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Maintenance policy selection in manufacturing firms

using the fuzzy MCDM approachFelix T.S. Chan

a& Anuj Prakash

a

aDepartment of Industrial and Systems Engineering, The Hong Kong Polytechnic University

Hung Hom, Hong Kong

Version of record first published: 27 Feb 2012.

To cite this article:Felix T.S. Chan & Anuj Prakash (2012): Maintenance policy selection in manufacturing firms using the

fuzzy MCDM approach, International Journal of Production Research, 50:23, 7044-7056

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International Journal of Production Research

Vol. 50, No. 23, 1 December 2012, 70447056

Maintenance policy selection in manufacturing firms using the fuzzy MCDM approach

Felix T.S. Chan*and Anuj Prakash

Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University,Hung Hom, Hong Kong

(Received 15 July 2011; final version received 22 December 2011 )

In manufacturing firms, there is a critical need for proper maintenance of manufacturing facilities. Themaintenance process enhances customer satisfaction and reliability of the products, and increases the profit ofthe manufacturer. Therefore, a proper maintenance policy selection is a critical issue for manufacturers, as aninefficient maintenance policy affects not only the direct cost of the firm but also the other aspects. In thepresent study, maintenance policy selection at the level of the firm rather than the equipment level is shown,and for selection various criteria have been identified. The presented work not only provides the bestalternatives but also provides an alternative ranking, which facilitates decision-makers in choosing alternativesaccording to their constraints. These selection criteria are different in nature, as some give a crisp value,

whereas others are defined in linguistic terms. To select the appropriate maintenance policy, a distance-basedfuzzy multicriteria decision-making (MCDM) approach has been employed. The proposed method providesthe means for integrating the economic figure of merit with the strategic performance variables. The MCDMapproach is efficient in incorporating data, in the form of linguistic variables, triangular fuzzy numbers, andcrisp numbers, into the evaluation process of maintenance policy alternatives. A comprehensive exampleillustrates the application of the distance-based fuzzy MCDM approach.

Keywords: maintenance policy; fuzzy; MCDM; reliability

1. Introduction

Nowadays, market conditions are characterised by the continuous introduction of new products, unforeseen

demand fluctuations, and reduction in the life cycle of products and profit margins. Manufacturers are seeking a

system that can work all the time, but every system needs maintenance. If the manufacturing systems are properly

maintained, they will be more productive (Renna 2011). Maintenance activity can reduce the breakdown rate with

minor sacrifices in production time (Sun and Li 2010). Firms are realising that there is a critical need for proper

maintenance of production facilities and systems (Stephen 2000, Cholasuke et al. 2004, Meulenet al. 2008). The role

and importance of industrial maintenance have increasingly been recognised by decision-makers (Pinjala et al. 2006,

Alsyouf 2007, 2009, Dowlatshahi 2008). Maintenance is a business function that serves and supports the primary

process in an organisation. It is defined as the combination of all technical and associated administrative actions

intended to retain an item in, or restore it to, a state in which it can perform its required function. In manufacturing

environments, maintenance of a machine is defined as all activities necessary to restore the machine to, or keep it in,

a specified operating condition (Batun and Azizog lu 2009). The maintenance process adds to customer value in

terms of profit, quality, time, and service (Zhu et al. 2002). Therefore, the maintenance function has become

essential for a manufacturing organisation in order to maintain its competitiveness (Al-Najjar and Alsyouf 2004).

Kamoun (2005) emphasised that as enterprises and customers count on availability, reliability, and quality of service

of corporate assets, any compromise in these areas will lead to both decreased revenues and increased costs.

