A model for predicting plant maintenance costs

Construction Management and Economics

ISSN: 0144-6193 (Print) 1466-433X (Online) Journal homepage: http://www.tandfonline.com/loi/rcme20

A model for predicting plant maintenance costs David J. Edwards , Gary D. Holt & Frank C. Harris To cite this article: David J. Edwards , Gary D. Holt & Frank C. Harris (2000) A model for predicting plant maintenance costs, Construction Management and Economics, 18:1, 65-75, DOI: 10.1080/014461900370960 To link to this article: http://dx.doi.org/10.1080/014461900370960

Published online: 21 Oct 2010.

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Construction Management and Economics (2000) 18, 65± 75

A model for predicting plant maintenance costs DAVID J. EDWARDS, GARY D. HOLT and FRANK C. HARRIS Built Environment Research Unit, School of Engineering and the Built Environment, University of Wolverhampton, Wulfruna Street, Wolverhampton, West Midlands WV1 1SB, UK Received 15 May 1998; accepted 17 December 1998

A model is presented that predicts the total cost of plant maintenance (i.e. direct cost of maintenance plus indirect cost of lost production) and is derived studying a random sample of tracked hydraulic excavators. Analysis is based on the machine history ® le data of 33 plant items, modelled using multiple regression (MR) analysis. Validation of the model was determined via the combination of an observed high R2 at 0.94 and various statistical tests which con® rmed the prerequisites of a rigorous MR analysis. Machine weight, type of industry and company attitude towards predictive maintenance were found to be the best predictor variables of total plant maintenance cost. The paper also discusses reasons underlying the inclusion of predictor variables in the ® nal model, and concludes with clear directions for future research in this ® eld. Keywords: Plant maintenance cost, tracked hydraulic excavators, construction plant, plant downtime

Introduction Certain sectors of the construction industry, for example, the extractive sector, believe that construction plant is merely a cost item requiring effective utilization to justify its existence (Edwards et al., 1998a). Within this sector, pro® t evolves from the sale of materials extracted and represents the difference between total production cost (including construction plant cost) and net selling price. Therefore, an increase in plant operating cost(s) ultimately reduces pro® t, so it is understandable that quarrying and mining managers consider such costs an `evil’ to be minimized at all times (Edwards et al., 1998e). Conversely, the plant hire sector holds an alternative viewpoint. Here, it is considered that plant does `earn’ pro® t, this being the difference between net return from hire charges and total expenditure (Harris and McCaffer, 1991). In this context total expenditure includes administrating, maintaining, and operating units of plant. Viewpoints differ regarding determination of plant costs and de® nition of pro® t, and are not con® ned to the various sectors of construction. Construction professionals’ perspectives yield the greatest divergence,

e.g. between production manager and mechanical engineer. Production managers understandably concentrate on machine output, whereas mechanical engineers are more aware of direct maintenance costs (Edwards et al., 1998a). Arguably, ® nance managers are best placed to consider the full spectrum of plant maintenance cost, but their (tendency to) lack of mechanical engineering knowledge makes them less likely to interpret these ® gures to their full extent. This paper addresses part of this problem by presenting a model for predicting the total cost of plant maintenance (Edwards et al., 1997a). Notwithstanding divergence of opinion pertaining to total maintenance cost, the model will equip construction managers with a decision tool by which to judge cost ef® ciencies of current plant strategies.

Model development: methodology Predicting the total cost of plant maintenance proved problematic, for two reasons. First, in general practitioners were unwilling to relinquish tendersensitive cost information on plant, since such exposure

Construction Management and Economics ISSN 0144± 6193 print/ISSN 1466-433X online € 2000 Taylor & Francis Ltd

