Management and Administrative Sciences Review
e-ISSN: 2308-1368, p-ISSN: 2310-872X
Volume: 3, Issue: 7, Pages: 1174-1191 (November 2014)
© Academy of Business & Scientific Research
www.absronline.org/journals

Research Paper
Selecting and Ranking the Best Maintenance Strategy Using
Combined Techniques of Factor Analysis (FA), AHP, TOPSIS
Habib Farajpoor-Khanaposhtani1*, Mohsen Shafiei Nikabadi2, and Azim zarei3
1. Master of Operations and Production Management, Industrial Management Department,
Semnan University, Semnan, Iran.
2. Assistant Professor of Industrial Management Department, Semnan University, Semnan, Iran.
3. Assistant Professor of Business Management Department, Semnan University, Semnan, Iran.
Today's maintenance plays a big role in organization's success. This paper proposes a decision
making model for selecting the best maintenance strategy for an oil refinery. The machines are
clustered in three groups after a criticality analysis based on internal procedures of the oil
refinery. The best maintenance strategy must be selected for each group of machines. In this
regard, Factor analysis is applied to reduce the decision sub-criteria, Analytical Hierarchy
Process approach is used for weighting the decision criteria and TOPSIS method is applied for
ranking alternatives for each category of equipment.
Keywords: Maintenance strategy, Ranking, AHP, TOPSIS, Factor Analysis
INTRODUCTION
Today, due to technological development as well
as industrial automation and increase in the
number of industrial machines, the volume of
investments by organizations in physical capitals
and machineries are highly increased (Bevilacqua
& Braglia, 2000). Since manufacturing industries
are facing with hyper competition in today global
situation, it is highly important to have a
production line with high productivity in order to
mitigate the costs (Hong & kamaruddin, 2012). To
achieve and guarantee survival, manufacturing
system should act more efficient, more effective
and more economic and, in this line, they need
proper maintenance. Some companies considered
maintenance as an unavoidable cost source. For
these companies, maintenance has a demolishing
role and is conducted only in emergency
conditions. However, such thinking is no longer
acceptable due to important reasons such as
quality in production, unit security and mitigating
the costs of maintenance unit (between 15% and
75% of total costs depending on industry type)
(Bevilacqua & Braglia, 2000). Types of maintenance
strategies that have the highest applications in
thematic
literature
include:
preventive
maintenance (PM), condition based maintenance
*Corresponding author: Habib Farajpoor - Khanaposhtani
Master of Operations and Production Management,
Industrial Management Department, Semnan University, Semnan, Iran
E-Mail: [email protected].
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(CBM), predictive maintenance (PDM), total
productive maintenance (TPM) and reliability
centered maintenance (RCM). In this vein,
corrective maintenance, preventive maintenance
and condition based maintenance were the most
common approaches in maintenance effective
management (Gandhare & akarte, 2012).
(Bevilacqua & Braglia, 2000). Overall, this strategy
is executable in companies with high margin and
is highly appropriate for trivial equipment or those
ones which can be easily repaired (organization of
the petroleum exporting countries, 2013).
Since decision making and judgment on selecting
maintenance strategies in usually complicated and
unstructured which faced with multiple
limitations and insights, the most important submeasures are identified by 1st and 2nd
confirmatory factor analyses and then maintenance
strategies are rated by using multi-measure
decision making techniques such as AHP and
TOPSIS. In present study, it is attempted to help
managers to improve decision making process to
select proper maintenance strategies by combining
suitable tools. To this end, a decision making
structure is provided to select the best
maintenance strategies by using relevant literature
and tools.
It is also called reliability centered maintenance
and scheduled maintenance strategy. Preventive
maintenance is to use planned visits, regulating,
repairing and replacing in equipment or factory.
Preventive maintenance makes it possible to plan
and schedule repairing works without any stop in
production planning and improving equipment
accessibility. The main activities in preventive
maintenance include regular visits, preventive
replacements and assessments (Shyjith et al, 2008).
Concerning above points, present paper attempts
to answer the main question of the research
namely what are proper maintenance strategies in
studied industry and how they can be selected and
rated by considering organizational goals as well
as limitations and criteria which should be
considered by organizational decision makers in
selection process.
MAINTENANCE STRATEGIES
Corrective maintenance (CM)
It is also called as maintenance based on error,
disabling maintenance or use-to-out of order
maintenance. It is the main maintenance strategy
used in industry (Waeyenbergh & Pintelon, 2002).
In this strategy, the equipment is allowed to be
faced with error before repair. The main attribute
of corrective maintenance is that maintenance
activities are performed when the machine is
broken and no maintenance is done before error
Preventive Maintenance (PM)
Condition based maintenance (CBM)
In this strategy, maintenance decisions are made
by measured data. The necessity to execute CBM is
the existence of a system to gather data and a set of
devices to monitor the performance of the machine
during running. By continuous monitor on
machine working conditions, one can easily
determine abnormal conditions and can make
necessary controls timely and, if necessary, can
stop the machine before any error (Bevilacqua &
Braglia, 2000).
Predictive maintenance (PDM)
It is a planned approach on maintenance which
prevents errors or breaking the equipment.
