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Maintenance Scheduling Optimization in a Multiple Production Line Considering Human Error M. Sheikhalishahi,1,2 A. Azadeh,1 L. Pintelon,2 P. Chemweno,2 and S. F. Ghaderi1 1 School of Industrial Engineering and Center of Excellence for Intelligent-Based Experimental Mechanic, College of Engineering, University of Tehran, Tehran, Iran 2 Department of Mechanical Engineering, Centre for Industrial Management/Traffic and Infrastructure, KU Leuven, Heverlee, Belgium

ABSTRACT An analytical multiobjective maintenance planning model that maximizes reliability while minimizing cost and human error is proposed. In order to incorporate human error, the model minimizes the maximum human error over the planning horizon. Human Error Assessment and Reduction Technique (HEART) is used to quantify the human error. Maintenance activities include adjustment and replacement activities, in which each of them consumes a certain amount of human resource, spare parts, and budget and brings about a specified level of reliability and human error. Economic dependence is also considered, in which grouping maintenance activities reduces total cost. However, this may increase human error probability due to operator fatigue or time pressure. The main purpose is to investigate the relationship between human factors and maintenance activities to find the preferred maintenance plan. A multiple production line is considered as a case study. A sensitivity analysis is performed, and the effects of grouping and human factors on the preferred maintenance plan are discussed. It is shown C 2016 Wiley Periodicals, Inc. how human proficiency may affect reliability and cost. Keywords: Human factors; Maintenance scheduling; Multiple production line; Economic dependence; UGF

1. INTRODUCTION Maintenance includes planned (preventive) and unplanned actions carried out to retain a system at or to restore it to an acceptable operating condition, while optimal maintenance programs aim to provide

Correspondence to: M. Sheikhalishahi, School of Industrial Engineering and Center of Excellence for Intelligent-Based Experimental Mechanic, College of Engineering, University of Tehran, Tehran, Iran. Phone: +98 21 88021067; Fax: +98 21 82084194. Email: [email protected]; [email protected] Received: 11 September 2015; revised 24 May 2016; accepted 1 July 2016 View this article online at wileyonlinelibrary.com/journal/hfm DOI: 10.1002/hfm.20405

optimum system reliability and availability at the lowest possible maintenance cost (Azadeh, Sheikhalishahi, Firoozi, & Khalili, 2013). Two general categories of preventive maintenance activities are adjustment (repair) and replacement. Adjustment activities could change the aging characteristics of components, and if done correctly, ultimately decreases the rate of failure, while after replacement, the components would be as good as new. A preventive maintenance scheduling problem generally tries to find the best sequence of maintenance actions for each component in each period over a planning horizon such that overall cost is minimized subject to a constraint on a reliability, or the reliability of the system is maximized subject to a constraint on budget (Moghaddam, 2008; Sheikhalishahi, Ebrahimipour, & Farahani, 2013; Sheikhalishahi, Ebrahimipour, Shiri, Zaman, & Jeihoonian, 2013).

Human Factors and Ergonomics in Manufacturing & Service Industries 00 (0) 1–12 (2016)

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2016 Wiley Periodicals, Inc.

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Sheikhalishahi, Azadeh, Pintelon, et al.

