vibration theory", Journal of Sound Vibration, Vol. 11 No. 1, pp.3-18. Curadelli, R.O., Riera, J.D., Ambrosini, D. and Amani, M.G. (2008), "Damage detection by means of structural damping identification", Engineering Structures, Vol. 30 No. 12, pp.3497-3504. Ge, M. and Lui, M. (2005), "Structural damage identification using system dynamics properties", Computer and Structures, Vol. 83 No. 27, pp.2185-2196. Huynh, D., He, J. and Tran, D. (2005), “Damage location vector: A non-destructive structural damage detection technique”, Computers and Structures, 83, pp.2553-2367. Jacobsen, L.S. (1930), Steady force vibration as influenced by damping, Trans. ASME APM-52-15. Jeary, A.P. (1987). Damping in Chimneys, CICIND Conference in Hong Kong. Jeary, A.P. (1996), "The description and measurement of non-linear damping in structures", Journal of Wind Engineering and Industrial Aerodynamics, Vol. 59 No. 2-3, pp.103-114. Lee, U. and Shin, J. (2002), "A frequency response function-based structural damage

identification method", Computers and Structures, Vol. 80 No. 2-3, pp.117132. Kareem, A. and Gurley, K. (1996), "Damping in structures: its evaluation and treatment of uncertainly", Journal of Wind Engineering and Industrial Aerodynamics, Vol. 59 No. 2-3, pp.131-157. Kim, J.T. and Stubbs, N. (2003), "Crack detection in beam-type structure using frequency data", Journal of sound and vibration, Vol. 259 No. 1, pp.145-160. Kwok, S.M. (2003), Hpc with metkaolin and polyproprenely under elevated temperature, BSc Thesis, City University of Hong Kong. Pandey, A.K., Biswas, M. and Samman, M. M. (1991), "Damage detection from changes in curvature mode shapes", Journal of Sound and Vibration, Vol. 145 No. 2, pp.321-332. Wang, Z., Lin, R.M. and Lim, M.K. (1997), "Structural damage detection using measured FRF data", Computer methods in applied mechanical and engineering, Vol. 147 No. 1-2, pp.187-197. Wong, C.K. (2001), Identification of non-linear damping of tall buildings by the random decrement, PhD Thesis, City University of Hong Kong. Xia, Y. and Hao, H. (2002), "Statistical damage identification of structures with frequency changes", Journal of Sound and Vibration, Vol. 263 No. 4, pp.853870. Yang, Z., Wang, L., Wang, H., Ding, Y and Dang, X. (2009), "Damage detection in composite structures using vibration response under stochastic excitation", Journal of Sound and Vibration, Vol. 25 No. 4, pp.755-768. Zaitsev, Y.B. and Wittmann, F.H. (1981), "Simulation of crack propagation and failure of concrete", Materials and Structures, Vol. 14 No. 5, pp.357-365.

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Determining the probability distribution of rework costs in construction and engineering projects a

Peter E.D. Love & Chun-Pong Sing

a

a

School of Built Environment , Curtin University , Perth , WA , Australia Published online: 09 Mar 2012.

To cite this article: Peter E.D. Love & Chun-Pong Sing (2013) Determining the probability distribution of rework costs in construction and engineering projects, Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance, 9:11, 1136-1148, DOI: 10.1080/15732479.2012.667420 To link to this article: http://dx.doi.org/10.1080/15732479.2012.667420

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Structure and Infrastructure Engineering Vol. 9, No. 11, November 2013, 1136–1148

Determining the probability distribution of rework costs in construction and engineering projects Peter E.D. Love* and Chun-Pong Sing School of Built Environment, Curtin University, Perth, WA, Australia

Downloaded by [Curtin University Library] at 07:41 11 November 2013

(Received 12 August 2011; final version received 2 December 2011; accepted 8 December 2011; published online 9 March 2012) Rework arises due to design errors, changes and omissions during design and has been found to contribute to 52% of a project’s cost overrun. The statistical characteristics of rework costs experienced from contract award in 276 construction and engineering projects were analysed. The skewness and kurtosis values of rework costs are computed to determine if the empirical distribution of the data follows a normal distribution. The empirical distributions for rework costs are found to be non-Gaussian. Theoretical probability distributions are fitted to the rework data. The Kolmogorov–Smirnov and Anderson–Darling non-parametric tests are used to determine the ‘Goodness of Fit’ of the selected probability distributions. A Generalised Pareto probability function is found to provide the best overall distribution fit for rework costs. The Generalised Pareto distribution is used to calculate the probability of rework being experienced for the selected sample. Projects with a contract value 5A$1million had higher rework probabilities than that of 4A$101 million. Larger projects may be better managed and longer completion times provide an opportunity to make adjustments to facilitate cost control. The anticipation that rework will occur using the probabilities that are derived can enable a quantitative risk assessment to be undertaken prior to the commencement of construction. Keywords: rework; direct cost; indirect cost; contract value; Generalised Pareto distribution