Continuous monitor on real conditions of
equipment by non-destructive tests are conducted
during services and they show the health of
serviced equipment (Sharma et al, 2011). Basically,
this approach attempts to predict deficiencies by
different approaches and, on this basis, it proposes
a corrective performance it uses CMB techniques.
However, in contrary to CBM, needed controlling
data is analyzed to find possible time trend in PM.
In this way, one can prevent when controlled
quantity would exceed a threshold or would
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achieve a determined level. So, maintenance staff
will be able to plan replacement or revision based
on such conditions (Ghandhary & Akarte, 2012).
Therefore, the aim of this approach is to prevent
errors which my pose heavy costs and even
security threats. This maintenance strategy is
proper to achieve safety and it increases
production process accessibility (Sharma et al,
2011).
Total Productivity maintenance (TPM)
The main aim of TPM is to maximize effectiveness
of equipment and their productivity (Nakajima,
1988) and to eliminate of machinery wastes, to
create the feeling of equipment ownership among
users through training programs and their
involvement and to disseminate continuous
improvement through the activities by small
groups
including
production
employees,
engineering and maintenance. Any organization
has its own and unique definition on TPM
(Campbell & Picknel, 1995). In most cases, there
are joint elements including asset strategy,
empowerment, planning, resource schedule,
systems
and
procedures,
measurements,
continuous improvement teams and processes
(Ghandhary and Akarte, 2012). This strategy
combines maintenance principles and quality
through daily inspections by trained users in order
to eliminate main wastes due to stops. Its
successful execution needs high level of
employees’ contribution. Also, TPM successful
implementation requires organizational culture
change which is time-consuming and may be
failed (Sharma et al, 2005). TPM principles
(Mobley, Higgins & Wikoff, 2008) include:
autonomous maintenance, planned maintenance,
maintenance mitigation, equipment efficiency
promotion, equipment accessibility increase,
performance efficiency advancement and quality
improvement.
Reliability centered maintenance (RCM)
This strategy is defined by Moubray (1997) and is a
way which determines the requirements to assure
that equipment would meet expected function. The
main goal of RCM strategy is to increase machine
accessible time and to improve its reliability level
instead of returning it to ideal situation (Sharma et
al, 2005). RCM relates to designing and inherent
reliability parameter of the machine. For any
performance, related functional errors are defined
and their impacts are analyzed (Sharma et al,
2011). RCM provides a way to keep full
performance and by balancing high costs of
corrective and preventive maintenance, RCM is
designed to minimize maintenance costs (Hong&
kamaruddin, 2012).
Opportunistic maintenance (OM)
The possibility of using OM is determined by the
proximity of replacing different components of a
machine or factory. This kind of maintenance
needs to stop total factory to do all maintenance
activities in one time (Bevilacqua & Braglia, 2000).
In industry, it is also called Turn around
Maintenance,
Shutdown
Maintenance
or
Overhaul.
MEASURES
STRATEGY
TO
SELECT
MAINTENANCE
By reviewing the literature and using the opinion
of maintenance experts, four main factors were
selected in decision making on selecting
maintenance strategy as main measures: cost,
added – value, safety, execution.
Below, by reviewing the literature (Zaeri et al,
2007; Wang, Chu & Wu, 2007; Zaim et al, 2012) and
using the opinions of maintenance scholars, all
possible sub-measures for each main measure
were identified. Totally, 37 sub-measures were
identifies: 12 for cost, 9 for added – value, 7 for
safety and 9 for execution as shown in table 1.
TABLE 1 HERE
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For proper decision making which can respond
organizational needs, it is vital to regard
mentioned measures.
METHODOLOGY
Here, we summarily address to factor analysis
(FA), AHP and TOPSIS.
Factor analysis (FA)
Factor analysis is the general name for a group of
statistical methods. The main aim of factor analysis
is to decrease the number of variables and to the
aspects of variables matrix through the structure of
hidden relations among variables and providing a
set of common factors which is an effective method
(Lattin,Carrol & Green, 2003). The concept of
hidden factors was coined by Galton (1988) and
then it was developed by Garnett. FA analysis data
dependent structure and summarizes many factors
in few ones while the lowest data losing happens.
Each variable is impacted by lower factors. The
impact of certain factor on one variable may be
higher than other ones. Such impact is determined
by correlation power (Fruchter, 1954). This tool
helps authors to describe their model by lower
variables rather than being involved in all
variables. Factor analysis is used as exploratory or
confirmatory methods. In explorative method, the
author has no background on hidden structure of
variables and his aim is to analyze the exploration
of possible existing structure. Confirmatory
method is used when the author imagines the
structure and relationship among variables and
conducts such analysis to test respective structure
(Thompson, 2004). In present paper, we use 1st
and 2nd order confirmation factor analysis.