Maintenance Scheduling Optimization Considering Human Error

Multiobjective maitenance planning has been studied from different viewpoints. Cost, reliability, and availability are among the most important objective functions (Azadeh et al., 2013; Azadeh, Sheikhalishahi, & Monshi, 2015; Sheikhalishahi, Ebrahimipour, & Farahani, 2013; Sheikhalishahi, Ebrahimipour, Shiri, et al., 2013). Kralj and Petrovic (1995) developed a large-scale multiobjective combinatorial optimization model. They considered minimization of total fuel costs, maximization of reliability in terms of expected unserved energy, and minimization of technological concerns as the objective functions. Bris, Chatelet, and Yalaoui (2003) considered cost and availability as the systems criteria in their research. They optimize a model, including cost in the objective function and availability as the constraint by using a genetic algorithm to find the best preventive maintenance schedule. Pereira, Lapa, Mol, and Da Luz (2009) proposed a particle swarm optimization (PSO) approach for preventive maintenance scheduling optimization. They focused on reliability and cost, allowing flexible intervals between maintenance. Scheduling various maintenance activities in one period may reduce setup and downtime costs. However, this means that some maintenance operations are not performed at their individual optimal intervals. Furthermore, by combining maintenance activities, workload and task complexity would be increased (J. Park, Jung, & Ha, 2001). This could increase the human error probability during maintenance due to aspects such as fatigue, workload, task complexity, mental load, and long, continuous working time (Noroozi, Khan, MacKinnon, Amyotte, & Deacon, 2014; Toriizuka, 2001). Thus, the overall reliability of the system would be reduced. Human factors have been considered from different points of view in the maintenance literature. A series of research have incorporated human error in maintenance optimization problems (Wang & Sheu, 2003) and reliability of systems (Agnihotri, Singhal, & Khandelwal, 1992; Dhillon & Yang, 1995); training (Endsley & Robertson, 2000), human recovery factor (Wang & Hwang, 2004), work improvement through performance shaping factors (Toriizuka, 2001), and plant operators’ maintenance proficiency (Cabahug, Edwards, & Nicholas, 2004). Organizational and work psychological factors are also studied in this area (Reiman & Oedewald, 2007). Kiassat, Safaei, and Banjevic (2014) presented a novel method to quantify the effects of human-related factors on the risk 2

of failure in manufacturing industries. They proposed a model that can provide a decision maker with costbenefit analysis that allows him or her to choose among various intervention methods to deal with operatorrelated risk. Several other studies related to this paper have also been performed by Lim and Park (2007); Shirmohammadi, Zhang, and Love (2007); Taboada, Espiritu, and Coit (2008); Tam, Chan, and Price (2006); and Wang and Tsai (2012). Research on human factors in maintenance has mainly focused on human errors calculation models and methods (Aju kumar & Gandhi, 2011; Kim & Park, 2012; More, Tanscheit, Vellasco, Pacheco, & Swarcman, 2007). Comprehensive studies in the area of crew resource management, operator allocation, and personnel recruitment are very rare. Fatigue (Chen & Huang, 2014; H. Park, Kang, & Son, 2012), knowledge and experience (Ruiz, Foguem, & Grabot, 2014; Usanmaz, 2011), and coordination and communication (Langer, Biller, Chang, Huang, & Xiao, 2010; Liang, Lin, Hwang, Wang, & Patterson, 2010) are cited among the most important human factors affecting maintenance. However, their role is relatively new in the area of maintenance planning. Thus, in this paper, we investigate the relationship between human factors and maintenance planning. In order to address human error, the proposed model minimizes the maximum human error over the planning horizon. Human error of each activity is quantified using Human Error Assessment and Reduction Technique (HEART). Hence, by grouping maintenance activities, total human error is calculated for each period. By grouping maintenance activities, the total maintenance cost is decreased (economic dependence). However, this will cause an increase of the human error. Noteworthy to mention, replacement activities consume more resources. and their human errors are higher than adjustment activities; replacement activities would improve overall reliability of the system. Therefore, the proposed model selects the preferred activity for each component in each period. The novelty of this research could be summarized as follows: First, a novel multiobjective maintenance planning is proposed by considering human error in addition to cost and reliability as objective functions. Incorporating human error in a maintenance planning problem is a relatively new approach. Second, a multiple production line, which has not received enough attention in the literature, is considered (Ebrahimipour, Najjarbashi, & Sheikhalishahi, 2015), and time

Human Factors and Ergonomics in Manufacturing & Service Industries

DOI: 10.1002/hfm


required for maintenance and replacement actions are taken into account. Thus, some aspects of real-world problems are incorporated into the model of preventive maintenance scheduling. Also, HEART methodology is applied, suggesting a straightforward approach toward reducing human error in maintenance through scheduling. The proposed approach provides a framework that supports decision makers to evaluate mitigation measures for tasks with higher human error probability to reduce overall human error. Advantages of using HEART are as follows (Humphreys, 1995; Kirwan, 1996; Kirwan, Kennedy, Taylor-Adams, & Lambert, 1994; Williams, 1986, 1988):

r Very easy and straightforward to apply r Needs a small amount of resource r Provides useful suggestions to reduce the occurrence of errors

r Allows to conduct cost-benefit analyses Applicable in a wide range of areas The remainder of this paper is organized as follows: In Section 2, the problem description and formulation, optimization method, and human error calculation approach are presented. Efficiency of the optimization method is examined thorough solving a case study in Section 3. Concluding remarks and suggestions for future research are presented in Section 4.