66 might exert detrimental forces upon company competitiveness. Second, although collaboratory contractors were willing to supply direct maintenance cost data (i.e. replacement parts and periodic servicing), they were unwilling to supply data on operational indirect costs (i.e. the cost of postponed production plus the cost of irrecoverable overheads in the event of plant downtime). This was because such data are voluminous and would exhaust considerable time and resources to collate. To overcome this predicament, a procedure was devised by which to approximate absent indirect costs. This procedure consisted of four stages: 1. calculation of machine productivity per hour; 2. calculation of machine hire rates per hour; 3. calculation of average machine downtime per hour; and 4. mathematical manipulation of (i) to (ii) to determine machine downtime cost. A description of these stages will now be given. Calculation of machine productivity (per hour) Machine productivity is the product of machine cycle time and machine bucket capacity, making due allowance for utilization. Caterpillar machine performance data (Caterpillar, 1997) suggested that maximum machine cycle time Y increases at a decreasing rate with machine weight X, creating a curvilinear trend. A log10 transformation (Chat® eld and Collins, 1996) of machine weight Z, however, created a linear trend (Figure 1) and therefore facilitated linear bivariate regression analysis for paired data (Lapin, 1993) to be conducted. This produced the model: Y = 1.051 6 + 10.756 4 Z This model proved robust, having an R2 of 0.87 (i.e. 87% of total variation of machine cycle times about their mean could be explained by machine weight). Residual analysis was used to test model appropriateness, i.e. for linearity and constant variance

Figure 1 Scatter plot of machine cycle time to machine weight log transformation

Edwards et al. (Kvanli et al., 1995). The random scatter of residuals on the residual scatter plot for cycle time re¯ ected the linear relationship of these variables. Such a plot would seem ideal for regression analysis. However, utilization of maximum cycle time would prove unrealistic. This is because the Caterpillar performance handbooks state a `typical’ cycle time to be an average between minimum and maximum values. To determine the average value, initial analysis modelled maximum cycle time before scaling down this ® gure at equal increments to the average cycle time. This created a parallel trend between maximum and minimum cycle times across the machine sample weight range. This was an assumption which proved incorrect upon further scrutiny of Caterpillar machine performance data. Between maximum and minimum cycle times, output actually increases with machine weight and therefore is not constant. To remedy this inaccuracy, both minimum and maximum values of cycle time for each machine weight required modelling to determine the true machine cycle time range. Subsequently, via interpolation, a more precise calculation of the average cycle time was made. A scatter plot of minimum machine cycle times to machine weights revealed a strong positive yet curvilinear relationship. Once more it was necessary to conduct a transformation of machine weight to create a linear relationship. Machine weight log10 Z and machine cycle time Y were then modelled using bivariate regression for paired data. This analysis produced a rather weak coef® cient of determination (0.77), and consequently a multiple regression (MR) solution (Hildebrand and Ott, 1991) was required. Independent variables added to this MR analysis included: 1. whether the machine was new or old; 2. whether the machine was a front shovel or backhoe; 3. individual operators and hence operator competence; 4. machine manufacturer; 5. whether the plant company manufactures its own components or not; 6. company attitude to used oil analysis; and 7. type of ground conditions prevalent. Because these variables were qualitative, each was allocated a binary code to create a quantitative representation for MR analysis. For example, binary coded variables were classi® ed as follows: X1 = 1 (front shovel); and X2 = 0 (backhoe) (Bryman and Cramer, 1997). For a given variable, the option assigned the value 1 is arbitrary because estimated cycle time will be the same, regardless of coding procedure used (Kvanli et al., 1995). Of these binary coded variables, old machine/new machine, when combined with machine weight log10 produced the best model of the form: Y = 8.748 010 (± 4.323 311; if the machine is a new model) + 19.428 910 Z

67

Predicting plant maintenance costs where Z is the re-expression of machine weight. It is interesting to note at this point that new Caterpillar machines seem to have an improved speed of minimum cycle time of > 4.32 seconds as exhibited by the minus constant in the MR equation. An alternative interpretation of this minus coef® cient would be to say that `old’ machines have cycle times that are + 4.32 seconds slower than new machines. Either way, the underlying ® nding is the same. Such an observation is a fundamental feature of the binary coded variable and is a consequence of the arbitrary decision to allocate the binary code 1 to new vis-… -vis old model (Edwards et al., 1998c). Again, model accuracy was acceptable, R2 = 0.86. This was validated further by residual analysis; no de® ned patterns were revealed within the resulting scatter plot, con® rming that multivariate assumptions (NourusÆ is, 1993) had not been violated. However, machine production depends also upon machine job ef® ciency. Job ef® ciency, which can be de® ned as plant utilization on a time usage basis, depends upon the four factors of operator skill, ground conditions, swing angle, and site obstructions (Caterpillar, 1997). Caterpillar specify that, combined, these factors account for job ef® ciencies of between 67% and 100%, but that an `average’ ® gure of 83% is robust; this equates to 50 seconds utilization in any minute of machine `operation’ and, consequently, less cycles `production’ per minute or hour. Table 1 provides an example of linear cycle time calculations between minimum, maximum and average cycle times for the CAT211 (16.6 tonne) backhoe tracked hydraulic excavator at 83% job ef® ciency. Prior analysis used for determining maximum and minimum cycle times (14.17 seconds and 32.45 seconds, respectively), allowed the range of machine cycle times to be calculated. This was 18.28 seconds, with an average cycle time of 23.31 seconds. The range of cycle times (column B) was divided into 3000 seconds per hour to determine cycles per adjusted hour, i.e. 50 seconds per minute (column C), which multiplied by bucket capacity in m3 (column D), produces output per hour m3 (column E). The average cycle time equates to lost production, which can be quanti® ed by subtracting the Table 1