Analytical Hierarchy Process (AHP)
Saaty first introduced AHP method in 1980. When
you it is needed to consider both quantitative and
qualitative aspects simultaneously. AHP is a
powerful tool for Multi-variant decision-making
that transform complex issues to multi-level
hierarchical structure and displays relationships
among the main objectives, criteria, sub criteria
and solutions. AHP helps analysts to transform
critical aspects of a problem into a hierarchical
structure similar to a decision tree and by reducing
complex decisions to a series of simple
comparisons and rankings and combining the
results, helps analysts to make the best possible
decision by a clear logic. AHP method is
appropriate to solve the problems with multiple
criteria for evaluating them. By applying the AHP
all non-quantitative assessments can be mixed
with quantitative assessments in a combined entity
Ranking. AHP is one of the most widely used
MADM methods and this fact is probably due to
some AHP important characteristics (Madu &
kuei, 1994 . shyjith et al , 2008 ) , such as :
1. judgment of decision makers can be accurately
assessed 2. AHP does not make decision itself but
help analysts deciding makers to make decision 3.
AHP helps analysts to transform criteria and subcriteria of an issue into a hierarchical structure
similar to a decision tree 4. Paired comparisons
make it possible to instead numeral weighing of
criteria, the weight of criteria and options values
obtained by comparing matrices 5. sensitivity
analysis is possible 6. integrates quantitative and
qualitative information 7. supported with different
software.
The steps of Analytic Hierarchy Process
In summary, using AHP has sequential steps,
which are described below (Hshiung et al, 2011):
1 Create a hierarchy structure.
2 Making paired comparisons.
3 Set priorities.
4 Assess logical inconsistent of the judgment
matrix.
Create a hierarchical structure
For hierarchical analysis, the issue should be
transformed to a hierarchy of multiple levels. At
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this stage the relationship of the element of
decision-making in hierarchical structures on
different levels, is organized. Elements of decisionmaking are including decision criteria and the
options. The highest level is representing the main
purpose of decision making. Intermediate levels
are indicating the criteria and sub-criteria of
decision making issue. In addition, at the lowest
level or last level there are desired options.
Making Paired comparisons
The proportional importance or priority of the
criteria to each other is evaluated in this step. Then
each option with respect to the criteria are assessed
relatively to other options. Weighting the criteria,
sub- criteria and alternatives according to their
importance relative to the current element is
performed at a higher level to gain weight and
arrangement, the AHP method uses simple paired
comparisons to Decision-makers be able to focus
only on two factors at one time. For example, one
of the questions that may arise during the paired
comparisons is:
How important is Selecting of maintenance
strategies with respect to the ability to perform
maintenance and repairs and maintenance
strategies.
The answer may be "fairly important", "slightly
more important" or others.
A verbal answer is become quantitative, and using
9-point Likert scale was converted into a numerical
score. At the end of this step the matrices will be
obtained that indicate of paired comparisons.
Almost all calculations steps of the analytic
hierarchy process are based on the initial judge of
the decision maker. That appears in the form of the
paired comparisons matrix. Number of matrices
depends on the number of elements in each level.
The questionnaire used for the analysis of
hierarchical and multi-criteria decision making
analysis known as the expert questionnaire. For
Expert questionnaire, the paired comparisons are
used. For each level of the hierarchy, an expert
questionnaire is prepared. The nine measures scale
used to rate. In Table 2 kinds of evaluation of
criteria of are shown.
TABLE 2 HERE
If C = {Cj │ j = 1,2, ..., n} is the set of criteria, the
result of Paired comparisons between the n
criteria, forms the A (n×n) Judgment matrix.
Each elements of the judgment matrix are criteria
weights. aij means of the relative weight of the
criteria i than j-th criteria.
a11
a 21
A=[⋯
a n1
aij =
a12
a 22
⋯
a n2
… a1n
… a 2n
⋯ ⋯]
⋯ a nn
i , j = 1,2, … , n Equation 1
1
, ∀i, j
aji
aji = 1
Equation 2
∀i
Equation 3
Set priorities
After all the comparisons and consists of all
matrices, the relative weight of each element
multiplied in the weight of the higher elements to
obtain the final weight. Eigenvectors, the relative
weight and the maximum eigenvalue for each
matrix is calculated. By doing this step, the final
weight values obtained for each option. Finally,
the choices are prioritized.
Review logical
judgment
inconsistent
of
the
matrix
Since the AHP method is based on the judgment of
the decision makers, any errors or inconsistencies
in the comparison and identification of options
and criteria flawed final calculations’ result.
Priorities with help of eigenvectors (w)
corresponding to the largest eigenvalue (λmax) is
obtained according to Equation 4:
𝐴𝑤 = 𝜆𝑚𝑎𝑥 𝑤
Equation 4
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When the rank of matrix A is equal to one and
λ_max = n (n = number of options), paired
comparisons were quite consistent and in this case,
the weights are acquired with normalizing any of
the rows or columns of a matrix A.
In TOPSIS, the procedure
based on a simple principal
the selected option is the
solution and the farthest
negative ideal solution.
The Incosistency Ratio is a parameter that
determines the consistency of judgment matrix
and show how is possible to the trust done
comparisons.
To
determine
the
logical
inconsistency of the matrix A, the consistency
index (CI) is calculated. The criteria are used for
assessing Inconsistency between judgment of
decision makers at all levels of the hierarchical
structure. Consistency index calculated according
to equation 5.