2. MODELLING APPROACH A multiple series-parallel production line consisting of N components is considered. The failure rate of the components follows Weibull distribution (λ(t) = βλ(λt)β−1 ) and hence models the degradation in the model (Van Horenbeek & Pintelon, 2013). The proposed model finds the preferred schedule, including adjustment and replacement activities over the planning horizon [0, T]. At the end of period j, the system is either, adjusted, replaced, or no action is taken. Durations of adjustment and replacement activities follow the uniform distribution. The component will be as good as new after replacement; while adjustment reduces the effective age of the component with coefficient α, which is between 0 and 1. Human error is considered in which, by increasing the workload, the probability of human error would be increased. Moreover fixed maintenance setup cost is incorporated into the model to take into account preparation and logistic costs. The general form of a series-parallel system is illustrated in Figure 1. In the following sections,

Figure 1


A binary-state series-parallel system.

mathematical formulation and optimization procedure are declared.

NOMENCLATURE I Component j x time period Pl Set of components in production line l fi (t) Failure rate of component i pi,j (z) Probability mass function of working state for component i in period j ti,j Effective age of component i at the start of period j ti,j Effective age of component i at the end of period j α Age reduction factor of adjustment activities M Human resource required for maintenance activities R Human resource required for replacement H Total available human resource B Maximum budget for replacement activities E[Ni,j ] Expected number of failure for t = ti,ji,j fi (t) component i in period j Ui,j (z) Utility function for component = (pi,j (z))z1 i in period j, where z1 is the + (1 − pi,j (z))z0 state that the component is normal and z0 is the state when the component is failed S1 Number of spare parts required for each adjustment S2 Number of required spare parts for each replacement S Total available spare parts


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dm Duration of each adjustment dr Duration of each replacement mi,j 1, if component i at period j is adjusted, 0, otherwise ri,j 1, if component i at period j is replaced, 0, otherwise Mi Unit cost of adjustment on component i Ri Unit cost of replacement on component i Z Fixed set up cost for maintenance heir Human error probability of replacement on component i m Human error probability of adhei justment on component i

2.1.

Minimize Cost:

N T

+

+

T

N Z 1 − (1 − (mi,j + ri,j ))

j =1

[1]

[⊗ ∅ (u1,j (1), u2,j (1), ..., un,j (1))]

[2]

Minimize Human Error: N Maximum heim mi,j + heir ri,j , ∀j

[3]

j =1

i=1

s.t. ti,1 = 0 i = 1, ..., N

[4]

ti,j = (1 − mi.j −dm )(1 − ri.j −dr )ti,j −1 + mi,j −dm (α.ti,j −dm )

i = 1, ..., N; j = 1, ..., T 4

[8]

N T

(dm .mi,j + dr .ri,j ) ≤ 0.3T

[9]

i=1 j =1 x+max{d m ,dr }

mi,j + ri,j ≤ 1 i = 1, ..., N;

Ri .ri,j ≤ B

[10]

[11]

i=1 j =1

Maximize Reliability:

i

(S1 .mi,j + S2 .ri,j ) ≤ S

i=1 j =1

N T

i=1

T

[7]

x = 1, ..., (T − max{dm , dr })

(Mi .mi,j + Ri .ri,j )

(M.mi,j + R.ri,j ) ≤ H

N T

Fi E[Ni,j ]

i=1 j =1

[6]

i=1 j =1

i=1 j =1 N T

i = 1, ..., N; j = 1, ..., T

j =x

Mathematical Model N T

= ti,j + T J ti,j

[5]

In the above model, three objectives, including cost, reliability, and human error, are considered. In the first objective function, total cost is minimized. The first, second, and third terms are failure cost, adjustment and replacement costs, and setup cost of maintenance activities, respectively. Equation 2 represents reliability function, which has to be maximized using the universal generation function (UGF) method. Equation 3 minimizes the maximum human error probability over planning horizon. It should be noted that human error probabilities are calculated at the first planning horizon, and they will be updated for the next planning horizons according to the most recent human error data. It is assumed that the initial age of each component at the start of a planning period is equal to zero, and this is represented by Equation 4. Effective age of component i at the start of period j is determined using Equation 5. Equation 6 calculates the relation between effective ages at the start and end of each period j. It should be noted that maintenance activities are performed on components at the end of a period. Maximum available manpower, spare part, and downtime threshold are determined by Equations 7, 8, and 9, respectively. Equation 10 ensures that either adjustment or replacement can be performed on a component in each period, and before finishing the current activity,