Introduction Rework can have an adverse impact on the time and cost of construction and engineering projects (Construction Industry Institute (CII) 2001, Hwang et al. 2009, Love et al. 2009a). A considerable amount of research has examined the causal nature of rework (e.g. Burati et al. 1992, Josephson et al. 2002, RobinsonFayek et al. 2004, Hwang et al. 2009, Love et al. 2009a,b). Factors that have been identified as contributing to rework include poor project definition, inadequate pre-project planning, poor communication and a lack of constructability (Hwang et al. 2009). There is limited knowledge available about rework costs, particularly those of an indirect nature. This is because there is generally an absence of systems within projects to monitor and control rework (Hwang et al. 2009). Building upon research reported in Love et al. (2009a), the probability of rework occurring during construction from contract award is determined. Rework is considered to be a ‘random continuous variable’, as it can take an infinite range of values. The empirical rework distribution derived from 276 construction and engineering projects is fitted to the ‘best fit’ statistical distribution to determine reliable probabilities of occurrence.

*Corresponding author. Email: [email protected] ISSN 1573-2479 print/ISSN 1744-8980 online Ó 2013 Taylor & Francis http://dx.doi.org/10.1080/15732479.2012.667420 http://www.tandfonline.com

Rework Several definitions of rework within the construction and engineering management literature have been propagated. Rogge et al. (2001) defined rework ‘as activities in the field to be done more than once in the field or activities which remove work previously installed as part of the project’. Robinson-Fayek et al. (2003, 2004) refer to rework as the ‘total direct cost of re-doing work in the field regardless of initiating cause’. Robinson-Fayek et al. (2003, 2004) specifically state that their definition excludes change orders and errors due to off-site manufacture are not considered as rework. A broader definition of rework can be found in Love (2002a) who defines it ‘as unnecessary effort to re-doing a process or activity that was incorrectly implemented the first time’. According to Love (2002a), change orders can contribute to being undertaken rework on-site and therefore should be included in its calculation of costs. In addition, focusing simply on the direct rework costs neglects the intangible but real costs that may associated with disruption and schedule delays that may arise. With this in mind, Love (2002a) has suggested that rework should be expressed as:

Structure and Infrastructure Engineering TRc ¼

X

Drc þ

X

Indc

ð1Þ


where TRc ¼ Total rework cost (% of contract value at award). Drc ¼ Direct rework cost expressed (% of contract value at award). Indc ¼ Indirect rework cost expressed (% of contract value at award). Only by considering the direct and indirect rework costs can an assessment of its realistic impact be made. The determination of rework costs in construction and engineering projects has, however, been limited to date. In addition, research has tended to focus only on the determination of direct costs, which adversely influence a project’s contract value. Direct costs have been found to be significant in construction and engineering projects (Barber et al. 2000, CII 2001, Palaneeswaran et al. 2008, Hwang et al. 2009). Research undertaken by Love (2002a) revealed that rework contributed to 52% of a project’s cost overrun. Burati et al. (1992) reported rework costs to be 12.4% of contract value with 79% being attributable to design changes. Josephson and Hammarlund (1999) found the costs of rework to range from 2 to 6% of contract value. Similarly Love and Li (2000) examined a residential and industrial building and found direct rework costs to be 3.15% and 2.4% of contract value, respectively. In examining two road projects, Barber et al. (2000) revealed rework to be 16% and 23% of contract value. Yet, these estimates included an allowance for the cost of delays that were incurred. If these were removed then rework costs would have amounted to 6.6% and 3.6% of contract value. The inclusion of indirect costs of this nature clearly highlights the ‘real’ costs of rework that can occur. It has been suggested by Love (2002b) that indirect rework can have a ‘multiplier effect’ of up to six times the actual (direct) cost of rectification. Rework predominately arises due by errors, changes and omissions during design, which manifest during construction after a prolonged period of incubation (Burati et al. 1992, Love et al. 2011a). According to Love et al. (2009b), the underlying contributors of rework are strategic decisions taken by top management or key decision-makers who stimulate the conditions for the adoption of inappropriate structures, processes, practices and technologies for projects. Contrastingly, Hwang et al. (2009) suggest that poor leadership and communication, uncertainty and ineffective decision-making cause rework. Considering the proclivity for rework to emanate during the pre-construction phase of a project, an assessment of its probability of occurrence can be made. In an attempt to predict rework, Rogge et al.