To achieve all the above-mentioned goals in a manufacturing plant, an appropriate maintenance policy shouldbe selected. According to Panagiotidou and Tagaras (2008), an appropriate maintenance policy not only reduces the

probability of equipment failure but also improves the working condition of the equipment, resulting in lower

production costs and/or higher product quality. According to Al-Najjar and Alsyouf (2003), maintenance policy

affects the total operating budgeting costs, but the consequences of an inefficient maintenance policy go far beyond

the direct costs of maintenance. Most researchers have worked with various maintenance policies, but very few have

reported on the selection of the best policy for a production system. In the present study, selection of a maintenance

*Corresponding author. Email: [email protected]

ISSN 00207543 print/ISSN 1366588X online

2012 Taylor & Francis

http://dx.doi.org/10.1080/00207543.2011.653451

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policy in a manufacturing plant has been taken into consideration. The selection of the maintenance policy does not

depend on a single criterion (Azadivar and Shu 1999). Therefore, maintenance policy selection is considered as a

multicriteria decision-making (MCDM) problem. In this area, it has been found that the most important criterion is

maintenance cost, as discussed by many researchers such as Pascual and Ortega (2006) and Bartholomew-Biggs

et al. (2009) who have worked on this issue. In various studies, it has also been found that some factors have fuzzy

forms or qualitative forms. Some researchers such as Yuniarto and Labib (2006) and Marmier et al. (2009) have

adopted fuzzy environments for research in maintenance. Keeping in mind all these ideas, a fuzzy MCDM approachhas been employed in this study.

According to Zeydan and C olpan (2009), a unidimensional approach in recognition of real systems cannot

provide and supply a solution for measurement and evaluation, and can even result in unrealistic decisions. Thus,

MCDM methods have been used for efficient measurement and evaluation in maintenance systems. Some MCDM

approaches include the Simple Additive Weighting (SAW), Weighted Product Method (WPM), Technique for

Order Preference by Similarity to Ideal Solution (TOPSIS), and Analytic Hierarchy Process (AHP), etc. The

TOPSIS technique is based on the concept that the chosen alternative should have the shortest Euclidean distance

from the ideal solution (Rao 2008). TOPSIS is more efficient in dealing with the tangible attributes and the number

of alternatives to be assessed (Bhangale et al. 2004, Olson 2004, Yurdakul and Ic 2005). Most MCDM procedures

require information on the weights that decision-makers assign to criteria. Since human judgments are often vague,

it is therefore very difficult to get exact numerical value of weights assigned to the preferences. A more realistic

approach may be to use linguistic assessments instead of numerical values, that is, to suppose that the ratings of the

alternatives by decision-makers for the criteria in the problem are assessed by means of linguistic variables (Chen2000, Herrera and Herrera-Viedma 2000, Vahdani and Zandieh 2010). Therefore, linguistic variables have been used

to give importance weights to criteria.

On the basis of the literature review, it can be concluded that there is a need for appropriate maintenance policy;

otherwise it can be disadvantageous to the manufacturing firm. To select such a maintenance policy, an MCDM

approach is required, and this should address the problem with crisp data, fuzzy numbers, and linguistic terms.

By considering all the above factors, research has been carried out on the selection of maintenance policy on the

basis of several selection criteria. The novelty of the research is that it is considered as a strategic decision because

the selection has been made at the plant or organisation level instead of the equipment level. Simultaneously, a

distance-based fuzzy MCDM approach has been employed that enables decision-makers to use linguistic terms

while making qualitative assessments, and thus reduces their cognitive burden in the evaluation process. The

precisely defined criteria values and vaguely defined quantitative as well as qualitative criteria values are integrated

in the decision-making process. Hence, the proposed method provides the means for incorporating the economic

figure of merit as well as the strategic performance variables by allowing for consideration of both the crisp data and

the fuzzy data expressed by linguistic variables or triangular fuzzy numbers. The employed approach provides the

best maintenance policy and also the ranking of all the maintenance policies. The proposed approach is of great help

to the decision-maker for selecting appropriate alternatives according to their own constraints. A numerical example

is given to show the effectiveness of the algorithm and also to show the selection process for a maintenance policy in

a manufacturing firm.