The positive ideal solution is a combination of the
most important criteria of available values and the
negative ideal solution is the worst values of
available criteria. In following, options are ranked
according the closeness with the ideal solution
(Huang and Yoon, 1981).
𝜆𝑚𝑎𝑥 − 𝑛
(𝑛 − 1)
is different. TOPSIS
and on the idea that
least positive ideal
distance from the
Therefore, an ideal point by increasing of the
number of options or criteria in a group, does not
affect and this property makes TOPSIS method as
an appropriate method.
Equation 5
TOPSIS method has the following steps (Hshiung
et al , 2011 ):
Another parameter called the consistency ratio
(CR) is calculated according to equation 6.
𝐶𝐼
𝐶𝑅 =
Equation 6
𝑅𝐼
Set the options are defined as A = {Ai│i = 1,2, ..., n}
and a set of criteria C = {Cj│ j = 1,2, ..., m}
𝐶𝐼 =
RI is a random index and obtained with the
experimental data (Table 3). If the CR is less than
0.1, results are acceptable and otherwise to reduce
conflicts, judgments must be revised.
Set X = {Xij│ i = 1,2, ..., n; j = 1,2, ..., n} consisting of
function rate and w = {wj│j = 1,2, ..., m} is a set of
weighted criteria .
The information table is defined as I = (A, C, X, W)
(Table 4):
TABLE 3 HERE
The Technique for Order Preferences
Similarity to an Ideal Solution (TOPSIS)
TABLE 4 HERE
by
TOPSIS is given by Yoon & Huang in 1981 (Huang
and Yoon, 1981) and due to its advantages, widely
is used for multi-criteria decision-making issues.
As the AHP method is based on paired
comparisons, by increasing the number of
elements in a group of paired comparisons,
because of Limited human capacity to process data
analysis, decision-making is difficult. The fact that
increasing the number of parameters or options,
calculation time is increased with the complexity,
reducing to a set consists of a maximum of 7
elements in a comparison group is relevant for the
human (Yeh & chang, 2009).
Equation7 calculates the first step in TOPSIS
normalized rating.
𝑟𝑖𝑗 (𝑥) =
𝑥𝑖𝑗
, 𝑖 = 1, … , 𝑚 ‫ = 𝑗 ؛‬1, … , 𝑚 Equation 7
√∑𝑛𝑘=1 𝑥𝑖𝑗2
Then weighted normalized rates are calculated
by Equation 8.
ℎ𝑖𝑗 (𝑥) = 𝑤𝑗 𝑟𝑖𝑗 (𝑥), 𝑖 = 1, … , 𝑛 ‫ = 𝑗؛‬1, … , 𝑚
Equation 8
Furthermore, positive and negative ideal solutions
are identified. Positive ideal solution (A +) as the
best performance of all the options of a criteria
Calculated by Equation 9.
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In contrast to the negative ideal solution (A-) as the
worst of all options of a criteria calculated by
Equation 10 .
One of the crucial issues in oil refinery, is
describing the effect of each component of
equipment downtime that by designing a
appropriate
maintenance
strategy and a
convenient and efficient maintenance. The failure
+
𝐴𝐽
in rating effecting on the amount and quality of
= {(𝑀𝑎𝑥ℎ𝑖𝑗 (𝑥)|𝑗 ∈ 𝐽), (𝑀𝑖𝑛ℎ𝑖𝑗 (𝑥)|𝑗 ∈ 𝐽), 𝑖 = 1,2, … , 𝑛} Equation 9 production, safety and environmental impact
reduced to implement the most appropriate
𝐴𝐽−
= {(𝑀𝑖𝑛ℎ𝑖𝑗 (𝑥)|𝑗 ∈ 𝐽), (𝑀𝑎𝑥ℎ𝑖𝑗 (𝑥)|𝑗 ∈ 𝐽), 𝑖 = 1,2, … , 𝑛} Equation 10 strategy in a refinery, it is necessary to select
appropriate strategy for the same machinery.
Then, after identifying the positive and negative
ideal solutions, the distance of each alternative Since hundreds or thousands of equipment is
from the positive and negative ideal solutions by available in a refinery,
Equation 11 and Equation 12 can be determined as It is classified into different groups and to equip
follows :
each category of equipment the appropriate
maintenance to be determined.
𝑚
+
(ℎ𝑖𝑗 − ℎ𝑗 + )2
, 𝑖 = 1,2, … , 𝑛 Equation 11
(ℎ𝑖𝑗 − ℎ𝑗 − )2
, 𝑖 = 1,2, … , 𝑛 Equation 12
𝐷𝑖 = √(∑
𝑗=1
𝑚
𝐷𝑖 − = √(∑
𝑗=1
That Di + and Di- , respectively, indicate the
distance between the points of options with
respect to all criteria and all positive and negative
measures.
Calculating the relative closeness to the ideal
solution
𝑅𝑖 = 𝐷𝑖 − ⁄(𝐷𝑖 + + 𝐷𝑖 − ) , 𝑖 = 1, … , 𝑛
Equation 13
RI value in TOPSIS method is the ultimate
performance and for all i in Fasalh[ 0,1 ] is located.