Calculation of machine hire rates as an approximation to operational costs In the absence of production cost data, hire cost data provide an appropriate alternative cost of operation per hour. This is because hire companies have a similar relationship with plant manufacturers as do private owners of equipment (Harris and McCaffer, 1991). In both instances, the cost of plant maintenance (e.g. depreciation, administration and so on) must be recouped plus a pro® t. Hire costs were modelled because not all of the machines present within the sample were available for hire. For example, only machines at the larger end of the weight spectrum could be obtained from specialist mining hire contractors. Hence, one could not simply obtain hire rates directly from hire companies. To model hire cost, a random sample of 26 machines was selected for analysis from specialist quarrying and mining hire contractors. These machines ranged in weight from 13 tonnes to 214 tonnes. A scatter plot of machine hire cost Y to machine weight X revealed a positive linear relationship between these variables, i.e. the greater the weight the greater the hire charge. However, the analysis also identi® ed the heaviest excavator in the sample as an extreme outlier. This could produce asymmetric skewness and disrupt the normality of any further parametric analysis (Chat® eld, 1995). To reduce the detrimental in¯ uence of this outlier upon the regression model, a transformation (log10) of both variables was necessary. Transformation of one variable alone created a curvilinear trend. The lower and upper outlier threshold limits (for de® nition of outliers) were calculated as 0.80 and 2.14, respectively, via: 25th percentile ± (IQR ´ 1.5 constant) = lower outlier threshold, and 75th percentile + (IQR ´ 1.5 constant) = upper outlier threshold (Siegel and Morgan, 1996), where IQR = interquartile range. The transformed data improved the normality

Calculation of lost production cost (CAT 211)

A Range in lost production

Maximum Minimum Average

respective average output per hour from maximum output per hour, e.g. 182.07 m3 (column E). Hence, for the average cycle time, lost production would equal 182.07 (100%) minus 110.68, i.e. 71.39 m3 per hour.

B Cycle time

C Cycles per hour

(secs)

(No./h)

14.17 32.45 23.31

211.71 92.44 128.70

D E F G Bucket Output Lost Lost capacity per adjusted production production hour cost (m3) (m3/h) (m3/h) (£/h) 0.86 0.86 0.86

182.07 79.50 110.68

0 102.56 71.39

0 7.98 5.55

H Cost per hour (£/h) 14.57 22.55 20.12

J K Average Cost of B/D hours breakdown per M/C (h) (£/h) 0.018 0.018 0.018

0.26 0.41 0.36

68 assumption signi® cantly, as exhibited by the same mean and median values (1.51). Having determined normality, linear regression for paired data was then conducted on the sample to produce the bivariate model: Q = 0.110 568 + 0.863 109 Z where Q represents the re-expression of the Y variable machine hire charge (Z). Natural hire values in £ sterling can be determined by taking the antilog of Q. The coef® cient of determination for this model was extremely high at 0.95, most probably due to the fact that the sample lacked a representative number of machines above 50 tonnes. Representation of more machines within this heavier weight class certainly would have reduced the strength of correlation between machine weight and machine cycle time. However, the fewer instances of heavy equipment in the hire industry is to be expected, particularly since demand for such is currently low. In this respect, the random sample mirrored distribution of machines currently available within the specialist quarrying and mining hire industry. To test model appropriateness, residual values were charted on a scatter plot. Because the scatter plot exhibited no apparent pattern it could reasonably be assumed that the regression model was indeed appropriate. Referring back to Table 1, the cost per hour of operating a machine within the maximum and minimum cycle times was found through mathematical manipulation of the hire cost model. For companies to generate maximum pro® t and ownership cost recovery, their machines should optimally operate at 100% ef® ciency. This is unrealistic in practice, and any reduction in output will ultimately cost the business. Lost production cost was determined by taking the predicted hire cost per hour of £14.17 and dividing by the respective maximum output per hour 182.07 m3 to obtain a cost per m3, i.e. » 0.078 £/m3. Lost production in m3 in column F of Table 1 was then multiplied by this cost per m3 to obtain the cost of lost production (column G). The addition of this monetary ® gure to the direct hire cost per hour allowed calculation of the total cost per hour at average productivity. Having determined an average cost per hour, the analysis now required the rate of downtime per hour of operation to determine downtime cost. Calculation of average downtime per hour of operation Average downtime per hour of operation was obtained by summing the downtime for each individual machine and dividing this by actual hours worked. The term