The remainder of the paper is organised as: Section 2 provides an insight about the popular maintenance

policies, and Section 3 reveals the selection criteria with brief descriptions. Section 4 provides knowledge on the

fuzzy logic and MCDM approaches, and the methodology of the proposed approach is explained in section 5. The

numerical example of maintenance policy selection is presented in Section 6. The results are shown and analysed in

Section 7. Finally, the paper is concluded in Section 8.

2. Maintenance policies

Maintenance policy or strategy is the set of decisions for the identification of faults, researching the cause, and

execution of many inspections, replacing the parts or repairing the parts (Al-Najjar 1997, Kelly 1997). In the present

paper, five maintenance policies, Failure-Based Maintenance, Preventive Maintenance, Condition-Based

Maintenance, Total Productive Maintenance, and Total Quality Maintenance, have been taken into consideration

for the analysis. Brief descriptions of the above-mentioned maintenance policies are given below.

Failure-Based Maintenance (FBM) is the maintenance policy that is performed only when a failure or

breakdown occurs. In this policy, only repair or replacement actions are taken, but no action is taken to detect the

International Journal of Production Research 7045


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(3) Maintenance downtime: This is the time when the system is unavailable in providing its intended function. It

is a composite factor of maintenance time, logistic delay time, and administrative delay time. The value of

this criterion is given as a fuzzy value.

(4) Reliability: This can be defined as an ability of the system, which will perform in a satisfactory manner for a

given period of time when used under specified operating conditions in a given environment. This is given a

linguistic value for the study.

(5) Capability: This shows the capability of the various policies to handle the heavy and continuously changingproduction loads, i.e. number of parts produced. It is also given a linguistic value.

(6) Repair load: This is an indicator of the ratio of repair resources over the production resources. In other

words, it shows the traffic density for the repair process. For example, FBM requires fewer repair resources,

but TQMain requires a good number of repair resources.

(7) Operator skills: It shows which maintenance policy has skilled operators. It is given as a linguistic value.

(8) Flexibility: This is the ability of the system to adopt the changes within no time. It is shown in linguistic

symbols.

(9) Efficiency: This shows how the system works efficiently, i.e. providing quality products with less repair.

(10) Facility utilisation: This criterion shows that all the repair facilities are utilised in an appropriate manner.

It is also shown in linguistic symbols.

(11) Resource availability: This defines the availability of repair resources at the time of maintenance. It is also

provided in linguistic values.

With these 11 selection criteria, an MCDM approach is required to select a suitable maintenance policy. In the

above-mentioned selection criteria, two criteria are defined as crisp values: one is the fuzzy value and the other

linguistic terms. Therefore, a fuzzy-based MCDM approach is employed to select the appropriate policy from the

five maintenance policies.

4. Fuzzy-based MCDM approach

In this section, fuzzy logic is first described briefly after the MCDM approach is described.

4.1 Fuzzy logic

Fuzzy logic was first introduced and applied by Zadeh (1965), and has evolved as a robust and effective tool tohandle vagueness, impreciseness, or uncertainty in data. In many problems, uncertainty and vagueness are due to a

lack of data. This theory is particularly applicable in cases where the problems are too complex to define precisely,

but are easily controllable and operable by human inference, the help of past experience and inherent expertise.

Various researchers such as Zadeh (1965, 1968, 1973, 1975, 1978), Mamdani and Gains (1981), and Lee (1990) have

extended the application of fuzzy systems and their various attributes. Based on fuzzy sets, Mamdani (1974) was

first to propose an architecture that has been successfully applied to diverse areas, from medical applications to

plant layout (Wilhelm et al. 1987, Raoot and Rakshit 1991, 1993). In this theory, all the values are defined by a

membership function. A membership function is a curve that defines how each point in the input space is mapped to

a membership value (minimum 0 to maximum 1). The membership function itself can be an arbitrary curve whose

shape can be defined, based on simplicity, convenience, speed and efficiency. The following discussion provides a

basic insight into the mathematical aspects of fuzzy set theory.