The selected option has the highest level of
performance.
The phenomenon of negative ratings on TOPSIS
Most investigators remarked the phenomenon of
negative ratings in MADM methods. This
phenomenon is due to adding unrelated factors
and remove of important measure and causes the
obtained results in this way be incorrect.
Prioritizing of equipment
One way to classify equipment is the use of
importance indicators. As mentioned in the
literature review, braglia and bevilaskua in 2000
used importance indicators to classify equipment
in an Italian refinery. Moreover, it defined three
different groups of devices with different
significance. The importance indicator is definable
with the different methods and formulas.
This index depends on factors such as production,
safety, environmental and related equipment
performance. To determine the significance of any
equipment effecting factors must be identified and
assessed.
For example, a calculation method for CI is the
way that braglia and bevilaskua (2000 ) used to
calculate the importance indicator.
Their used formula is the following:
CI = {(S *1.5) + (LP *2.5) + (MC*2) + (FF*1) +
(DL*1.5) + (OC*1)} * AD
The S is Safety, IP related to process equipment,
MC maintenance costs, FF the error repeat, DL
stoppage time, OC functional requirements, AD
access to the machine. Another example of
clustering methods is using risk priority number
(RPN) that used in the FMEA method.
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RPN is product of three numbers of deterioration
the number of events and the likelihood of errors
that occurs in the equipment concerned. The
number of deterioration the event number and the
probability of detection defined and determined in
accordance with tables and by calculating the Risk
Priority Number for the different equipment, it can
be classified into different categories according to
importance.
Equipment classification in different groups based
on importance, in addition to determining the
appropriate maintenance strategies for each group,
needs another benefit. Revealing the importance of
each equipping it is possible to prioritize functions
and maintenance tasks to be determined for each
group. For example, in the event of a fault in the
equipment that has a key role to the performance
of manufacturing processes, maintenance activities
should be carried out promptly and quickly to
resulting costs be minimal.
Confirmatory Factor Analysis for Sub-measures
To execute CFA, data adaptive to reality is needed
which describes relations among measures. To this
end, a questionnaire was devised and the
information of 171 maintenance elites was
gathered. Upon using CFA on data, the results are
shown in below figure:
Results from analyzing factors and relations
between factors and measures were submitted to a
team of maintenance evaluators including relevant
scholars and elites. Upon defining a general aim as
selecting maintenance strategies, it was attempted
to build an image of a network structure including
measures and sub-measures to achieve the general
aim shown in figure 1. The aim is to select the best
maintenance strategies which include four
measures including cost (C), added – value (A),
security (S) and execution (E). Cost measure
consists of four sub-measures including equipment
cost (COT), raw material and wastes cost (COM),
train and research cost (COA) and software cost
(CON). Added – value involves two sub-measures
including equipment and employees’ return (BAZ)
and profitability (SOD). Security includes two submeasures: equipment and employees’ security
(EMK) and environmental effects (ASM).
Execution consists of three sub-measures including
acceptance by stakeholders (PAZ), complexity
(PIC) and necessary equipment (TAJ). This
networked structure can highly help proper
decision making to select maintenance strategies
by organizations. It is just sufficient that relevant
teams complete paired compared matrices and
select proper strategy. Below, a case study is
expounded.
FIGURE 2 HERE
FIGURE 1 HERE
Since are factors loads are greater than 0.5,
considered construct enjoys necessary validity
(construct validity). Equipment cost, raw material
cost, train and research cost and software costs are
all allotted to cost factor. Studying these measure
indicates that they have cost nature. Equipment
and employees’ return and profitability are
allotted to added – value factor. Environmental
effects and equipment and employees’ security are
allotted to security factor. Acceptance by
stakeholders, complexity and necessary equipment
are allotted to execution factor.
CASE STUDY
Research case study is conducted in Tehran Oil
Refinery. The aim was to resolve decision making
problem in selecting proper maintenance strategy
in an oil refinery by considering used
methodology in current study. Due to difficulties
in gathering relevant data, the number of factors
which should be considered, the amount of factors
subjectivity and high number of refinery
equipment, selecting maintenance strategy was too
complicated. Selected refinery has over 20,000
different
equipment
(pump,
compressor,
electromotor, and others) and the management
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should decide which maintenance approach can be
selected for each equipment. These decisions
would lead into important results. Currently, to do
daily maintenance which is considered as
corrective maintenance, general trend is that
Permit-to-Work (PTW) is issued by operational
unit to do all maintenance works. If it needs to do
maintenance on equipment in workshop, the
operational unit would issue the permit to send
the equipment to workshop. Usually, operational
unit personnel inspect visually all equipment in
each working shift and control them in terms of
sense, temperature and voice of such equipment as
electromotor, pumps and compressors and report
any error to the supervisor of operational unit. He
would ask for maintenance by issuing relevant
permission. Maintenance personnel can ask for
maintenance after inspecting equipment in
scheduled
investigations.
In
this
vein,
management tends to adopt new maintenance
policy with high investments. Considering
mentioned methodology in present paper, the aim
is to select the best strategy among four RCM,
PDM, PM and CM strategies.