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(2001) developed the Field Rework Index (FRI) to determine the risk of rework before construction commenced so that corrective action to lower its risk levels can be undertaken. The FRI rates 14 variables, such as a design firm’s qualifications for the specific project, degree to which design schedule is compressed and commitment to constructability of the design and construction team on a scale of 1–5 to develop a score to determine the potential for rework to occur during construction. The computed FRI score falls into one of three categories: . over 46 is ‘concern’ and the likelihood of rework occurring during construction is high; . 30–45 ‘normal vigilance’ and there is a chance rework may or may not arise and . 529 there is an ‘excellent prospect of low rework’ and projects a likely to have a successful outcome. While the approach developed by CII (2001) is practical, it relies on a high degree of subjective judgment and neglects the complexities and interdependency between variables that contribute to rework. Hubbard (2010) suggests that using a scale of 1–5 to determine risk is ambiguous and can inherently include human biases. In addressing the shortcomings of the FRI, a quantitative assessment of the likelihood of rework (including direct and indirect) at contract award is undertaken. Research approach The dataset presented in Love et al. (2009a) for Australian construction and engineering projects is used to develop ‘best fit’ statistical distributions so that probabilities for cost overruns at contract award can be determined. For the purpose of clarity, the method of data collection and dataset characteristics will be presented again. Questionnaire survey The questionnaire survey developed for the study reported in Love et al. (2009a) was used to extract cost overrun information as well as that relating to rework costs and causes. Stratified random sampling was used to select the study sample from the telephone directory, Yellow Pages1 for the various regions of Australia. Two main benefits can be derived from using a stratified sample: (1) It can ensure that adequate and representative respondents within each subgroup under study are acquired.

1138

P.E.D. Love and C.-P. Sing


(2) Stratification also ensures that respondents within the same group are homogeneous. Before the sample size for the main study could be determined, a pilot survey was completed with 30 construction and 20 civil engineering contractors. As the survey of construction contractors was undertaken first, it was considered to be reliable, and then used to pilot the civil engineering sample. The firms sampled comprised of design and engineering consultants, project managers and contractors. The rationale was to test the suitability, clarity and comprehensibility of the questionnaire as well as to measure the response rate. Participating firms were contacted by telephone and informed of the research aims and objectives, and also informed that all responses would remain strictly confidential; albeit, generalisations of the findings would be made available to all participants. On participant consent, questionnaires were mailed to the sample, with a stamped addressed return envelope enclosed. Participants were invited to critically review the questionnaires’ design and structure by annotating comments onto the document itself in order to provide constructive feedback. Comments received were positive and therefore the questionnaire remained largely unaltered for the main surveys; albeit, a few minor layout changes were made to increase clarity. A total of 25 responses were received in the building project pilot survey, giving an 83% response rate. For the civil engineering project survey, a total of 17 responses were received, giving an 85% response rate. These high response rates were obtained because prior consent to support the work was obtained from all survey participants. In the main survey, 420 and 300 questionnaires were distributed to design consultants, contractors and project managers for construction and civil engineering projects, respectively. As there were no fundamental changes required to either of the pilot questionnaires, they were added to the samples. For the building and civil engineering projects, 161 and 115 responses were received, respectively, which represents a total consolidated response rate of 36% for both surveys, which is within an acceptable range for a survey with industry practitioners (Alreck and Settle 1985). Data reliability Data reliability relates to data source and the identification of the position held by the respondent completing the questionnaire (Oppenheim 1992). Therefore, it was critically important that only selected senior personnel who had sufficient knowledge and experience about the procurement processes associated with a project answered the questionnaire. From the

total responses gathered, 133 respondents provided information relating to their individual job position and title, and it was revealed that most respondents held senior positions within their organisations. Based upon this finding, the direct mailing to individuals in organisations seemed to have achieved its objective of reaching senior staff who plays a significant role in the construction project management. In addition, questionnaires were mailed to organisations in different States in Australia and therefore the risk of duplicating projects was minimised. Analysis procedure Descriptive statistics such as the mean (M), SD and inter-quartile were calculated. A one-way analysis of variance (ANOVA) was used to determine if rework costs significantly varied between construction and engineering projects at a 0.05 significance level. Probability density functions (PDF) were developed using the software EastFit Professional 5.5. A PDF for a continuous distribution can be expressed in terms of an integral between two points: Zb

fðxÞdx ¼ Pða X bÞ:

ð2Þ

a

The cumulative distribution functions (CDF) were also produced. For theoretical continuous distributions, the CDF is expressed as a curve and denoted by: FðxÞ ¼

Zx fðtÞdt:

ð3Þ

1

The empirical CDF, which is displayed as a stepped discontinuous line and dependent on the number of bins, is represented by: Fn ðxÞ ¼