Let there be a universe of discourse Uand its fuzzy subsetArepresented mathematically by its membership value

denoted byA(x), withxas an element of the universe of discourse, conceptually denoting the grade of membershipof x. The fuzzy subset A is designed as, A A u =u u 2 Uj

. The linguistic variable is represented in natural

language by the name, e.g. x and the set term S(x) of the linguistic value ofx. Further, a triangular fuzzy number

Ti (ai, bi, ci) has a membership function defined as

Ti x

0 x4 ai

x ai = b i ai ai5x5 bi

x ci = b i ci bi5x5 ci

0 x5 ci

8>>>>>:



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LetA and B be two triangular fuzzy numbers; these are expressed as A (a1, a2, a3) andB (b1, b2, b3) respectively.

The algebraic operations, such as addition, subtraction, multiplication and division in triangular fuzzy numbers, are

expressed as follows:

(1) Addition:

A B a1 b1, a2 b2, a3 b3

(2) Subtraction

A B a1 b1, a2 b2, a3 b3

(3) Multiplication

A B ffi a1b1, a2b2, a3b3 Ifa1, a2, a3 0, b1, b2, b3 0,

If one triangular fuzzy number is multiplied by a constant number C, it can be expressed as follows:

k A ka1, ka2, ka3 If k4 0

(4) Division

A

Bffi

a1

b1,a2

b2,a3

b3

4.2 MCDM approach

MCDM refers to an approach of problem-solving that is employed to solve problems involving selection from a

finite number of alternatives. The MCDM method is a procedure that specifies how criteria information is to be

processed in order to arrive at a choice. Often the terms MCDM, multiple attribute decision-making (MADM), and

multiple objective decision-making (MODM) are confused or used with the same meaning (Crispim and Pinho de

Sousa 2009). Generally, the basic steps of MCDM methods are as follows: establishing the system evaluation criteria

for achieving the goals; generating alternatives; assessing alternatives in terms of criteria; applying a MCDM

method; determining and ordering the alternatives from the best (optimal) to the worst; and finally, if this solution is

unacceptable, collecting the new data and repeating all the steps (Zeydan and C olpan 2009). Many MCDM methods

have been defined in the literature (Hwang and Yoon 1981).

In the present study, a distance-based fuzzy MCDM approach has been employed. The approach is based on the

distance from the ideal and non-ideal solutions. This was initially proposed by Karsak (2002). The novel feature of

this approach is that it can handle problems that are having both crisp and fuzzy data. This approach is interrelated

with technique for order preference by similarity to ideal solution (TOPSIS) (Hwang and Yoon 1981).

The traditional TOPSIS approach uses the Euclidean norm to normalise the original attribute values, and the

Euclidean distance to calculate each alternatives distance from the ideal and anti-ideal solutions. The normalisation

and distance functions form the key components of the TOPSIS approach. Normalisation is performed to make the

criterion values unit-free and comparable. Besides the cumbersome computations required for applying the square

root operator to fuzzy data, a drawback of applying the Euclidean norm is that the minimum and the maximum

values of the normalised scale are not equal for each criterion, which results in difficulties in making inter-criterion

comparisons (Karsak 2002). In the present approach, some changes have been made to make it easier for

computation.

In the present MCDM approach, a linear scale transformation for normalisation, with an interval of 0 to 1, hasbeen employed. Therefore, there is no need to obtain the square root of fuzzy data, and it can address the problem

with crisp data, triangular fuzzy numbers, and linguistic terms simultaneously. The methodology of the proposed

approach is presented in the next section.

5. Methodology

In this study, the alternatives for maintenance policy are identified and ranked by employing a fuzzy MCDM

approach. This approach works according to the various criteria for selection.