DOI: 10.1002/hfm


the next activity may not start. Finally, Equation 11 limits the maximum available budget for replacement activities. To calculate reliability of the series-parallel system, the UGF method is used. This method is very effective for high-dimension combinatorial problems (Levitin & Lisnianski, 2000). In this method, the z-transform of each random variable Xi that implies component i in the system, represents its probability mass function (p.m.f.) (xi0 , ..., xik ), (pi0 , ..., pik )in the polynomial

form ui (z) = kji=0 pij zxij , where xij represents the working level of component i in period j, and pij is the corresponding probability. Reliability of component i is equal to the derivative of ui (z) = 1 when z = 1, which indicates its average working level. As discussed earlier, in a binary system, each component has two states: working or failure. Thus, for the u-function of component i and the system, the following equations are applied: ui (z) = p1 z1 + (1 − p1 )z0

minimize f =

m

wi fi (x)

[13]

i=1

subject to x ∈ X m

wi = 1, wi ≥ 0, i = 1, ..., m

i=1

Where x is an n-dimensional vector of design variables, X is the feasible design space, m is the number of design objectives, fi (x) is the objective function for the ith design objective, f(x) is the design objective vector, and wi is the weight of objective i (Tian et al., 2008). It should be noted that the objectives have to be scaled first. To do so, the optimization problem is solved by each objective function separately to find the optimal value of each one. Afterward, by dividing the functions by their optimal values, the weighted-sum method is applied to solve the problem with integrated objective function as follows: + w2 (Z2 /(Z2 ∗ ) + w3 (Z3 /(Z3 ∗ ))

(XN 1 , ..., XN n ))

[14]

[12]

The u-function of variable Xi is ui (z) and the ufunction of the function f(X1 , . . . ,Xn ) is U(z) = ࣹf (u1 (z), u2 (z), . . . , un (z)). For more information about the UGF method and calculation procedure, see Levitin and Lisnianski (2000).

2.2.

sum method takes the following form:

Minimize f = w1 (Z1 /(Z1 ∗ ))

U (z) = ∅ser (∅par (X11 , ..., X1n ), ..., ∅par Rsystem = U (1)


Multiobjective Optimization

In the proposed model, three objectives, including cost, reliability, and human error, are considered. A general multiobjective problem tries to find the best values that optimize a set of objectives (Azadeh et al., 2015; Sheikhalishahi, 2014). However, because of the conflicting nature among different design objectives, it is typically impossible to find the best values for all objectives simultaneously. One of the most widely used methods for multiobjective optimization problems is the weighted-sum method. It converts a multiobjective optimization problem into a single-optimized objective, by using a weighted sum of all the multiobjective functions. The mathematical model of the weighted-

2.3. Human Error Calculation Human reliability assessment approaches could be classified into two categories—those using a database and those using an expert opinion. In the first category, a database of generic error probabilities is applied by the assessor to extrapolate from the generic data to the specific situation being assessed. This manipulation is usually based on the assessor’s assessment of contextrelated Performance Shaping Factors (PSF) (Kirwan, 1996). In this paper, HEART (Williams, 1986, 1988) is applied based on the ergonomics literature. This technique uses a set of basic error probabilities modified by the assessor according to the structured PSF. The following formula is used to calculate the effect of each error producing condition (EPC): Effect of the EPC = ((Max Effect − 1) × Proportion of Effect + 1 Classifying activity, identifying related EPCs and defining the extent of the negative influence for each identified EPC, is based on assessor judgments. Generic


DOI: 10.1002/hfm

5


Figure 2


1, 2, 3, 6, and 7, while Production Line 2 is composed of Components 4, 5, 6, and 7. All components can be adjusted or replaced. Table 1 illustrates problem parameters for each component. Maximum available human resource “H,” spare parts “S,” and replacement budget “B,” are set to 240, 1,100, and 3,700, respectively. In addition, downtime cost “Z” is 500. Table 2 shows the human error probabilities for adjustment and replacement activities. A generic category of tasks, error-producing conditions, and proportion of effects are specified by three independent experts using generic categories of tasks and error-producing conditions and their maximum effects (Williams, 1986, 1988). The experts were experienced maintenance managers from various fields of mechanical, electrical, and industrial engineering, who were introduced to the HEART procedure. Experts’ opinions were gathered independently and in case of any conflicting opinions, the three experts agreed on the final decision through a consensus approach (Dyer & Forman, 1992). The most relevant error-producing conditions were identified as follows:

