This document presents a novel approach for maintenance planning that considers grouping strategies and human factors. The proposed approach models various steps from system configuration to maintenance plan review. It incorporates work complexity and pays special attention to how human factors during maintenance planning can impact error. Fatigue and time pressure are shown to affect the preferred maintenance plan. The consecutive maintenance grouping approach is then compared to genetic algorithm and simulated annealing approaches on a case study of a petrochemical plant in Iran. The results show that while consecutive maintenance grouping cannot handle variable setup costs and work complexity from a theoretical standpoint, it can be used to generate initial solutions for metaheuristic algorithms to improve final solution quality.

1. Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409
Contents lists available at ScienceDirect
Process Safety and Environmental Protection
journal homepage: www.elsevier.com/locate/psep
An integrated approach for maintenance planning
by considering human factors: Application to a
petrochemical plant
M. Sheikhalishahia,b
, L. Pintelonb
, A. Azadeha,∗
a School of Industrial Engineering and Center of Excellence for Intelligent-Based Experimental Mechanic, College of
Engineering, University of Tehran, Tehran, Iran
b Department of Mechanical Engineering, Centre for Industrial Management/Traffic and Infrastructure, KU Leuven,
Celestijnenlaan 300A, BE-3001 Heverlee, Belgium
a r t i c l e i n f o
Article history:
Received 15 March 2016
Received in revised form 6 February
2017
Accepted 11 April 2017
Available online 20 April 2017
Keywords:
Maintenance planning
Human factors
Dynamic grouping strategy
Multi-component system
Genetic algorithm
Simulated annealing
a b s t r a c t
In this paper a novel approach is presented for maintenance planning by considering group-
ing strategy and human factors. The proposed approach describes various steps from system
configuration to maintenance plan review. In previous studies, it has been shown that group-
ing maintenance activities would reduce total maintenance cost by saving set-up costs. In
order to model a more realistic situation, work complexity is incorporated to the model.
Also, a special attention is paid to human factors during maintenance planning to investi-
gate whether human error would be increased by performing various activities at the same
period. It is shown fatigue and time pressure have impact on the preferred maintenance
plan. Consecutive maintenance grouping approach is compared with two well-known meta-
heuristic algorithms including genetic algorithm and simulated annealing. In order to show
the applicability of the proposed approach a petrochemical plant in Iran is selected as a case
study. According to the results of the case study, however from theoretical point of view,
consecutive maintenance grouping is not capable of handling variable setup cost and work
complexity, it could be used for generating initial solution for meta-heuristic algorithms to
improve the quality of final solution.
© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction
Multi component systems provides various opportunities for improv-
ing maintenance plan (Dekker et al., 1997; Nicolai and Dekker, 2008).
Xia et al., 2008 considered shortest-remaining lifetime-first (SRLF) rule
for joint replacement maintenance problem. Positive and negative
effects of grouping activities for parallel k-out-of-n multi-unit sys-
tems are investigated by Bohlin and Wärja (2012). Van Horenbeek and
Pintelon (2013a) quantified the added value of prognostic information
(RUL) considering different levels of economic, structural and stochas-
tic dependence. Dekker (1995) derived penalty functions which serve
as basic elements to determine optimal combinations of activities in a
∗
Corresponding author at: School of Industrial Engineering and Center of Excellence for Intelligent-Based Experimental Mechanic, College
of Engineering, University of Tehran, Tehran, Iran. Fax: +98 21 82084194.
E-mail address: aazadeh@ur.ac.ir (A. Azadeh).
maintenance plan. Wildeman et al. (1997) proposed a rolling-horizon
approach that takes a long-term tentative plan that yields a dynamic
grouping policy that assists the maintenance manager in his planning
job.
Another version of grouping strategy is opportunistic maintenance.