7048 F.T.S. Chan and A. Prakash


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The problem of selection is a matrix of maintenance policies and selection criteria. For instance, there are n

maintenance policies and p selection criteria. The assessed value of criteria j for maintenance policy iis denoted as

vij. The criteria measurements are of a different nature, some are measured in crisp values, and some are in linguisticterms, or in other words some are assessed in quantitative forms, and others are in qualitative forms. The

importance weights are also assigned to each criterion by a committee of decision-makers. The weighted distances

are calculated for each maintenance policy from the Fuzzy Positive Ideal Solution (FPIS) and the Fuzzy Negative

Ideal Solution (FNIS). According to the weighted distance, the proximity ratio ( Rp) is calculated. According to

the value of the proximity ratio, the alternatives are sorted in descending order and it provides the rank to

alternatives. The proposed methodology is presented in Figure 1, and the whole procedure is explained in the

following steps:

(1) A committee ofc decision-makers is built up and identifies the maintenance policies (i 1, 2, 3, . . . , n) and

also the selection criteria (j 1, 2, 3, . . . p).

(2) Assess each criterion for each maintenance policy and make a decision matrix. The value of each element of

the matrix may be a crisp value or a triangular fuzzy number or a linguistic term. The element of the matrix

is denoted by vij.(3) Normalise all the crisp values for each criterion individually. Therefore, the values become unit free and

comparable. To normalise the crisp values, the following formula is:

aij

vij v

j

vj v

j

j 2 B

vj vij

vj v

j

j 2 C

8>>>>>:

Identify the

Maintenance Policies

Identify the Selection

Criteria

Prepare the decision matrix

of policy and criteria

Normalise the crisp values

Normalise the Triangular

fuzzy values

Defuzzify the linguistic

variables

Assess the importance

weights to each criterion

Estimate the weighted distance

from FPIS and FNIS

Calculate the Proximity Ratio

Ranking of the maintenancepolicies according to proximity

ratio

Select the best Maintenance

Policy

Figure 1. Conceptual model of distance-based fuzzy MCDM methodology.



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where B is the benefit related criteria, and C is the cost-related criterion.

vj maxi

vij

vj mini

vij:

The normalised value of the crisp data is presented in triangular fuzzy number format ( ~aij aij, aij, aij).

(4) The triangular fuzzy numbers (xij,yij, zij) are also normalised, and these are also categorised as benefit

criteria or cost criteria. The formula for both criteria is as follows:

zi zij

where

zi maxi

zij

xj mini

xij:

(5) Defuzzify the linguistic terms in the form of a triangular fuzzy number.

(6) Define the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) as follows:

FPIS P1, P2, P

3, . . . , P

p

FNIS P1, P2, P

3, . . . , P

p

where

P1 1,1,1 8j

Pj 0,0,0 8j:

(7) Assign weights to the selection criteria as to their importance according to the experts committee. The

weights are given in linguistic terms.

(8) Defuzzify the weights in the triangular fuzzy numberwjc, for thejth slection criteria by thecth expert of the

committee and calculate the aggregate weight of each selection criterion. The aggregate weight is calculated

as follows:

wj1

c wj1 wj2 wj3 wjc:

(9) Calculate the weighted distance from FPIS and FNIS. The distance is calculated as the area of trapezoidal

with a height of 1 (Bojadziev and Bojadziev 1995). The distance K between two triangular fuzzy numbers (let

A a1, a2, a3 andB b1, b2, b3) can be calculated by the following formula:

kA, B 1

2fmax a1 b1j j, a3 b3j j a2 b2j jg

AsPj 1,1,1 andP

j 0,0,0, the weights are represented as wj wxj, wyj, wzj, and the distance from

FPIS can be written as:

Ki Xpj1

1

2fmaxwxj axij 1

, wzjazij 1 wyjayij 1 g,

whereas the distance from FNIS can be expressed as:

Ki Xpj1

1

2fmaxwxj axij 0

, wzj azij 0 wyj ayij 0 g:



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(10) Calculate the proximity ratio for each alternative of the maintenance policies using the following formula:

Rpi Ki

Ki Ki

:

(11) Rank the maintenance policies according to the values ofRpi, with the policy with the highest Rpibeing the

best among all the alternatives.