1 ½Number of observations x: n

ð4Þ

The PDF, CDF and distribution parameters (m; k; s) for continuous distributions were examined using the estimation method Maximum Likelihood Estimates. Using software StatAssist 5.5, the ‘best fit’ distribution was then determined using the following ‘Goodness of Fit’ tests, which measures the compatibility of a random sample with a theoretical probability distribution: . Kolmogorov–Smirnov statistic (D): Based on the largest vertical difference between the theoretical and empirical CDF:

1139

Structure and Infrastructure Engineering i1 i ; Fðxi Þ : D ¼ max Fðxi Þ 1in n n

Results

ð5Þ

. Anderson–Darling statistic (A2): A general test to compare the fit of an observed CDF to an expected CDF. The test provides more weight to distribution tails than the Kolmogorov– Smirnov test. The Anderson–Darling statistic is defined as: A2 ¼ n

n 1X ð2i 1Þ n i¼1


½In Fðxi Þ þ Inð1 Fðxniþ1 ÞÞ:

ð6Þ

The above ‘Goodness of Fit’ tests were used to test the null (H0) and alternative hypotheses (H1) that the datasets: H0 – follow the specified distribution and H1 – do not follow the specified distribution. The hypothesis regarding the distributional form is rejected at the chosen significance level (a) if the statistic D and A2 is greater than the critical value. For the purposes of this research, a 0.05 significance level is used to evaluate the null hypothesis. The P-value, in contrast to fixed a values, is calculated based on the test statistic, which denotes the threshold value of significance level in the sense that H0 will be accepted for all values of a less than the P-value. Once the ‘best fit’ distribution was identified, rework probabilities were calculated using the CDF. Then, to simulate the samples randomness and derive rework probabilities, a Mersenne Twister, which is a pseudo-random number generating algorithm, was used to generate a sequence of numbers that approximated the sample to 1000 (Matsumoto and Nishimura 1998).

Table 1.

Total Direct Indirect

Tables 1 and 2 present the descriptive statistics and percentiles for the total, direct and indirect rework costs that were incurred in the sampled projects. The mean total rework cost as a proportion of the original contract value was revealed to be 11.30% (SD ¼ 12.75). Means were also determined for the two groupings of project types, construction and civil

Range (A$m)

Mean (%)

Variance

SD (%)

Coefficient of variation

SE

Skewness

Excess kurtosis

79.5 49.9 50

11.30 5.87 5.45

162.6 49.586 47.097

12.75 7.04 6.86

1.128 1.1994 1.2581

0.767 0.42386 0.41309

2.287 2.6974 2.4627

6.520 9.2533 8.3975

Percentiles for rework costs.

Rework cost Total Direct Indirect

Rework costs

Descriptive statistics for rework costs.

Rework cost

Table 2.

Data from a total of 276 construction (n ¼ 161) and civil engineering (n ¼ 115) projects were obtained. In the case of construction projects, these ranged from banks to hospitals and hotels. For the civil engineering sample, these ranged from tunnelling to road construction and sewerage treatment plants. The summary statistics reveal that the mean original contract value was A$23,142,486 (SD ¼ A$41,171,772; minimum ¼ A$132,347; maximum ¼ A$390 million) and the mean actual contract value was A$25,455,372 (SD ¼ A$45,090,928; minimum ¼ A$136,671; maximum ¼ A$420 million). The actual construction period was an average 4.7 years (SD ¼ 3.3 years), ranging from 3 months to 3.75 years. To better understand the composition of the sample, an examination of respondent stratification and geographical dispersion was completed for the sample. In terms of respondent stratification, 45% were design consultants (architects, quantity surveyors, and structural, mechanical and electrical engineers), 31% were contractors and 24% comprised project managers. With regards to geographical dispersion, organisations were situated across states: Victoria (45%), New South Wales (17%), Queensland (27%), South Australia (9%) and Western Australia (2%).

Minimum

5%

10%

25% (Q1)

50% (median)

75% (Q3)

90%

95%

Maximum

0.5 0.1 0

1 0.5 0

1.5 1 0.185

3 1.5 1

7 3.5 3

15 8 7

28.6 15 15

35.45 20 20

80 50 50


1140

Figure 1.