Edwards et al. downtime itself requires further de® nition in that, for this research, downtime included both unscheduled stoppages and scheduled ® xed-time-to maintenance (otherwise erroneously known as preventive maintenance). The resultant ® gure was of little value to the practitioner, for several reasons. First, only an individual machine’ s history could be analysed, whereas realistically data on several machines would be required to determine average downtime for that particular machine. Second, the sample did not represent all 33 subsample machines, since history ® le data on 15 machines was crude, giving only total annual ® gures (not ® gures for individual downtime observations). Consequently, such crude ® gures excluded the use of transformations (Bird and May, 1982). Third, and perhaps more importantly, not every type of machine available for purchase was present within the subsample. Thus the average downtime was `machine speci® c’ and, consequently, of little value for owners of other than CAT machines. To overcome these shortcomings, the sample data on downtime across all machines with full history (18 No.) were then used to predict average downtime per hour of operation for machines operating in quarrying and mining. These machines ranged in weight from 16.6 tonnes to 335 tonnes. However, taking an average in this way is open to the criticism that downtime may increase for larger machines. If this hypothesis were true, then average downtime would be an overestimate for small machines and, conversely, an underestimate for larger machines. To test this theory summary statistics were used for each individual machine (Table 2). Table 2 illustrates that downtime is chaotic and not necessarily a function of machine size. For example, three machines were considered in isolation, all of a similar age, all belonging to the same company (hence, no deviation in maintenance practice), and all working on the same site environment (mass excavators in opencast coal). Machine N at 27.01 tonnes has a median downtime value of 2.75 hours and an IQR of 1.00± 7.25 hours; machine H at 335 tonnes has a median of 1.75 and an IQR of 0.62± 5.87 hours; and machine L at 185 tonnes has a median of 2.00 and an IQR of 0.92± 5.37 hours. Although a relatively small sample of machines was utilized, the observations recorded against each were substantial, constituting several hundred cases. This provides strong evidence that downtime does not increase with machine weight and, therefore, an average across the sample of all machines was justi® ed. The distribution of individual observations of downtime was severely negatively skewed. Because of this asymmetry, a log10 transformation was employed to create a more normal distribution. As a test of

69

Predicting plant maintenance costs Table 2 M/C A B C D E F G H I J K L M N O P Q R

Summary statistics for machine downtime Weight (tonnes)

Frequency

Mean

Median

31.00 20.37 31.00 20.37 20.37 20.37 20.37 335.00 47.27 47.27 16.60 218.00 218.00 27.01 45.00 68.42 47.27 68.42

87 8 22 6 8 2 3 173 60 71 20 149 185 106 11 22 21 38

9.43 4.90 4.84 15.16 6.96 1.37 20.00 6.11 8.12 10.03 20.65 4.93 4.79 5.41 2.90 1.90 2.23 4.06

4.00 2.50 2.50 14.00 4.75 1.37 10.00 1.75 5.00 4.50 18.00 2.00 2.00 2.75 2.00 1.50 1.00 2.00

normality, the IQR (0.81) was divided by the standard deviation (0.565) (Siegel and Morgan, 1996) to determine how close the actual distribution was to the ideal value of 1.40. A resultant ® gure of 1.43 suggested that the re-expression of machine downtime was nearnormal distribution. To obtain the rate of downtime per hour of operation, the sum of downtime log10 427.19 was divided by the number of observations (975) to produce a ® gure of 0.438, which converted back into natural values equals 2.74 hours. Multiplication of this ® gure by the number of observations (975) equals 2 673.92, and divided by the total sum of hours worked for all machines (140 860.5 hours) this equates to 0.018 hours downtime per hour of operation. As an aside, multiplication of average downtime by 3000 hours operation per annum (assuming 12 hour days, ® ve days per week, and 50 weeks per annum) would indicate that four days and nine hours are lost through machine downtime in the quarrying and mining industry, per machine, per annum. With reference to Table 1, the cost per hour in column H is multiplied by downtime per hour of operation (column J) to obtain downtime cost (column K).