Jia (2010) focused on the opportunistic maintenance of an asset with
multiple nonidentical life-limited components. Cui and Li (2006) con-
sidered a multi-component cumulative damage shock model with
stochastically dependent components. A component fails when its
cumulative damage exceeds a given threshold, and any such a fail-
ure creates a maintenance opportunity. Ding and Tian (2012) developed
opportunistic maintenance policies by the component’s age threshold
http://dx.doi.org/10.1016/j.psep.2017.04.016
0957-5820/© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

2. Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409 401
Nomenclature
i Component
C
p
i
Preventive maintenance cost of component i
Cc
i
Corrective maintenance cost of component i
di Preventive maintenance duration
i(x) Long-term average cost of component i
x∗
i
Optimal maintenance interval for component i
˜x∗
i
Optimal maintenance interval for component i,
when maintenance duration is negligible
ti1 The first tentative maintenance execution time
of component i
tij jth occurrence of maintenance activity for com-
ponent i
te
i
Operational time elapsed from the last preven-
tive maintenance of component i
t∗
Gk
Optimal maintenance time for group k
t Shift from the optimal time
Q(Gk) Set-up cost reduction due to group k
i
Di Cumulative maintenance durations before the
execution of component i
hS
i
( t) Penalty function for short term shift
hE
i
(Gk) Human error penalty function of group k
Pil Cost increment percentage of activity i for being
in the lth position of the group
Yil 1, if activity i is scheduled in the lth position of
a group; 0, otherwise
S Fixed set-up cost
Si Set-up cost of component i
D Total maintenance duration in the planning
horizon
In Cost-effective maintenance interval
values, and different imperfect maintenance thresholds are introduced
for failure turbines and working turbines. Hu et al. (2012) proposed a
novel opportunistic predictive maintenance-decision (OPM) to find the
optimal maintenance time with minimal cost and safety constrains. Do
Van et al. (2013) proposed a new algorithm to optimally update online
the grouped maintenance planning by taking into account the main-
tenance opportunities. Patriksson et al. (2012) studied the stochastic
opportunistic replacement problem, which is a more general setting in
which component lives are allowed to be stochastic.
Human factors play an important role in product life cycle phases
including design, installation, production and maintenance. Various
aspects of human factors in maintenance have been investigated.
Hobbs (2004) mentioned that in comparison to other threats to the
safety, the mistakes of maintenance personnel have the potential to
remain latent. Reason and Hobbs (2003) reviewed the types of error
and violation and the conditions that provoke them. Krulak (2004)
identified inadequate supervision, attention/memory errors, and judg-
ment/decision errors as the most important factors in 1016 aircraft
mishaps. Dhillon (2007) identified several aspects of human factors and
reasons for the occurrence of human error in aircraft maintenance.
Hackworth et al. (2007) identified use of event–data reporting, cre-
ation of a fatigue management program, and increased use of data for
error tracking purpose as the best targets of opportunity for improve-
ment. Johnson and Hackworth (2008) showed that the first challenge in
maintenance is fatigue. Violations, design, detection, decision-making,
problem-solving behaviors (assumptions), plant design, and organi-
zational communication are identified as the most-frequent factors
lead to the incidents and failures in petroleum industries (Antonovsky,
2010; Antonovsky et al., 2014). Some other aspects of human factor
in maintenance are as follows: human error and reliability calcula-
tion in maintenance environment (Okoh and Haugen, 2014; Wang and
Hwang, 2004; Dhillon and Liu, 2006), situational contexts and factors
(Zhang and Yang, 2006; Abdul Razak et al., 2008; Kim et al., 2009), work-
place and organization condition (Collins and Keeley, 2003; Anderson,
2004; Reiman and Oedewald, 2004; Lind and Nenonen, 2008; Nicholas,
2009), human performance (Cabahug et al., 2004; Edwards et al., 2005),
training (Patankar and Taylor, 2008; Usanmaz, 2011), crew resource
management (Safaei et al., 2008; Martorell et al., 2010; Langer et al.,
2010). Atak and Kingma (2011) investigated safety culture of an aircraft
maintenance organization. They stressed the value of a process view
on organizational development for the analysis of safety culture and
the paradoxical relationship between safety and economic interests.
Gerede (2015) explored the challenges to the successful application of
safety management system (SMS) in aircraft maintenance organiza-
tions. According to the results, key challenge to the performance of
SMS is culture. Okoh (2015) examined how maintenance grouping and
the potential human error can be balanced to reduce the major accident
risk. It is shown that grouping maintenance may reduce the frequency
of exposure of maintenance personnel to major hazard which could
reduce the maintenance-related risk.
Reviewing the literature shows that although human factors in
maintenance have been studied from various viewpoints, human fac-
tors in the area of maintenance scheduling have not received enough
attention. Also, in previous maintenance grouping studies, some sim-
plifying assumptions are considered. For example, identical set up
cost is assumed for different activities. To have a comprehensive
approach, we cover this research gaps by focusing on human factors
in maintenance scheduling in more realistic way. Through a real case
study, the applicability and efficiency of the proposed maintenance
scheduling approach is shown. Ignoring human factors during mainte-
nance grouping could lead to the misleading results that may increase
operational, environmental or human related risks. Also, grouping
maintenance activities minimizes potential risk of maintenance per-
sonnel exposure to the hazardous activities. It should be mentioned,
risk of delaying maintenance activities because of grouping is also con-
sidered as a part of total cost.