Series-parallel manufacturing system.

categories of tasks and error-producing conditions and their maximum effects can be found in Williams (1986, 1988). To apply the HEART technique, human error probability for each activity is calculated. Then, the maintenance activities are scheduled so that human error probability over the planning horizon is minimized. In this study, we test the hypothesis that human error would affect maintenance planning, hence it could be considered as a negative economic dependence. The assumptions and modeling decisions are based on insights gained by in-depth analyses of available human error records from industrial data sets and discussions with field experts.

r A shortage of time available for error detection and correction (Code 2)

r No means of conveying spatial and functional information to operators (Code 5)

r Ambiguity in the required standards (Code 11) r Operator inexperience (Code 15)

3. ILLUSTRATIVE EXAMPLES

For example, for adjustment of Components 1 and 2, human error calculation procedure is as follows:

To show the applicability and effectiveness of the proposed model, a manufacturing system, consisting of components in series-parallel structure, is applied as a case study. In the case study, 90 periods are assumed for planning, and each time period represents a day. Figure 2 illustrates the structure of the system that consists of two production lines with seven components (Ebrahimipour et al., 2015). Components 1 and 2 are similar. Production Line 1 is composed of Components

Components 1 and 2: [(8 − 1)∗ 0.7 + 1]∗ [(5 − 1)∗ 0.9 + 1]∗ [(3 − 1)∗ 0.6 + 1]∗ 0.003 = 0.179

3.1.

Computational Results

In this section, computational results are presented. BARON, BONMIN, and DICOPT solvers in GAMS

TABLE 1. Test Problem Parameters Components 1 2 3 4 5 6 7

6

Lambda

Beta

Alpha

F

M

R

hm

hr

dm

dr

Sone

Stwo

0.062 0.062 0.085 0.088 0.084 0.082 0.068

2.2 2.2 2 2.05 1.9 1.75 2.1

0.32 0.32 0.28 0.25 0.2 0.18 0.35

250 250 240 270 210 220 280

35 35 32 65 42 50 38

200 200 210 245 180 205 235

1 1 1 1 1 1 1

1 1 1 1 2 2 2

1 1 2 1 2 1 1

2 2 2 1 2 2 2

4 4 5 6 5 3 3

6 6 8 8 6 5 5


DOI: 10.1002/hfm



TABLE 2. Human Error Probabilities

Component

Generic Category of Task

Nominal Human Unreliability

Error-Producing Conditions (nominal amount)

Proportion of Effect

Human Error Prob.

Adjustment

1 2 3 4 5 6 7

F F E D D E F

0.003 0.003 0.02 0.09 0.09 0.02 0.003

5(8),11(5),15(3) 5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3)

0.7,0.9,0.6 0.7,0.9,0.6 0.9,0.7,0.9,0.6 0.9,0.7,0.9,0.6 0.9,0.7,0.9,0.6 0.9,0.7,0.9,0.6 0.9,0.7,0.9,0.6

0.179 0.179 11.941 53.737 53.737 11.941 1.791

Replacement

1 2 3 4 5 6 7

E E D C C D F

0.02 0.02 0.09 0.16 0.16 0.09 0.003

5(8),11(5),15(3) 5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3) 2(11),5(8),11(5),15(3)

0.9,1,0.9 0.9,1,0.9 0.8,0.9,1,0.9 0.8,0.9,1,0.9 0.8,0.9,1,0.9 0.8,0.9,1,0.9 0.8,0.9,1,0.9

2.044 2.044 82.782 147.168 147.168 82.782 2.75

Also, in order to show the applicability of the proposed model for presenting the preferred maintenance plan, the preferred schedule for a set of weights is shown by Table 4 .

3.2. Sensitivity Analysis

Figure 3 Cost-reliability trade-off for different values of maximum number of tasks in each period.