Calculation of Weights
To calculate the weight the Expert Choice software
is used. Because the proposed framework to use
AHP is just to determine the weights of criteria
and sub- criteria to each other, in the Expert
Choice software the criteria only used to determine
the weight to be completed. But the AHP analysis
was performed in full and at the end, the AHP
method were compared with the results of the
proposed model. Comparisons and assessments
made by the experts of maintenance collected and
the data entered into the Expert Choice program.
The results of the analysis conducted by the
program determined the weights. The results
obtained for Group 1 weight with the degree of "
low importance" is summarized in Table 5 .
Consistency ratio calculated by the software for
judgment on the group is 0.11, but it was
considered acceptable.
TABLE 5 HERE
The obtained results for equipment Group 2 by the
“average importance”, summarized in Table 6.the
Consistency ratio is 0.07 and less than 0.1 and was
acceptable.
TABLE 6 HERE
The results and weights obtained for 3 with a "high
importance" is summarized in Table 7 . The
obtained results and weights for equipment Group
3 by the “high importance”, summarized in Table
7.the Consistency ratio is 0.07 and less than 0.1 and
was acceptable.
TABLE 7 HERE
The weights of strategies ( options ) with respect to
the selection criteria listed in Table 8.
TABLE 8 HERE
Nevertheless, if at this stage the data into the
software Expert Choice by AHP method to select
the most appropriate maintenance strategy
analysis, we obtained the results in Table 9 and
Table 10.
TABLE 9 & 10 HERE
Evaluation of Maintenance
TOPSIS method
Strategies
with
Table 8 data of weight options (maintenance
strategy) is normalized according to Equation 7,
the results are shown in Table 11.
TABLE 11 HERE
Normalized weight of each sub-criteria calculated
from product of the criteria weights in the original
measure. For Equipment groups 1,2,3 respectively
calculated and presented in Table 12 , Table 13 and
Table 14 has.
TABLE 12 & 13 HERE
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For each group of equipment the normalized
weights of options (maintenance strategy) would
be multiplied in normalized weight of sub-criteria.
The results for equipment groups 1, 2 and 3 got
respectively.
TABLE 15,16 & 17 HERE
In this section, depending on the kind of subcriteria and its impact of the decision making
purpose, positive and negative ideals are
determined. For attributes that have a positive
impact on the issue objective, the positive ideal
will be the maximum amount of that sub-criterion.
For example, the higher safety the desirable .
Therefore, using the proposed model for the
equipment by "low importance", CM strategy is
selected as the best maintenance strategy, for the
equipment by the importance of "medium" and
"high", PDM strategy was chosen as the most
appropriate maintenance strategy.
TABLE 21 HERE
The final rating for each category of equipment
that is presented in Table 21. As can be seen, the
results in Table 21 (results of the proposed
method) with results of Table 10(results obtained
from AHP) are the same.
Likewise, the criteria for which it would have a
negative impact on the objective, the positive ideal,
will be the lowest value of that sub-criterion. For
example, the lower cost the desirable.
CONCLUSION
Maximum and minimum values for normalized
weight multiplied by the normalized weight of
options calculated for each group.
1.
Selecting the criteria: during using AHP or
TOPSIS, improper measures may be considered for
decision making or important measures may be
ignored. Using FA mitigates such possibility.
Positive Ideal for the cost criteria is minimum and
for the rest of the criteria, is maximum and the
negative Ideal for sub-criterion is the maximum
and minimum for the rest. However, because of in
paired comparing time about cost criteria lower
cost is a priority, so, for all of the sub- criteria the
maximum value is a positive ideal and the
minimum is negative ideal.
TABLE 18 HERE
Euclidean distance of each alternative from the
positive ideal and negative ideal distance to any
option, based on the Equation 11 and Equation 12
is calculated that results are shown in Table 19.
TABLE 19 HERE
Then by using Equation 13 to calculate the relative
closeness to the ideal solution for options, we
calculated it for each group. The results are
reported in Table 20.
TABLE 20 HERE
The most important results from combination of three
FA, AHP and TOPSIS techniques are:
2.
Problem structure: multi-measure decision
making methods such as TOPSIS do not create
hierarchical structure. However, one of the
strengths of AHP is to use hierarchy structure.
3.
Weight determination: in AHP, a
systematic method is defined to determine the
weight of measures and options.
4.
Investigating: one of the Weaknesses of
AHP is its limitation in paired comparison of
criteria. In contrast, TOPSIS has no problem with a
large number of criteria and easily ranks the
options.