This remainder of the paper is organized as follows: in Section 2
various steps of the proposed methodology including analytical model
are presented. In Section 3, three different solving methods including
consecutive grouping structure, simulated annealing and genetic algo-
rithm are proposed. The solving methods are used to find the preferred
solution of mathematical models which are presented in Section 2. The
case study and related computational results are presented in Section
4, and Section 5 is dedicated to conclusion.
2. Methodology
The proposed dynamic maintenance planning approach is
illustrated in Fig. 1. In the proposed approach, the required
data is collected according to the system configuration and
boundary definition. The quality of the final solution is
extremely reliant on the data set (Huo et al., 2005). Sys-
tem configuration and boundary definition specifies type of
data, function of each component, equipment and subsys-
tem, and component dependencies. The next step would be
data mining as well as human factor analysis. Various dis-
tribution functions may be fitted to the data set to detect
the system behavior. Maintenance, failure and human fac-
tors records will be analyzed to model the actual situation. In
order to consider human factors in maintenance planning, the
relationship between human factors and maintenance plan-
ning should be determined, and an appropriate quantification
approach must be applied. According to the previous steps,
maintenance schedule is presented as follows:
- Individual maintenance optimization and construction of
tentative maintenance plan;
- Penalty functions calculation;

3. 402 Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409
Maintenance
Scheduling
Data collection
(Maintenance data, Failure
data, human factors, …)
Data mining
Tentative
maintenance plan
Penalty function
calculation
Individual
optimizationMaintenance grouping:
- Consecutive grouping
- Simulated annealing
- Genetic algorithm
System
configuration
Human factor
analysis
Maintenance
execution
Rolling
horizon
Previous information is
changed
Fig. 1 – The proposed dynamic maintenance planning framework.
- Maintenance activities grouping;
- Updating rolling-horizon.
Dynamic maintenance planning approach is applied in
this paper by considering maintenance grouping (Wildeman
et al., 1997). First, the multi-component maintenance problem
is decomposed into n single-component maintenance opti-
mization models. By considering an age-based replacement
policy, and by assuming that failure behavior of component
i is modeled by a Weibull distribution (with shape parameter
i > 0 and shape parameter ˇi > 1), long-term average cost of
component i can be determined as follows using the renewal
theory (Ross, 1996). Weibull distribution is selected because
of its advantages in failure analysis (Abernethy et al., 1983;
Murthy et al., 2004). It is very flexible and through an appro-
priate choice of parameters and model structure, many types
of failure rate behaviors could be modeled. Also, Weibull distri-
bution could provide reasonably accurate failure analysis and
failure forecasts with extremely small samples (even two or
three failures). Furthermore, by investigating Beta (ˇ) param-
eter, the analyst may determine whether or not scheduled
inspections and overhauls are needed.
i(x) =
C
p
i
+ Cc
i
· (x
⁄ i)
ˇi
x + di
(1)
and optimal interval for preventive maintenance ( ˜x∗
i
) can be
calculated as follows:
˜x∗
i
= i
ˇi
C
p
i
Cc
i
.(ˇi − 1)
(2)
where C
p
i
and Cc
i
are preventive and corrective maintenance
cost of component i, and it is assumed that the maintenance
duration (di) is negligible. A finite planning horizon is defined,
in which the current date is selected as tbegin and tend is cal-
culated as follows:
tend = tj1 + di where tj1 = max ti1
i=1:N
(3)
In this way, all components are preventively maintained at
least once in the horizon, and shifting maintenance actions
forward and backwards in time is possible. The first tentative
maintenance time of component i (ti1 ) is calculated as follows:
ti1 = tbegin − te
i
+ x∗
i +
i
Di (4)
Also, jth occurrence of maintenance activity for component
i is calculated as follows:
tij = t∗
ij−1 +
i
Di + x∗
i (5)
According to the proposed approach, to find the pre-
ferred maintenance plan, maintenance grouping is applied
that brings about various costs and savings. First, a penalty
function can be defined to measure the effect of shifting main-
tenance actions from t∗
i
. The penalty function for the short
term shift t, the shift from the optimal time, is defined as
follows (Wildeman et al., 1997):
hS
i
( t) = Cc
i
x∗
i
+ t
i
ˇi
+ Cc
i
x∗
i
− t
i
ˇi
− 2Cc
i
x∗
i
i
ˇi
−x∗
i < t < x∗
i (6)
It should be noted that the penalty function is strictly con-
vex and symmetric around zero (Wildeman et al., 1997). The
optimal maintenance time t∗
Gk
is calculated as follows:
HGk
(t∗
Gk
) = min
t
⎛
⎝
i ∈ Gk
hS
i
(t)
⎞
⎠ (7)
Another penalty function that is considered in this paper
is human error cost, in which it is assumed by grouping
more activities in a group human error probability would be
increased. The following equation is used to calculate the
penalty function of maintenance grouping due to the human
error:
hE
i (Gk) =
i,l
C
p
i
.Pil.Yil (8)
where Pil is the percentage of cost increment of activity i for
being in the lth position of a group. Also, Yil is a binary variable

4. Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409 403
and is equal to 1 when activity i is scheduled in the lth position
of a group. On the other hand, the execution of a group of
maintenance activities requires only one set-up, that results
in the following saving for group Gk (Wildeman et al., 1997):
Q(Gk) = (|Gk| − 1) × Si (9)
In which, Si is set-up cost of component i. In this paper, it
is assumed that set-cost for all the activities is the same,
because set-up cost due to the production loss is much higher
than component or activity related set-up costs. However, the
proposed meta-heuristic algorithms are capable of handling
variable set-up cost, in order to compare the results with con-
secutive grouping structure, fixed set-up cost is considered.