23.5 are applied to solve the test problem on a PC with Intel core i5 CPU, 2.67-GHz processor, 4-GB memory, and Windows 7 Professional operating system, and the preferred solution with lowest gap is presented. To show the effects of work complexity and human error, the maximum number of tasks that could be assigned in each period is fixed (Figure 3). It is obvious that, by decreasing the maximum number from three to one, total cost is increased; however, in some cases, the reliability is improved. The legend in Figure 3 (from 1 to 3) shows the maximum number of tasks in a period. W1 and W2 are the weights of reliability and cost, respectively. Table 3 shows the results of minimizing the maximum human error probability over the planning horizon. It is shown that increasing the weight of each objective function would improve its value.

To show the effect of human error on the preferred maintenance plan, it is assumed that, because of some modifications, human error probabilities are decreased. These modifications are managerial provisions to provide more time for detection and correction activities as well as to improve the information system. Thus, the proportion of effect of error-producing Factors 2 and 5 are reduced by 0.6 and 0.5 units, respectively. Table 5 shows human error probabilities after the Modifications. Table 6 shows the results after these modifications. It can be easily inferred that, in all situations, the human error probability as well as total value of objective function is improved. However, behavior of cost and reliability objective functions is not completely predictable. In general, after the modification, the cost is improved; however, in some cases, in order to improve the reliability, replacement activities are increased, which leads to the higher cost. Also, in order to show how human error affects the maintenance plan, the preferred schedule for a different set of weights is shown by Table 7. The results of Table could be compared with the results of Table 4.


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TABLE 3. Obtained Results for Minimizing Maximum Human Error Probability Weights

Objective Functions Values

Reliability

Cost

Human Error

Reliability

Cost

Human Error

0.2 0.3 0.6 0.5 0.75

0.75 0.55 0.3 0.2 0.2

0.05 0.15 0.1 0.3 0.05

0.731 0.702 0.718 0.688 0.756

0.959 0.968 0.906 1.000 0.921

1.000 0.365 0.565 0.365 1.000

TABLE 4. Preventive Maintenance (PM) Schedule for Weight Combination 0.75-0.2-0.05 Periods Components 1 2 3 4 5 6 7

16

21

23

25

36

48

58

Adj Adj

Adj Adj Rep

Rep Rep

Adj

Rep

Rep

Adjustment

Replacement

0.072 0.072 1.943 8.743 8.743 1.943 0.291

1.064 1.064 14.36 25.53 25.53 14.36 0.478

According to results, by increasing the weight of the human error objective function, the maximum number of tasks in a period is decreased from five to four. Although the total number of replacement activities is decreased, the total number of adjustments is increased, which leads to lower reliability and higher cost. Also, to show the effects of modifications on the preferred schedule, Table 8 shows the optimal plan after modifications. Because the human error probabilities are reduced, more replacements are planned; hence, cost and reliability values are improved with respect to the previous plan (Table 7). According to the results, reliability and cost values are improved up to 7.2% and 2.3%, respectively. Another factor which affects the optimum plan is the fixed cost of maintenance activities or set-up cost.

61

Rep Rep

Adj Adj

Component

8

45

Adj Adj

TABLE 5. Human Error Probabilities after the Modifications

1 2 3 4 5 6 7

39

63

75

Rep

Rep

Rep Adj Rep

Table 9 shows the effects of fixed set-up cost on the maintenance schedule. According to the results, by increasing the fixed setup cost, the total number of periods in which replacement and adjustment tasks are scheduled are decreased. Also, cost and reliability objectives are deteriorated. The only exception is the reliability function at the fixed cost of 5,000, which is improved compared to the fixed cost of 2,000. This is because, by reviewing the preferred schedule, the total number of replacements is increased for the fixed cost of 5,000. This decision slightly affects the total cost while improving the overall reliability. The behavior of human error at the fixed cost of 5,000 is also interesting. At first, by increasing the fixed setup cost, replacement activities were replaced by adjustment activities to reduce the total cost, which leads to the lower human error. However, at the fixed cost of 2,000, the number of scheduled periods is reduced to four, which increases human error probability. Finally, as mentioned before, for the last scenario, it is better to perform more replacement activities to improve reliability, which significantly affects human error.

3.3.