The proposed methodology is explained in the following maintenance policy selection example.

6. Maintenance policy selection: an example

The present study shows the selection of an appropriate maintenance policy under various selection criteria. A

numerical example also has been taken into consideration for explaining the methodology in maintenance policy

selection in a manufacturing system.

In this study, five maintenance policies are evaluated and the best policy selected on the basis of 11 selection

criteria. These five maintenance policies are FBM, PM, CBM, TPM, and TQMain, and are described in Section 2.

The selection criteria are: capital cost, running cost, maintenance downtime, reliability, capability, repair load,

operator skills, flexibility, efficiency, facility utilisation, and resource availability. The description of all these criteria

is given in Section 3. In these criteria, capital cost and running cost are presented as crisp values; maintenancedowntime is presented as a triangular fuzzy number, and the rest are in the form of linguistic variables. To define

these criteria, the linguistic variables are: Very Poor (VP), Poor (P), Fair (F), Good (G), and Very Good (VG).

These linguistic terms are represented in graphical form in Figure 2, and the corresponding triangular fuzzy numbers

are shown in Table 1. In the numerical example, the value of the selection criteria for each maintenance policy is

given in Table 2.

Table 2. Data used to assess the ranking of maintenance policy alternatives.

Sample no. Selection criteria Type of data

Maintenance policies

FBM PM CBM TPM TQMain

1 Capital cost (M$) Crisp 0.9 1.6 1.4 2.6 2.82 Running cost (M$) Crisp 1.7 1.3 1.2 1.0 1.13 Maintenance downtime (days) Fuzzy (10, 13, 15) (3, 5, 8) (3, 5, 7) (2, 4, 6) (1, 3, 5)4 Reliability Linguistic VP G F G VG5 Capability Linguistic P F F G VG6 Repair load Linguistic P F F G VG7 Operator skills Linguistic G G F VG G8 Flexibility Linguistic P P VG G F9 Efficiency Linguistic VP F F VG VG

10 Facility utilisation Linguistic P P F VG G11 Resource availability Linguistic VG G G VG G

Table 1. Triangular fuzzy number for linguistic terms forselection criteria.

Sample no. Linguistic terms Triangular fuzzy number

1. Very Poor (VP) (0, 0, 0.2)

2. Poor (P) (0, 0.2, 0.5)3. Fair (F) (0.3, 0.5, 0.7)4. Good (G) (0.5, 0.7, 1.0)5. Very Good (VG) (0.8, 1, 1)

0 0.2 0.3 0.5 0.70.8 0.9 1.0

(x)

1

x

VP

P F G

VG

Figure 2. Membership functions for linguistic terms usedfor selection criteria.



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To select the best policy alternative, a committee of three decision-makers is formed, and these decision-makers

are known asMD1 ,MD2 , andMD3 . These decision-makers give the weight to each selection criteria according to their

importance. The weights to the selection criteria are also given in the form of linguistic variables. These linguistic

variables are: Medium (M), High (H), and Very High (VH). The graphical representation of these linguistic

variables is shown in Figure 3, and the value of the triangular fuzzy number for the weights is shown in Table 3. The

weights given by all three decision-makers to each selection criterion are shown in Table 4.

On the basis of all these data, the proposed methodology works and gives an insight for selecting the best

maintenance policy in a manufacturing system. The results obtained are discussed in the next section.