If the saving Q(Gk) is greater than penalty functions (6) and
(8), the group Gk is cost effective. The objective is to find the
optimal grouping that minimizes total cost over the planning
horizon. Total maintenance costs during planning horizon is
calculated as follows (Wildeman et al., 1997):
TC =
i
tend − D · ∗
i (10)
In which D is total maintenance duration. Noteworthy
to mention, in this paper, safety consequences are not
incorporated directly, however negative shift from optimal
maintenance time may cause operational cost, while positive
shift may lead to the safety consequences, reactive mainte-
nance costs and secondary failure. According to the previous
steps, maintenance schedule is presented. A rolling horizon
is considered in which whenever new information is available
or planning horizon is shifted, the proposed approach would
be re-started. Thus, an adaptive and dynamic maintenance
planning approach is developed. In the following section vari-
ous solving methodologies to find the preferred maintenance
grouping structure are proposed.
3. Solving methodologies
In this section three approaches are presented for main-
tenance grouping. The first one is consecutive grouping
structure proposed by Wildeman et al. (1997). However the
consecutive grouping structure would find the preferred
grouping structure very fast, it has some limitations. First of
all, penalty functions should satisfy predetermined assump-
tions and conditions. Also, human error for all maintenance
activities should be the same. This is only applicable for indus-
tries that maintenance activities are more or less similar.
Another drawback is that it is not possible to incorporate
fatigue into the model. Fatigue is a general effect of work and
leads to the performance deterioration. Industrial or “time-
on-task” fatigue describes accumulated fatigue during the
working shift which affects performance of the operators. Fur-
thermore, for using the consecutive grouping structure, set-up
cost must be the same for all the activities. Thus, in this paper,
two meta-heuristic algorithms including simulated annealing
(SA) and genetic algorithm (GA) are proposed to find the pre-
ferred grouping structure when one or more assumptions of
consecutive grouping structure are violated.
It is noteworthy to mention that SA and GA share the
fundamental assumption that it is likely to find good solu-
tions near already known good solutions instead of randomly
selecting from the whole solution space (Manikas and Cain,
1996; Mann and Smith, 1996). The reasons behind select-
ing these two meta-heuristics are as follows (Busetti, 2003;
Henderson et al., 2003; Solomon et al., 2014; Lin and Hajela,
1991):
- These algorithms are very easy to understand and they prac-
tically do not demand the knowledge of mathematics;
- SA advantages over other local search methods are its flex-
ibility and its ability to approach global optimality;
- SA can deal with highly nonlinear models, chaotic and noisy
data and many constraints, and it can be easily “tuned”;
- SA is quite versatile since it does not rely on any restrictive
properties of the model;
- Since the genetic algorithm execution technique is not
dependent on the error surface, we can solve multi-
dimensional, non-differential, non-continuous, and even
non-parametrical problems;
- Genetic algorithm evolves over time by using crossover and
mutation. Property of evolving over time makes it a good
choice for dynamic rule generation;
- GA is very suitable for discrete design variables;
Noteworthy to mention that the proposed approaches are
implemented in MATLAB and performed on a Core i5 CPU pro-
cessor with a 2.6 GHz and 4 GB of RAM. For meta heuristic
methods, in each instance, fifty independent runs were and
the best one is reported.
3.1. Consecutive grouping
A modified version of grouping strategy could be used to find
the optimal grouping structure. If one of the three proper-
ties including symmetry, congruency and dominance holds for
penalty function, there exists an optimal consecutive group-
ing structure (Wildeman et al., 1997; Van Horenbeek and
Pintelon, 2013b; Do Van et al., 2013). It should be noted that
set-up costs and human error probabilities must be the same
for all the activities. The following theorems may be used to
reduce the number of groups to be considered:
- Cost-effective maintenance interval is defined as In =
tn + t−
n , tn + t+
n , where tn is the tentative maintenance
time of activity n, t−
n and t+
n are the smallest and
largest solution of the equation hn( t) − S = 0, respectively.