Discussion

In this section, various experiments are done to investigate the effects of human error on maintenance


DOI: 10.1002/hfm



TABLE 6. Obtained Results for Minimizing the Maximum Human Error Probability after the Modifications Weights

Objective Functions Values

Reliability

Cost

Human Error

Reliability

Cost

Human Error

0.2 0.3 0.6 0.5 0.75

0.75 0.55 0.3 0.2 0.2

0.05 0.15 0.1 0.3 0.05

0.718 0.737 0.760 0.759 0.766

0.936 0.949 0.903 1.000 0.945

0.176 0.173 0.175 0.173 0.189

TABLE 7. Preventive Maintenance (PM) Schedule for Weight Combination 0.5-0.2-0.3 Periods Components 1 2 3 4 5 6 7

17

25 Adj Adj Adj

29

31

32

35

36

48

49

Adj Rep Adj

Adj

Adj

Adj

Adj

58

60

62

Adj Adj Adj

Adj

Adj Adj Adj

Adj Adj

Rep

TABLE 8. PM Schedule for Weight Combination 0.5-0.2-0.3-after Modification Periods Components 1 2 3 4 5 6 7

17

24

26

35

41

Adj Adj Adj

47

Rep

57

60

Rep

Rep

planning. From investigating the effects of human factors on maintenance planning, interesting operational insights could be derived. First, it is shown that, by incorporating human error into the model, the total number of maintenance activities scheduled in a period are reduced. This suggests a novel viewpoint in the area of maintenance planning and grouping, in which mostly positive economic dependence of maintenance grouping is discussed (Dekker, Wildeman, & Duyn Schouten, 1997; Noroozi, Khan, MacKinnon, Amyotte, & Deacon, 2014). Also, it is shown by increasing the weight of the human error objective function, the total number of activities in each period is decreased, or activities with lower probabilities of human error

69

74

Rep Rep

Adj Adj

62

Rep Adj

Adj Rep

Rep Rep

43

Rep

Rep Adj Rep

are selected. This shows that, by ignoring human error in maintenance planning problem, the preferred plan may be misleading. Second, the results show that by performing human factor programs for reducing the human error probability, cost and reliability of the maintenance plan are improved. This helps decision makers to implement cost-benefit analysis to find the preferred human factor program. For example, in the case study, providing more time for detection and correction tasks and improving information systems have improved total objective function, and in most cases, all three objective functions are improved. In various cases, reliability and cost objective function values are improved up to 7.2%


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TABLE 9. The Impact of Fixed Setup Cost on the Preferred Schedule (for 0.6-0.3-0.1 weights) Fixed Setup Cost (Z) 1 100 500 1,000 2,000 5,000

No. of Scheduled Periods

Cost

Reliability

Human Error

16 13 9 7 4 3

0.676 0.742 0.806 0.927 0.972 1.000

0.726 0.724 0.718 0.694 0.661 0.666

0.563 0.563 0.565 0.542 0.561 1.000

Highlighted gray area show the preferred value of the objective functions.

and 2.3%, respectively. However, these effects may differ in various case studies, which suggests that human factor programs could provide effective solutions for improving maintenance plan. Furthermore, sensitivity analysis shows the relationship between setup cost and human error. By increasing setup cost, it is cost effective to decrease total number of scheduled periods, which leads to the higher human error probability. Also, replacement activities are achieved by adjusting ones that have lower human error probabilities. Thus, HEART methodology provides a decision maker with a cost-benefit analysis that allows him or her to choose among various intervention methods to deal with human errors (Kiassat et al., 2014).

optimal maintenance schedule are investigated. The results of this study give an incentive to engage in efforts to reduce human error in industry. The research helps to deepen the insights on the effect of human error on maintenance cost and reliability. In this study, it is supposed that each activity has a certain probability of human error; hence, the correlation between various activities is not incorporated. For future studies, the impact of tasks complexities on each other and nonlinear relationships between fatigue and workload could be investigated.

ACKNOWLEDGMENTS We appreciate the comments of anonymous reviewers, many of which led to improvements in the manuscript.

4. CONCLUSION This paper presented maintenance scheduling problem focusing on two concepts, which are human factors and maintenance grouping. Reliability, cost, and human error are considered as objective functions. HEART is used to quantify human errors based on error-producing conditions. Two types of maintenance activities are also considered: adjustment and replacement activities. Each activity or task has a specific probability of human error. Through extensive experiments, the effect of human error on the preferred maintenance schedule is presented. According to the results, wherever the human error is critical, it is better to perform activities with higher probability of human error in separate periods. Also, reducing the maximum allowable task in each period leads to the higher-cost and lower-reliability values. It is also shown how human factor programs may affect the reliability of the system as well as the maintenance cost. Moreover, the fixed maintenance setup cost’s effects on reliability, cost, and 10

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