7. Numerical analysis and discussion

To select the best maintenance policy with consideration of the 11 selection criteria, the fuzzy-based MCDM

methodology, which works on the distance from the ideal and anti ideal solutions, has been employed. First, the

given values, of the selection criteria for each maintenance policy alternative, are normalised, according to the

nature of the value, i.e. the crisp, triangular fuzzy number or linguistic term, as shown in the methodology. After

normalisation, the decision-makers give an importance weighting to the selection criteria. On the basis of the

weights given individually by each decision-maker, the aggregate weights have been calculated, and are shown in

Table 5. By applying the aggregate weights, the weighted distance of each alternative of maintenance policy is

calculated from both FPIS and FNIS. After obtaining the weighted distance, the proximity ratio (RP) is calculated

as shown in the methodology. The distances from FPIS and FNIS with proximity ratio are shown in Table 6.The value of the proximity ratio provides the ranking of the maintenance policies. According to RP, Total

Productive Maintenance (TPM) is the best policy among the five alternatives on the basis of the 11 selection criteria.

The ranking order of all the alternatives of maintenance policy is as follows:

TPM4TQMain4CBM4PM4FBM

Table 5. Aggregate weights for each selection criterion.

Sample no. Selection criteria Aggregate weights

1 Capital cost (M$) (0.7, 0.9, 1.0)

2 Running cost (M$) (0.7, 0.9, 1.0)3 Maintenance downtime (days) (0.5, 0.73, 0.93)4 Reliability (0.6, 0.8, 1)5 Capability (0.6, 0.8, 1)6 Repair load (0.5, 0.73, 0.93)7 Operator skills (0.5, 0.73, 0.93)8 Flexibility (0.3, 0.57, 0.87)9 Efficiency (0.4, 0.67, 0.87)

10 Facility utilisation (0.3, 0.57, 0.87)11 Resource availability (0.4, 0 .63, 0 .93)

Table 4. Importance weights assigned by the committee ofexperts.

Sampleno. Selection criteria

Committee of experts

DM1 DM2 DM3

1 Capital cost (M$) H VH VH

2 Running cost (M$) VH VH H3 Maintenance downtime (days) M VH H4 Reliability H H VH5 Capability H H VH6 Repair load H VH M7 Operator skills VH M H8 Flexibility M H M9 Efficiency M M VH

10 Facility utilisation M M H11 Resource availability M H H

0 0.2 0.5 0.7 0.8 1.0

(x)

1

x

MH

VH

Figure 3. Membership functions for linguistic terms used forimportance weights.

Table 3. Triangular fuzzy number for linguistic terms forimportance weights.

Sample no. Linguistic termsTriangular

fuzzy number

1. Medium (M) (0.2, 0.5, 0.8)

2. High (H) (0.5, 0.7, 1.0)3. Very High (VH) (0.8, 1.0, 1.0)



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The main finding of this study is the ranking of the maintenance policies by considering 11 selection criteria and

following the procedure shown in the methodology. From the ranking, TPM is best, but if only the economical

aspect is considered, it is one of the worst policies. Therefore, the decision cannot be made by considering only one

aspect.

From Table 6, it is also clear that the decision cannot be made only on the basis of the weighted distance, as the

weighted distance of TQMain from the FNIS solution is greater than that of TPM. Therefore, TQMain would be

selected as the best policy, but TPM is the best policy on the basis of the proximity ratio. These results comply with

the fact that an alternative with the shortest distance from the FPIS may not involve the farthest distance from the

FNIS, and thus, the proposed decision algorithm that takes into account the distances from both the FPIS and

FNIS simultaneously appears to provide a more consistent ranking.

The results of the proposed decision-making algorithm are also compared with other decision making algorithmssuch as the Integral Value (IV) and Simple Additive Weighting (SAW), which are also known as fuzzy number

ranking methods. The procedure for calculating the integral value and SAW scores is described in Appendix 1. In

the Saw method, the index is calculated, and the obtained ranking is compared. The integral values at two different

values of ( 0.5, 0.8) have been calculated. All the values obtained from both the above-mentioned methods

are depicted in Table 7. From the table, it can be seen that they also give the same ranking, which also verifies the

results obtained from the proposed algorithm. The limitation of both methods is that they can be employed only

with fuzzy numbers, but the proposed algorithm can handle crisp values as well as fuzzy values. Consequently, the

proposed approach or fuzzy MCDM approach, which is based on the distance from FPIS and FNIS, basically

avoids the difficulties encountered with using fuzzy number ranking methods in evaluating alternatives.