For admissible groups, the intersection of intervals Ii,∀i ∈ Gk
is
not empty, and t∗
Gk
is in ∩i ∈ Gk
Ii.
- For being a part of the optimal grouping structure, the group
Gk cannot be split up into two groups with lower costs.
- Backtracking procedure is applied to find the optimal group-
ing structure.
- Two maintenance actions on the same component cannot
be scheduled in the same group.
3.2. Simulated annealing (SA)
Simulated annealing (SA) proposed by Kirkpatrick et al. (1983)
and by Cerny (1985) as a generic probabilistic meta-heuristic
algorithm for the global optimization problem. In order to uti-
lize SA to a specific problem, one must specify the state space,
the neighbor selection method, and simulated annealing
parameters. Various parameters of the proposed SA must be
specified including initial temperature, number of iterations at
a particular temperature, speed of the cooling schedule, maxi-
mum allowable computational time, and maximum allowable

5. 404 Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409
Table 1 – The required input data.
Component ˇi i Si Cip Cic di x∗
ij
tie
∗
i
ti1
C6 3.08 190 102 525 262 0.35 301.4 266.67 2.12 34.7
C5 2.11 229 93 98 49 0.72 333.9 280.60 1.09 53.3
C2 2.22 204 93 228 114 0.82 304.6 250.77 1.24 53.9
C23 2.02 223 110 271 136 0.96 318.1 257.28 1.53 60.8
C34 2.08 196 97 209 104 0.67 283.6 207.09 1.38 76.5
C45 2.19 205 69 75 37 0.64 305.4 222.52 0.54 82.9
C30 2.82 80 254 86 43 0.60 127.2 10.93 17.89 116.2
C18 1.40 186 71 276 138 0.76 159.8 29.68 0.75 130.1
C11 2.70 130 90 902 451 1.26 203.9 72.91 2.11 131.0
C17 3.69 98 69 97 48 0.78 154.4 23.35 1.78 131.0
C7 3.10 134 118 525 262 0.35 213.5 77.83 3.95 135.7
C20 2.04 111 119 98 49 0.72 159.1 16.15 3.52 142.9
C24 1.45 228 68 228 114 0.82 211.6 66.54 0.49 145.1
C37 2.28 130 91 271 136 0.96 196.0 47.28 1.89 148.7
C9 1.32 235 275 209 104 0.67 165.5 15.84 7.12 149.7
C26 3.41 116 66 75 37 0.64 184.1 33.37 1.18 150.7
C50 2.14 166 109 86 43 0.60 244.8 84.16 2.04 160.7
C1 2.80 130 77 276 138 0.76 205.5 42.39 1.48 163.1
C38 1.32 275 214 902 451 1.26 195.1 31.45 4.43 163.7
C19 2.21 127 76 97 48 0.78 190.2 24.73 1.18 165.5
C14 1.91 136 119 525 262 0.35 185.5 19.61 2.86 165.9
C32 2.11 183 120 98 49 0.72 266.2 97.61 2.20 168.6
C29 2.00 131 77 228 114 0.82 185.3 16.49 1.17 168.8
C41 2.51 160 112 271 136 0.96 248.8 78.75 2.50 170.0
C12 1.91 187 68 209 104 0.67 256.4 82.91 0.53 173.5
C31 1.78 147 90 75 37 0.64 188.6 14.83 1.51 173.7
C35 2.07 142 78 86 43 0.60 205.0 28.31 1.15 176.7
C15 2.12 157 90 276 138 0.76 229.5 51.72 1.48 177.8
C10 1.69 196 107 902 451 1.26 237.5 54.25 1.62 183.2
C25 2.69 153 260 97 48 0.78 241.1 57.76 9.33 183.3
C21 3.10 121 104 525 262 0.35 191.9 4.76 3.45 187.2
C13 1.86 213 137 98 49 0.72 284.9 94.17 2.26 190.8
C46 3.11 198 84 228 114 0.82 314.4 116.37 1.35 198.0
C43 2.76 134 124 271 136 0.96 212.1 13.56 3.83 198.5
C42 3.17 148 123 209 104 0.67 235.4 34.16 3.89 201.2
C27 2.77 144 70 75 37 0.64 226.7 25.05 0.98 201.6
C4 2.26 156 199 86 43 0.60 234.6 28.67 5.73 206.0
C8 1.78 176 95 276 138 0.76 225.1 18.16 1.43 206.9
C48 2.99 159 122 902 451 1.26 252.9 45.13 3.37 207.8
C39 2.15 172 92 97 48 0.78 253.0 38.39 1.44 214.6
C22 2.12 168 72 525 262 0.35 245.7 26.22 0.75 219.4
C44 2.05 208 103 98 49 0.72 299.3 77.33 1.45 222.0
C36 2.66 173 111 228 114 0.82 271.8 41.60 2.39 230.2
C28 1.70 241 122 271 136 0.96 292.5 52.91 1.66 239.6
C49 1.51 262 254 75 37 0.64 266.5 18.26 2.98 248.3
C33 2.00 205 181 86 43 0.60 290.3 33.42 0.67 256.9
C47 2.51 180 74 276 138 0.76 279.5 8.57 2.04 270.9
C40 2.84 179 107 902 451 1.26 283.8 11.32 2.71 272.5
C16 2.73 183 118 97 48 0.78 288.3 8.55 1.97 279.8
C3 2.39 215 102 209 104 0.67 329.3 4.22 0.70 325.1
2 1 4 3 5 6 8 7
Fig. 2 – An example of solution representation.