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1184
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Volume: 3, Issue: 7, Pages: 1174-1191
APPENDIX
Table 1:
Identified affecting measures and sub-measures on maintenance strategy selection
Execution (E)
Safety (S)
Added – value (A)
Cost (C)
1. Acceptance by
management
2. Spare parts
3. Acceptance by staff
4. Acceptance by
shareholders
5. HR capabilities
6. Software
7. Hardware
8.Technological
complexity
9. Practically technical
1. Equipment
2. Environmental
effects &
environmental
damages
3. Personnel safety
4. Social standards
5. Environmental
standards
6. Governance laws
7. Polluting air, land
and water
1. Product quality
2. Equipment &
personnel return
3. Customer
satisfaction
4. Creativity
5. Competitiveness
increase
6. Time productivity
7. ROI
8. Profitability
9. Developing the
experiences of
managers & ngineers
1. Amortization
2. Energy
3. R & D
4. Software
5. Salaries
6. Software
7. Production wastes
8. Training
9. Install &
commission
10. Spare parts
11. Eradicating the
wastes
12.Raw material
Table 2:
AHP method for judging measures of valuation criteria and options relative to each other
Value
1
3
5
7
9
2,4,6,8
Compare i with
respect to j
Same priority
Slightly more
important
More important
Much more
important
Completely more
important
Intermediate
Matrix
measures
3
RI
0/52
Expression
Option or criteria i have same importance to j or priority of them are
the same.
The i option/criteria is Slightly more important than j .
The i option/criteria is more important than j .
The i option/criteria is much more important than j .
The i option/criteria is completely more important than j .
Intermediate values are show, for example 8, indicating more
importance than 7 and less than 9.
Table 3:
RI values for the matrices with different dimensions
4
5
6
7
8
9
10
0/89
1/11
1/25
1/35
1/40
1/45
1/49
11
12
13
1/51
1/54
1/56
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Table 4:
Information on TOPSIS method
Criteria
Options
A1
A2
⋮
An
W
C2
…
Cm
X11
X21
⋮
Xn1
W1
X12
X22
⋮
Xn2
W2
…
…
⋮
…
…
X1m
X2m
⋮
Xnm
Wm
Table 5:
Weight values obtained for the Case Study Group 1
Safety
Cost (C) 0.403
Necessary Equipment (E3)
Environmental impacts (S1)
Safety of personnel and equipment (S2)
Equipment costs (C1)
Raw material costs and losses (C2)
train & research costs(C3)
Software (C4)
profitability (A1)
Efficiency equipment and staff (A2)
Value
added (A)
0.97
Complexity (E2)
(S)
0.299
Acceptance by stakeholders (E1)
The performance
capability (E) 0.202
C1
0/271
0/085
0/644
0/2
0/8
0/656
0/226
0/062
0/056
0/2
0/8
Table 6:
Weight values obtained for Group 2 equipment in case study
Value added (A).
0/144
Cost (C). 0/134
Safety (S).0/545
A2
A1
C4
C3
C2
C1
0/667
0/333
0/078
0/207
0/284
0/431
S2
0/833
The performance capability
(E). 0/177
S1
E3
E2
E1
0/167
0/172
0/068
0/759
Table 7:
Weight values obtained for Group 2 equipment in case study
Value added
Cost (C). 0/060
Safety (S).
The performance
(A). 0/196
0/636
capability (E). 0/109
A2
A1
C4
C3
C2
C1
S2
S1
E3
E2
E1
0/5
0/5 0/102 0/466 0/292 0/139 0/857 0/143 0/142 0/068 0/789
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Table 8:
Calculated weight of options in the case study
A2
CM
PM
PDM
RCM
A1
C4
C3
0/04
0/038
0/667
0/679
0/108
0/13
0/215
0/174
0/509
0/436
0/057
0/343
0/396
0/06
C2
C1
S2
S1
0/6
0/661
0/046
0/039
0/243
0/197
0/146
0/128
0/084
0/091
0/06
0/501
0/062
0/065
0/083
0/308
E3
E2
E1
0/6
0/626
0/091
0/205
0/626
0/226
0/492
0/108
0/097
0/342
0/341
0/087
0/097
0/342
Table 9:
Maintenance Strategies points of AHP method in a case study
CM
PM
PDM
RCM
Group 1
Group2
Group3
0/329
0/132
0/086
0/177
0/163
0/152
0/285
0/410
0/449
0/209
0/294
0/313
Table 10:
Maintenance strategies rated the AHP method in a case study
Group1 Group2 Group3
Rank 1
Rank 2
Rank 3
Rank 4
CM
PDM
PDM
PDM
RCM
RCM
RCM
PM
PM
PM
CM
CM
Table 11:
Normalized weight of options respected to the following sub-criteria in this case
CM
PM
PDM
RCM
A2
A1
C4
C3
C2
C1
S2
S1
E3
E2
E1
0/064
0/063
0/945
0/958
0/913
0/948
0/076
0/064
0/173
0/215
0/305
0/246
0/37
0/283
0/24
0/209
0/924
0/94
0/168
0/316
0/272
0/417
0/815
0/721
0/081
0/119
0/139
0/086
0/824