Percentage of rework and original contract value (A$).

engineering, and were found to be 12.03% (SD ¼ 13.56%) and 10.29% (SD ¼ 11.50%), respectively. As previously noted in Love et al. (2009b), rework was significantly correlated with cost and schedule overruns for both construction and engineering projects (P 5 0.05). For construction projects, the maximum cost overrun was 244% and a minimum 784% (i.e. cost under-run), which results in a range of 328%. For the civil engineering projects sampled, the maximum cost overrun was 109% and a minimum of 11%, which results in a range of 98%. In addition, no significant differences were found between procurement methods and project types for rework costs (P 5 0.05). The range of total rework cost that were incurred in projects varied from less than 1% of the original contract value, while others were found to be as high as 80%. The degree of the variability in the estimates provided by respondents suggested that they may have been unsure about the actual rework costs that had been incurred. For construction projects, mean total rework cost estimates for design consultants were 14.77% (SD ¼ 17.64), contractors 11.06% (SD ¼ 14.07) and project managers 8.67% (SD ¼ 8.27). In the case of the civil engineering sample, TRc estimates provided by engineering consultants were 10.99% (SD ¼ 12.39), contractors 10.35% (SD ¼ 12.59) and project managers 8.84% (SD ¼ 7.90). An ANOVA was undertaken to determine whether there were significant differences between respondents’ estimates for both project types for total rework cost (P ¼ 0.05). No significant differences were found, which suggests that there is a degree of agreement about the perceived

Table 3.

‘Goodness of Fit’ test for rework distributions.

Distribution type

N

General Pareto 276 Total rework costs Direct costs

Indirect costs

Anderson– Kolmogorov– Darling (A2) Critical Significant Smirnov (D) Critical value value a level 0.2 0.1 0.05 0.02 0.01 0.2 0.1 0.05 0.02 0.01 0.2 0.1 0.05 0.02 0.01

0.064 0.073 0.081 0.091 0.098 2.748 0.3141 0.348 0.389 0.417 0.0937 0.1068 0.1186 0.132 0.142

1.374 1.928 2.50 3.289 3.907 1.374 1.928 2.501 3.289 3.907 1.374 1.928 2.501 3.289 3.907

estimated costs of rework being experienced. To illustrate the spread of the dataset, the percentage of total rework costs for the sample is plotted against original contract value (Ocv) in Figure 1. It can be seen in Figure 1 that smaller projects experienced considerably larger rework costs than the two projects that were 4A$300m. Probability of rework The construction and engineering datasets were combined and the ‘best fit’ probability distribution


Structure and Infrastructure Engineering

Figure 2.

Pareto: Histogram of rework.

Figure 3.

Pareto: PDF for total rework costs.

was examined using the ‘Goodness of Fit’ tests: Kolmogorov–Smirnov and Anderson–Darling. The results of the ‘Goodness of Fit’ tests revealed that General Pareto distribution provided the best fit for the dataset for total, direct and direct rework costs (Table 3). For the sample of 276 construction and engineering projects, Kolmogorov–Smirnov test revealed a D-statistic of 0.06083 with a P-value of 0.24867 for total rework, a D-statistic of 0.0844 with a P-value of 0.03692 for direct rework and a D-statistic of 0.0907 with a P-value of 0.01997 for indirect rework.

1141

The Anderson–Darling statistic A2 was revealed to be 0.91732 for total rework, 10.168 for direct rework and 2.4209 for indirect rework. The ‘Goodness of Fit’ tests all accepted the H0 for the sample distribution’s ‘best fit’ at a level 0.02 and 0.01. A Generalised Pareto is a continuous probability distribution that is a skewed and heavy-tailed distribution. It is also akin to an exponential distribution and is typically used to modify the tails of other distributions. For example, if random influences during the manufacturing of concrete influence its water content, a standard probability distribution, such as a Normal,


1142


Figure 4.

Pareto: CDF for total rework costs.

Figure 5.

Pareto: Histogram of direct rework costs.

could be used to model its volume. While a Normal distribution may be appropriate near the mode, it may not be the best fit to real data at the tails. As a result, a more complex distribution is needed to describe the full range of the data. The Pareto distribution in this instance provides the ‘best fit’ as it takes into account the extreme values of rework, particularly in those projects with smaller contract values. The parameter k is a continuous shape parameter, s the continuous scale parameter (s 4 0) and m the

continuous location parameter. The domain for a Pareto distribution is denoted as m x 5 þ? for k 0 and m x 7s/k for k 5 0. The PDF is expressed as: 8 1 ðx mÞ 11=k > > > 1 þ k > 1 ðx mÞ > : exp s s

k 6¼ 0 : k¼0

ð7Þ

1143



Figure 6.

Pareto: PDF for direct rework costs.

Figure 7.

Pareto: CDF for direct rework costs.