number of temperature reductions when the objective func-
tion is not improved. These choices have significant impacts
on the SA’s effectiveness.
3.2.1. Solution representation
A string of numbers consisting N cells representing mainte-
nance activities, which are randomly divided into k (k = 1,. . .,N)
groups.
A sample solution is shown in Fig. 2 in which five first
activities are grouped together, and three other activities are
grouped in another group. Also, in the first group, activity 2 is
performed first, then activity 1 will be performed, and so on.
3.2.2. Neighborhood
Three types of moves including swap, insertion, and inversion
are used to find a new feasible solution from neighboring solu-
tions of the current solution. The swap randomly selects two
cells and exchanges their positions. The insertion randomly
selects a cell and inserts it into the position immediately
before another randomly selected cell. The inversion ran-
domly selects two cells, and then reverses the sequence
between them.

6. Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409 405
Table 2 – Time to the next failure vs. task number.
Task number 1 2 3 4 5 6 7 8 9 10
Percentage of expected TTF 100 97.3 93.4 87.2 80.9 74.0 70.4 68.7 66.3 65.2
3.3. Genetic algorithm
GAs are known as effective and robust methods, capable of
solving wide range of problems. The proposed genetic algo-
rithm steps are as follows:
3.3.1. Population size
The number of chromosomes in a generation will direct the
time for result an optimal solution to a given problem. Previous
studies show that moderate-size populations are best suited
for many practical problems (Rodrigo, 2007). In this study, pop-
ulation size (npop) is changed between 30 and 50 for various
cases according to the problem size. Initial set of solutions is
created in two ways:
I. Using consecutive grouping proposed by Wildeman et al.
(1997). However, consecutive grouping is only optimal in
some situations, it presents a good solution and may
improve the convergence speed of GA;
II. Generating npop−1 random solutions, by putting mainte-
nance activities into k (k = 1,. . .,N) groups.
3.3.2. Representation
Similar to the SA, each chromosome in the proposed GA con-
sist of N cells representing N maintenance activities, which
are randomly divided into k (k = 1,. . .,N) groups.
3.3.3. Fitness function
Fitness function is total saving that should be maximized and
is the difference between total saving (Eq. (9)) and total penalty
(Eqs. (6) and (8)).
3.3.4. Selection, crossover and mutation
In order to determine which individuals are selected for
crossover and mutation, a tournament selection is imple-
mented. A random subset of the whole population is first
chosen. The size of the subset is referred to as tournament
size and is used for adjusting the selection pressure. The win-
ner of each tournament (the one with lowest rank) is then
selected. We will cover the most common type roulette wheel
selection. Crossover is applied on two selected individuals and
combines their information to generate new offspring. Single
point crossover and the ordered crossover method (Goldberg,
1989) are used to find the preferred solution. Mutation oper-
ator is applied on randomly selected offspring regarding the
mutation rate. Three points swap is used for mutation opera-
tor.
4. Case study
A petrochemical plant in Iran that produces purified tereph-
thalic acid (PTA) and polyethylene terephthalate (PET) is
applied as a case study to show the applicability of the
proposed approach. 22 operators with average 9 years of expe-
rience perform maintenance tasks in three, eight-hour shifts.
ISO 14224 is used as a reference, and component level of its
taxonomy is selected. A wide range of equipment are available
including vessel, pump, compressors, boiler and heater, drum,
Table 3 – Time to next failure vs. work shift.
Day shift Night shift
Percentage of expected TTF 100% 89.9%
valve, heat exchanger, cooling tower, vacuum pump, etc. Fig. 2
shows a boundary definition for a pump as an example (Fig. 3).