0/802
0/166
0/146
0/623
0/549
0/655
0/085
0/087
0/099
0/119
0/507
0/556
0/134
0/146
0/632
Table 12:
Normalized weight values obtained for the Case Study Group 1
A2
A1
C4
C3
C2
C1
S2
S1
E3
E2
E1
0/078
0/019
0/023
0/025
0/091
0/264
0/239
0/06
0/13
0/017
0/055
A2
0/096
Table 13:
Normalized weight values obtained for the Case Study Group 2
A1
C4
C3
C2
C1
S2
S1
E3
E2
0/048
0/01
0/028
0/038
0/058
0/454
0/091
0/03
0/012
E1
0/134
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Table 14:
Normalized weight values obtained for the Case Study Group 3
A1
C4
C3
C2
C1
S2
S1
E3
E2
A2
0/098
0/098
0/006
0/028
0/018
0/008
0/545
0/091
0/015
E1
0/007
0/086
Table 15:
Normalized weight of options on the normal weight of sub-criteria: Group 1 of case study
CM
PM
PDM
RCM
A2
A1
C4
C3
C2
C1
S2
S1
E3
E2
E1
0/005
0/001
0/021
0/024
0/083
0/251
0/018
0/013
0/004
0/007
0/006
0/034
0/075
0/057
0/004
0/12
0/016
0/009
0/012
0/041
0/005
0/023
0/063
0/014
0/002
0/003
0/013
0/023
0/197
0/048
0/022
0/003
0/035
0/043
0/013
0/002
0/002
0/009
0/031
0/121
0/033
0/017
0/003
0/035
Table 16:
Normalized weight of options on the normal weight of sub-criteria: Group 2 of case study
CM
PM
PDM
RCM
A2
A1
C4
C3
C2
C1
S2
S1
E3
E2
E1
0/006
0/003
0/00988
0/027
0/035
0/0547
0/034
0/006
0/028
0/011
0/023
0/017
0/01
0/00318
0/007
0/014
0/0163
0/109
0/019
0/01
0/003
0/056
0/078
0/035
0/00084
0/003
0/005
0/005
0/374
0/073
0/005
0/002
0/085
0/053
0/031
0/00089
0/002
0/004
0/0069
0/23
0/051
0/004
0/002
0/085
Table 17:
Normalized weight of options on the normal weight of sub-criteria: Group 3 of case study
CM
PM
PDM
RCM
A2
A1
C4
C3
C2
C1
S2
S1
E3
E2
E1
0/006
0/006
0/00578
0/027
0/016
0/0079
0/041
0/006
0/014
0/007
0/014
0/017
0/021
0/00186
0/007
0/006
0/0024
0/131
0/019
0/005
0/002
0/036
0/08
0/071
0/00049
0/003
0/002
0/0007
0/449
0/073
0/003
0/001
0/054
0/054
0/064
0/00052
0/002
0/002
0/001
0/276
0/051
0/002
0/001
0/054
Negative Ideal Positive Ideal
Table 18:
Determining positive and negative ideal for equipment groups in the Case Study
A2
A1
C4
C3
C2
C1
S2
S1
E3
E2
E1
Group 1
0/063
0/014
0/02133
0/024
0/083
0/2506
0/197
0/048
0/12
0/016
0/035
Group2
0/078
0/035
0/00988
0/027
0/035
0/0547
0/0374
0/073
0/028
0/011
0/085
Group3
Group1
0/08
0/005
0/071
0/001
0/00578
0/00182
0/027
0/002
0/016
0/009
0/0079
0/0227
0/449
0/018
0/073
0/004
0/014
0/017
0/007
0/003
0/054
0/009
Group2
0/006
0/003
0/00084
0/002
0/004
0/005
0/034
0/006
0/004
0/002
0/023
Group3
0/006
0/006
0/00049
0/002
0/002
0/0007
0/041
0/006
0/002
0/001
0/014
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Table 19:
Euclidean distance of each positive option to positive ideal and distance of each option to negative ideal
distance to positive ideal
CM
PM
PDM
RCM
distance to negative ideal
Group 1
Group 2
Group 3
Group 1
Group 2
Group 3
0/195522
0/360742
0/426877
0/262743
0/069092
0/03256
0/252635
0/284992
0/334219
0/076178
0/085628
0/095237
0/260059
0/067789
0/031422
0/195602
0/360747
0/426878
0/267483
0/162909
0/179563
0/117352
0/217202
0/253861
Table 20:
Calculation of the relative closeness to the ideal solution for options in case study
Group 1
CM
PM
PDM
RCM
Group 2
Group 3
0/573342493
0/160741285
0/070869656
0/231675681
0/231041074
0/221762188
0/429270557
0/841812916
0/93143782
0/304941684
0/571418345
0/585710395
Table 21:
Ranking strategies for each category of equipment
Rank1
Rank 2
Rank 3
Rank 4
Group 1
Group 2
Group 3
CM
PDM
PDM
PDM
RCM
RCM
RCM
PM
PM
PM
CM
CM
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Graph 1: measurement model by using 2 nd rank CFA in standard estimation mood
1190
CM
FM
PDM
BAZ = equipment and employees’ return
Cost (C)
SOD = profitability
COT = equipment cost
Security (S)
COM = raw material and waste costs
COA = train and research costs
CON = software cost
Execution (E)
ASM = environmental effects
EMK = equipment and employees’ security
TAJ = necessary equipment
PIC = complexity
PAZ = acceptance by takeholders
Manag. Adm. Sci. Rev.
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Volume: 3, Issue: 7, Pages: 1174-1191
Figure 2:
Hierarchical structures formed for the case study
Prioritizing the measures to select
maintenance strategies
Added value (A)
RCM
1191