25th Percentile 1.50 0.68 0.50 1.75 1.75 0.75 5.00 0.62 2.00 1.75 2.37 0.92 1.00 1.00 1.00 1.00 1.00 1.00

75th Percentile

Range

12.00 11.50 4.75 25.00 7.62 ± ± 5.87 12.87 9.50 35.87 5.37 4.75 7.25 3.00 2.50 3.00 5.25

49.75 13.50 30.00 39.00 26.25 ± 40.00 80.25 37.75 55.00 52.25 60.00 80.50 49.50 11.50 5.50 7.50 19.50

Collins, 1996). Variables used for predicting total plant maintenance cost utilized both qualitative and quantitative variables (Table 3). Quantitative variables Quantitative variables were mainly machine speci® cation oriented. Examination of these possible (X) predictor variables revealed that they were positively, linearly related to each other. For example, machine bucket capacity and machine horsepower both increased with machine weight. These linear relationships could lead to the problem of multicollinearity, which produces (MR) model instability (NouruÆ s is, 1994). To overcome this problem, correlation analysis was used as an auxiliary tool (Rees, 1996) to distinguish machine speci® cation `predictor’ variables (X) which were most highly correlated with maintenance cost (Y), but which were not highly correlated with each other. Bucket capacity was the most highly correlated with total plant maintenance cost. However, discussions held with plant owners highlighted their concern that maximum capacity is too theoretical and not always achievable in practice. Therefore, the next most highly correlated variable, machine weight, was used for further analysis.

Multiple regression analysis The average indirect cost of maintenance was added to the direct maintenance cost to form the total plant maintenance cost per hour of operation. The total cost of plant maintenance Y could then be modelled by multiple regression analysis (Chat® eld and

Qualitative variables Qualitative variables such as whether the plant owner made regular use of the condition based monitoring technique used oil analysis (UOA) (Edwards et al., 1997b), environmental conditions, and whether

70

Edwards et al.

companies manufacture their own components or not, were entered into the regression analysis by allocating dummy variables.

Results of the analysis A stepwise MR procedure was used (NourusÆ is, 1994). The resulting R2 was high at 0.94 signifying that 94% of total variation of machine maintenance cost could be explained by machine weight, type of industry and whether the company utilized UOA regularly or not (Table 4). The ® nal model was of the form: Y = ± 7.070 434 + 0.205 169 (machine weight) + 7.949 102 (where opencast coal is excavated) + 4.167 105 (if used oil analysis is not used regularly) Table 3

Variables initially used for regression analysis

Variable

Unit of measurement

Flywheel power Operating weight Bucket capacity (heaped) Rated engine No. of cylinders Bore Stroke Displacement Max implement hydraulic pump output at rated RPM Maximum (lo-single) drawbar pull Maximum (hi) drawbar pull Maximum travel speed (lo-single) Maximum travel speed (hi) Track shoe width Overall track length Undercarriage ground contact Track gauge Fuel tank capacity Hydraulic system Purchase price

kW kg m3 RPM No. mm mm L

Machine age Cycle time

L/min kN kN km/h km/h mm mm m2 mm L L £ (UK £ sterling August 1997) h sec

Qualitative variables Operator ability Machine manufacturer Whether the company manufacturers its own components or not Company of ownership Old or new model Front shovel or backhoe Type of ground condition

where the latter two dummy variables add to the constant coef® cient. For example, if a machine operates in opencast coal mining, an extra 7.94 would be added to the ± 7.07 constant. The constant is negative in this instance because of the nature of the sample composition, that is, machines above 16 tonnes when multiplied by relevant regression coef® cients ensure that the cost calculated is positive. Such a model would not be appropriate when applied, therefore, to machines