The raw data consisted of maintenance and failure records
during 2013–2015. In order to standardize the data set, all
failure descriptions are analyzed based on “Failure causes
classification” of ISO 14224. Also, “local error-provoking fac-
tor” framework proposed by Reason and Hobbs (2003) is used
to interpret the failure causes. As in the previous step, three
experts analyzed and interpreted the failure records. Table 1
shows the required data for 50 components with ˇi > 1. The
components are sorted according to their first maintenance
execution time (ti1 ).
∗
i
, x∗
ij
and ti1 are obtained using Eqs. (1), (2) and (4), respec-
tively. Two human factors including fatigue and time pressure
are identified to be influenced by maintenance scheduling.
It should be mentioned that other factors such as individual
differences may influence workload (Xie and Salvendy, 2000).
However, in most of the process industries the required data
for detailed human factor analysis is not available. In other
word, it can be seen that by increasing workload, human per-
formance would deteriorate; but a detailed survey is required
to determine the influence of each contributing factor. In this
study, we focused on total number of tasks in each period
which represents aggregate effect of workload. According to
the framework proposed by Reason and Hobbs (2003), work
duration and working at night shifts are the most important
factors that could affect both fatigue and time pressure. Thus,
the data set is analyzed and quantified and the results are
presented in Tables 2 and 3.
Task number in Table 3 shows the sequence of tasks in a
period. For example, when task number is 3, two other tasks
are performed before doing this task in a same period. In other
word, TTF values are calculated when various number of tasks
were performed in a same period, and then TTF values are
compared with their maximum one. The same procedure is
implemented with tasks which were performed at day and
night shifts.
According to the results, for those activities which are
scheduled after one or more activities, average time to failure
is reduced. Also, working at night shift could reduce average
time to failure up to 10.1%.
4.1. Maintenance scheduling
According to the proposed approach maintenance schedule is
presented taking into account the grouping strategy. Table 1
shows the required data as well as optimal interval (x∗
i
) and
first tentative maintenance time (ti1 ) for various components.
In order to be able to compare the consecutive grouping struc-
ture with GA and SA, set up cost and human error are fixed
to 100 and 12.4 for all the activities, which are average set-
up cost and human error from historical data. Fig. 4 shows
the results of the proposed meta-heuristic algorithms against
the consecutive grouping structure. It should be noted that by

7. 406 Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409
Starting system Driver
Control and
monitoring
Lubrication
system
Fuel or electric
power
Miscellaneous
CoolantRemote
instrumentation
Power
Power
Transmission
Pump unit
Inlet Outlet
Boundary
Fig. 3 – Example of boundary diagram for a pump (ISO 14224).
0
500
1000
1500
2000
2500
3000
3500
4000
4500
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54
TotalSaving
No. of Activities
Consecutive Gruping
Proposed GA
Proposed SA
Fig. 4 – Comparing the results of proposed GA and SA with consecutive grouping.
considering fixed set up cost and equal human error for all
the activities, the consecutive maintenance grouping strategy
would present optimal solution.
According to the results, both meta-heuristic algorithms
could find the optimal solutions for the cases with less than 27
components. In other scenarios, results of SA are equal or bet-
ter than results of GA, and average gap for SA and GA are 0.012
and 0.017, respectively. On the other hand, the convergence
time of the proposed GA is less than SA’s one. Time which
is needed to find the preferred solution for GA is bounded
between 30 and 311 s for different cases with 10 and 55 com-
ponents, respectively, and time to find the preferred solution
using SA is varied between 32 and 457 s for the similar case
studies.
In order to show the capabilities of two algorithms to find
the preferred solution, sensitivity analysis is done. Firstly, SA
and GA are used to investigate the impact of human error on
the preferred solution. 50 components are considered and set
up cost is fixed to 100. Maximum human error is calculated as
0.32 based on historical data; but in order to show the effect of
human error on total cost, maximum human error is gradually
reduced to 0.09. According to the results, SA brings about bet-
ter solutions. Also, it is obvious by reducing maximum human
error, total number of scheduled periods would be decreased
(Table 4).
In order to show the advantage of grouping strategy, total
cost saving is calculated by varying set-up cost between 20 and
500, and the results are shown by Fig. 5. It is shown by increas-
ing fixed set-up cost, total cost saving would be increased and
maintenance grouping is more reasonable.
Table 5 shows the results of maintenance grouping by
using consecutive grouping, proposed SA and GA, and mod-
ified SA and GA for 50 components. In modified SA and GA
algorithms, the result of consecutive grouping structure is
used as an initial solution. Variable set-up costs and incon-
stant human errors are considered for different components.