8. Conclusion

The selection of an appropriate maintenance policy for a manufacturing system is a difficult task for the decision-

makers. In the present study, 11 selection criteria have been selected on the basis of the literature review. The five

most employed maintenance policies are also taken into consideration in the evaluation. To select the most

appropriate policy, a distance-based fuzzy MCDM approach has been employed. The main feature of this research

is that the maintenance policy selection has been made with 11 selection criteria of different natures. The selection

criteria are of a different nature; some have crisp values, some have fuzzy triangular values, and the rest are

represented in linguistic terms.

Table 7. Distance of alternatives from FPIS and FNIS and proximity ratio and ranking.

Sample no.Maintenance

policy alternativesIntegral

value ( 0.5) RankingIntegral

value ( 0.8) RankingSAW

method Ranking

1. FBM 2.98 5 3.59 5 0.11 52. PM 4.64 4 5.41 4 0.18 43. CBM 5.11 3 5.90 3 0.20 34. TPM 6.19 1 7.04 1 0.25 15. TQMain 5.97 2 6.75 2 0.24 2

Table 6. Distance of alternatives from FPIS and FNIS and proximity ratio and ranking.

Sample no.Maintenance policy

alternatives Ki Ki RPi Ranking

1. FBM 4.82 3.99 0.45 52. PM 3.78 5.92 0.61 43. CBM 3.37 6.43 0.66 3

4. TPM 2.58 7.60 0.75 15. TQMain 2.90 7.65 0.73 2



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The fuzzy MCDM approach evaluates the alternatives on the basis of the proximity ratio, not on the basis of the

distance from the FPIS and FNIS solutions. The results are also compared with two other ranking techniques.

From the comparison, it can be said that the proposed algorithm is adequate, and it can properly handle the

different natured data simultaneously. The selection of a better maintenance policy will improve the efficiency of a

manufacturing plant, as it will produce higher-quality products and will provide better economy or more

profitability.

From the perspective of future research, more selection criteria can be considered. The combination of twotechniques such as the AHP and the MCDM approach can be employed. AHP will be employed for the selection of

important criteria and will also provide importance weights to the criteria. On the other hand, to select the weights

for each criterion, any evolutionary algorithm such as GA, SA, etc. can be employed. The effectiveness of the

selection of the best policy can be evaluated in other terms such as product quality, enterprise efficiency,

productivity, and profitability.

Acknowledgements

The work described in this paper was substantially supported by a grant from the Research Gants Council of the Hong KongSpecial Administrative Region, China (Project No. PolyU 510410). The authors would also like to thank The Hong KongPolytechnic University Research Committee for financial support.

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Appendix 1

The integral value (IVi) of a triangular fuzzy number A (A(a1, a2, a3)) can be calculated as follows:

IVi 0:5f a3 a2 1 a1g:

Here, is the index of optimism, or in other words it shows the risk taking attitude of the decision-makers (Karsak 2002).

The value of is in the interval of 0 and 1 (0 1). In the present study, the results were obtained at two different values( 0:5, 0:8).

The SAW method, as presented by Al-Najjar and Alsyouf (2003), is also employed for decision-making, and the scores foreach alternative have been calculated by the following formulae:

SiX

i

wjMij,

where: i alternatives; j criterion;wj weight of the jth criteria (a triangular fuzzy number); Mij measure of the jth criteriafor the ith alternative (a triangular fuzzy number); and Si score of the ith alternative. Then, the scores Siare normalised bycalculating the indexFi:

Fi Si=Si:

The index value gives the normalised ranking. The alternative with maximum value ofFigives the best alternative.


how to choose between maintenance policies 4

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