The CDF is expressed as: 8 ðx mÞ 1=k > > > > ðx mÞ > : 1 exp s

k 6¼ 0 :

ð8Þ

k¼0

The parameters for the General Pareto were for total rework costs were found to be k ¼ 0.173, s ¼ 9.132, m ¼ 0.250, for direct rework costs k ¼ 0.221, s ¼ 4.394, m ¼ 0.2291 and indirect rework

costs k ¼ 0.199, s ¼ 4.605, m ¼ 70.297. Figures 2–10 present the histograms, PDF and CDF for rework costs based upon the calculated distribution parameters. The likelihood function (i.e. the measure for determining how likely an event is to occur) for the distribution parameters a and xm, given a sample x¼(x1, x2, . . . , xn) is expressed as (Newman 2005): Lða; xm Þ

n Y i¼1

a

n Y xam 1 n na a x : m aþ1 aþ1 xi i¼1 xi

ð9Þ


1144


Figure 8.

Pareto: Histogram for indirect costs.

Figure 9.

Pareto: PDF for indirect rework costs.

The logarithmic likelihood function is: ‘ða; xm Þ ¼ n In a na In xm ða þ 1Þ

n X

The maximum likelihood estimator for a is therefore be expressed as: Inxi

ð10Þ

i¼1

Noteworthy, ‘(a, xm) is monotonically increasing with xm. Since x xm, then: _ xm

¼ min xi : i

ð11Þ

To determine an estimate for a, the corresponding partial derivative is determined where it is zero: n X @‘ n ¼ þ n In xm In xi ¼ 0 ð12Þ @a a i¼1

â ¼ P

n ðInx In^ xm Þ i i

ð13Þ

It can be seen in Figure 2, for example, that 79% (218) of projects experienced total rework costs 516%. Figures 6 and 9 illustrate the PDF for direct and indirect rework costs. The calculated probabilities of rework being experienced are presented in Tables 4 and 5. The probability of experiencing a total rework cost of 410% is 15%. Delimiters have also been used to provide probabilities of rework costs. The probability of direct rework costs between 1% and 5%, for

1145



Figure 10.

Table 4.

Rework Total

Direct

Indirect

Pareto: CDF for indirect rework costs.

Discrete probabilities for rework costs.

Table 5.

Probability of cost overrun (%)

P(X 5 X1)

P(X 4 X1)

5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30

0.66 0.85 0.92 0.95 0.97 0.98 0.62 0.84 0.91 0.95 0.97 0.98 0.66 0.85 0.92 0.95 0.98 0.98

0.34 0.15 0.07 0.05 0.03 0.02 0.38 0.16 0.09 0.05 0.03 0.02 0.34 0.15 0.07 0.05 0.03 0.02

example, is 46%. For a mean total rework cost 11.30%, the likelihood estimate that a project exceeds this figure is 86% [P(X 5 X1) ¼ 0.86]. Figure 1 indicates that there is a negative relationship between contract value and the degree of rework that is experienced. Total rework costs for construction and engineering projects defined by contract value delimiters are: 5A$1m (M ¼ 19.43, SD ¼ 20.18), A$1–10m (M ¼ 10.12, SD ¼ 10.82), A$11–50m (M ¼ 12.06, SD ¼ 13.63), A$51–100m (M ¼ 12.93, SD ¼ 14.03), 4A$101m (M ¼ 6.00, SD

Rework Total

Direct

Indirect

Generic range of rework probabilities. Probability of a cost overrun between 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30% 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30% 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30%

P(X1 5 X 5 X2) 0.37 0.23 0.12 0.07 0.05 0.03 0.46 0.21 0.08 0.04 0.02 0.01 0.44 0.18 0.07 0.03 0.02 0.01

7.95). Table 6 provides a breakdown of rework costs by contract value for construction and engineering projects. Notably, projects 4A$101m experienced considerably less rework than those 5A$1m. A similar finding was reported in Hwang et al. (2009) who suggested that higher construction costs may make larger projects less sensitive to rework. Moreover, larger projects may be better managed and longer completion times may provide an opportunity to make adjustments to facilitate cost control (Jahren and Ashe 1990, Odeck 2004). It is suggested that this

1146 Table 6.

P.E.D. Love and C.-P. Sing Descriptive statistics for total rework by contract value.

Project type

Project size

N

Mean Ocv

Ocv SD

Mean % overrun

SD

Construction

5A$1m A$1m to A$10m A$11m to A$50m A$51m to A$100m A$101m to A$200m 4A$200m Subtotal A$1m to A$10m A$11m to A$50m A$51m to A$100m 4 A$101m Subtotal

14 70 60 12 6 2 161 61 43 7 4 115 276

A$513,546 A$3,874,368 A$21,860,966 A$66,883,333 A$162,666,666 A$376,000,000 A$25,521,927 A$8,136,604 A$24,906,930 A$77,285,714 A$165,250,000 A$22,092,965 A$24,093,193

A$344,668 A$2,830,183 A$10,099,633 A$15,062,888 A$22,339,800 A$19,798,989 A$51,957,899 A$3,464,888 A$10,487,326 A$12,499,523 A$25,051,613 A$33,897,118 A$45,275,566