It should be noted for consecutive grouping constant set-up
cost and human error are used to find the solution, and then
the final solution is calculated using variable set-up costs and
inconstant human errors and then it is compared with the
results of other algorithms.
According to the results, the preferred solution is obtained
using modified SA, followed by modified GA. Fig. 6 shows the
structure of the preferred maintenance grouping structure.
According to the results, in the preferred maintenance
plan, which is obtained using modified SA, 5 groups are
formed. The numbers in parenthesis show the order of
performing maintenance activities according to their first ten-
tative maintenance time (ti1 ). It is very interesting that the
preferred maintenance grouping plan is very similar to the

8. Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409 407
Table 4 – Comparing the results of SA and GA.
No of activities Human error Cost saving No of periods
SA GA SA GA
50 (0.02,0.05,0.09,0.13,0.16,0.19,0.25,0.32) 3226.0 3188.4 9 9
50 (0.02,0.05,0.09,0.13,0.16,0.19,0.25) 3257.6 3221.1 8 9
50 (0.02,0.05,0.09,0.13,0.16,0.19) 3319.7 3240.1 8 8
50 (0.02,0.05,0.09,0.13,0.16) 3321.6 3274.4 7 7
50 (0.02,0.05,0.09,0.13) 3377.9 3351.9 6 7
50 (0.02,0.05,0.09) 3545.9 3430.5 6 6
0
5000
10000
15000
20000
0 50 100 150 200 250 300 350 400 450 500
TotalSaving
Set-up cost
SA GA
Fig. 5 – Total cost saving vs. set-up cost.
Table 5 – The results of maintenance grouping by different approach.
Method Saving-grouping Saving-working shift Grouping penalty Human error penalty Total saving
Consecutive 4684 631.1 190.4 1932 3192.7
Proposed GA 3707.1 630.0 178.5 476.6 3682.0
Proposed SA 3784.1 628.5 122.8 529.3 3760.4
Modified GA 4684 627.5 190.4 1353 3768.1
Modified SA 4684 631.6 190.4 1302 3823.2
C23(4), C6(1),
C34(5), C5(2),
C2(3), C45(6)
C30(7), C7(1),
C11(9), C18(8),
C17(10)
12147 159
C9(15),C38(19),
C32(22),C20(12),
C14(21), C41(24),
C50(17),C37(14),
C31(26),C35(27),
C1(18),C29(23),
C19(20),C24(13),
C12(25),C26(16)
C25(30),C4(37),
C13(32),C43(34),
C42(35), C48(39),
C10(29),C21(31),
C8(38),C39(40),
C15(28),C46(33),
C22(41),C27(36),
C44(42)
C30(45),C49(46),
C28(44),C40(49),
C36(43),C47(48),
C16(50),C33(47)
2461960
t
Fig. 6 – The preferred maintenance grouping structure.
consecutive maintenance structure, in which only the order
of performing maintenance activities is changed. In other
words, maintenance activities in each group is similar to the
consecutive maintenance plan, while the order of perform-
ing maintenance activities is revised, so that maintenance
activities are sorted from activity with highest human error
to the lowest one in each group. The reason is that accord-
ing to the dataset and because of the fatigue, human error
probability would be increased after performing more than
two activities in a row. It is also interesting that for other
cases and for various number of components, the preferred
maintenance grouping structure consists of the same groups
as consecutive maintenance plan. Thus, an integrated SA-
consecutive maintenance grouping approach presents better
solutions comparing to the other methods.

9. 408 Process Safety and Environmental Protection 1 0 9 ( 2 0 1 7 ) 400–409
5. Conclusion
In this paper, maintenance planning approach is proposed by
considering maintenance grouping and taking into account
human factors. The proposed approach consists of various
steps from boundary definition to maintenance execution.
Two meta-heuristic algorithms including simulated annealing
and genetic algorithm are proposed and applicability of them
is verified by consecutive maintenance grouping strategy. It is
shown when assumptions of consecutive strategy are violated,
the proposed SA and GA could find the preferred solution with
small gap. In this work, human factors during maintenance
planning have been received special attention. According to
the literature, grouping maintenance activities would reduce
total maintenance cost by reducing set-up costs. In this paper,
it is proved that human error would be increased by preform-
ing various activities at the same period. In order to show
the applicability of the proposed approach a petrochemical
plant is selected as a case study. Two human factors includ-
ing time pressure and fatigue are identified and quantified
through data mining. According to the results, the proposed
meta-heuristic algorithms could find the optimal solution for
small and medium size problems. Also, for large size cases, an
integrated SA-consecutive grouping would find the preferred
solution in reasonable time.
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