19.43 9.49 12.86 9.03 16.89 6.81 12.03 10.28 10.99 8.16 4.38 10.29 11.30

20.18 10.35 14.49 16.02 9.64 – 13.56 10.96 13.22 7.63 10.85 11.05 12.74

Civil engineering


Total

may explain why the function in Figure 2 is monotonically decreasing. Using the Pareto PDF, the probability of total rework was calculated for a range of contract values, which are presented in Tables 7 and 8. For a project with a contract value of 5A$1m experiencing 5% rework is 72%. For construction projects with a contract value of 4A$101 (M ¼ 6.81%), the probability of rework is P(X 5 6.81%) ¼ 0.85, P(X 4 6.81%) ¼ 0.15. Similarly, for civil engineering projects with a contract value in the range of A$11–50m (M ¼ 10.99%), the probability of rework is P(X 5 X1) 0.66, P(X 4 X1) ¼ 0.34. The anticipation that rework will occur using the probabilities that have been derived can enable a quantitative risk assessment to be undertaken prior to the commencement of construction. A reduction in rework can significantly improve the performance of projects. Foresight and anticipation can enable strategies to be put in place to minimise its impact on project cost and schedule. Acknowledging that rework will arise may be perceived by design consultants to directly question their professionalism and quality of work. Such recognition may also be perceived to lead to potential punitive action from clients or contractors. What may be perceived to be minor design errors at a particular point in time can later lead to disastrous outcomes (Adamski and Westrum 2003). For example, wrongly specified and inadequate gusset plate thickness contributed to the collapse of the I–35w Minneapolis Bridge, which subsequently killed 13 people. Adamski and Westrum (2003) suggest that designers should anticipate for what might go wrong and test for problems during the design process. Building Information Modelling (BIM), for example, can enable this to occur, but this technology alone will not reduce errors and omissions (Love et al., 2011b). According to Love et al. (2011b), a number of strategies, such as an

Table 7. value.

Discrete probabilities rework cost by contract

Contract value 5A$1

A$1m to A$10m

A$11m to A$50m

A$51m to A$100m

4A$101m

Probability of cost overrun (%)

P(X 5 X1)

P(X 4 X1)

5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30

0.26 0.46 0.58 0.66 0.73 0.78 0.38 0.65 0.79 0.86 0.91 0.93 0.39 0.60 0.74 0.81 0.87 0.90 0.41 0.65 0.76 0.81 0.86 0.88 0.49 0.74 0.87 0.94 0.97 0.98

0.72 0.64 0.42 0.34 0.26 0.22 0.62 0.35 0.21 0.14 0.09 0.07 0.61 0.40 0.26 0.19 0.13 0.10 0.59 0.45 0.24 0.19 0.14 0.12 0.51 0.16 0.13 0.06 0.03 0.002

integrated procurement method, risk/reward incentives and stage gate reviews throughout a project life cycle, need to be implemented in congruence with BIM to reduce and contain errors and subsequent rework during construction. Even if BIM and other strategies are implemented, there still remains a likelihood that rework will occur during construction.

Structure and Infrastructure Engineering Table 8. value.

Range of probabilities for rework by contract

Contract value (A$m) 5A$1


A$1m to A$10m

A$11m to A$50m

A$51m to A$100m

4A$101m

Probability of a cost overrun between 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30% 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30% 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30% 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30% 1 and 5% 5 and 10% 10 and 15% 15 and 20% 20 and 25% 25 and 30%

P(X1 5 X 5 X2) 0.23 0.17 0.12 0.09 0.06 0.05 0.33 0.27 0.14 0.07 0.04 0.03 0.32 0.21 0.12 0.08 0.05 0.02 0.39 0.24 0.10 0.05 0.03 0.002 0.36 0.24 0.12 0.06 0.03 0.001

Conclusions To manage and control the risk of rework, there is a need to determine its probability of occurrence to construction. Rework is comprised of direct and indirect costs. Therefore, the probabilities for both components need to be derived to establish the ‘real’ costs of rework. Using data obtained from 276 construction and engineering projects, the statistical characteristics of rework costs (direct and indirect) were analysed. The mean total rework cost was revealed to be 11.30% of a project’s original contract value. The empirical distributions for rework costs (direct and indirect) were found to be non-Gaussian. Non-parametric ‘Goodness of Fit’ tests were used to select the best-fit probability distribution. A Generalised Pareto probability function was found to provide the best overall distribution fit to calculate the probability of rework. As well as providing single probability points for rework from 5 to 30% in 5% increments, ranges were also calculated. It was revealed that projects 5A$1m experienced the highest rework costs. The research has provided the initial

1147

platform to examine the probability of rework. Determining the best-fit distribution is pivotal to calculating realistic rework probabilities. Further research, however, is required to extend the dataset and test the reliability of probabilities that have been produced.

Acknowledgements The authors would like to thank the three anonymous reviewers for their constructive comments which have helped improve the quality of research reported in this manuscript. The authors would also like to acknowledge Professor David Edwards, Professor Peter Davis and Professor Derek Walker who contributed to the study.

References Adamski, A.J. and Westrum, R., 2003. Requisite imagination: the fine art of anticipating what might go wrong. In: E. Hollnagel, ed. Handbook of cognitive task design. Mahwah, NJ: Lawrence Erlbaum Associates, 193–220. Alreck, P.L. and Settle, R.B., 1985. The survey research handbook. Homewood, IL: Richard D. Irwin. Barber, P., et al., 2000. The cost of quality failures in major civil engineering projects. International Journal of Quality and Reliability Management, 17 (4/5), 479–492. Burati, J.L., Farrington, J.J., and Leadbetter, W.B., 1992. Causes of quality deviations in design and construction. ASCE Journal of Construction, Engineering and Management, 118 (1), 34–49. Construction Industry Institute (CII), 2001. The field rework index: early warning for filed rework and cost growth. Austin, TX: The University of Texas at Austin. Report No. RS 153-1, May. Hubbard, D.W., 2010. How to measure anything: finding the value of ‘‘intangibles in business’’. 2nd ed. Hoboken, NJ: John Wiley & Sons. Hwang, B.-G., et al., 2009. Measuring the impact of rework on construction cost performance. ASCE Journal of Construction Engineering and Management, 135 (3), 187–198. Jahren, C. and Ashe, A.M., 1990. Predictors of cost overrunrates. ASCE Journal of Construction Engineering and Management, 116 (3), 548–552. Josephson, P.-E. and Hammarlund, Y., 1999. The causes and costs of defects in construction: a case study of seven building projects. Automation in Construction, 8 (6), 681–687. Josephson, P.-E., Larrson, B., and Li, H., 2002. Illustrative benchmarking rework and rework costs in the Swedish construction industry. ASCE Journal of Management in Engineering, 18 (2), 76–83. Love, P.E.D., 2002a. Influence of project type and procurement method on rework costs in building construction projects. ASCE Journal of Construction Engineering and Management, 128 (1), 18–29. Love, P.E.D., 2002b. Auditing the indirect consequences of rework in construction: a case based approach. Managerial Auditing Journal, 17 (3), 138–146. Love, P.E.D. and Li, H., 2000. Overcoming the problems associated with quality certification. Construction Management and Economics, 18 (2), 139–149.


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Love, P.E.D., Lopez, R., and Edwards, D.J., 2011a. Reviewing the past to learn in the future: making sense of design errors and failures in construction. Structure and Infrastructure Engineering (in press). Love, P.E.D., et al., 2009a. Congruence or divergence? A path model of rework in building and civil engineering projects. ASCE Journal of Performance of Constructed Facilities, 23 (6), 480–488. Love, P.E.D., et al., 2009b. Project pathogens: the anatomy of omission errors in construction and resource engineering projects. IEEE Transactions on Engineering Management 56 (3), 425–435. Love, P.E.D., et al., 2011b. Design error reduction: toward the effective utilization of Building Information Modelling. Research in Engineering Design, 22 (3), 173–187. Matsumoto, M. and Nishimura, T., 1998. Mersenne Twister: a 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Transactions on Modelling and Computer Simulation, 8 (1), 3–30. Newman, M.E.J., 2005. Power laws, Pareto distribution and Zipf’s Law. Contemporary Physics, 46 (5), 323–351.

Odeck, J., 2004. Cost overruns in road construction – what are their sizes and determinants? Transport Policy, 24, 43–53. Oppenheim, A.N., 1992. Questionnaire design, interviewing and attitude measurement. London: Pinter. Palaneeswaran, E., et al., 2008. Mapping rework causes and effects using artificial neural networks. Building Research and Information, 36 (5), 450–465. Robinson-Fayek, A., Dissanayake, M., and Campero, O., 2003. Measuring and classifying rework: a pilot study. Alberta, Canada: Department of Civil and Environment Engineering, Construction Owners Association of Alberta. Robinson-Fayek, A., Dissanayake, M., and Campero, O., 2004. Developing a standard methodology for measuring and classifying construction fieldwork. Canadian Journal of Civil Engineering, 31 (6), 1077–1089. Rogge, D.F., et al., 2001. An investigation into field rework in industrial construction. Austin, TX: Construction Industry Institute. Report No. RR153-11.