31

CHAPTER 3

MAINTENANCE STRATEGY SELECTION

USING AHP AND FAHP

3.1 INTRODUCTION

Evaluation of maintenance strategies is a complex task. The typical

factors that influence the selection of maintenance strategy are life of the

machine, safety, environmental conditions, budget constraints, available

manpower, mean time between failures and time to repair. This chapter

details about the development and application of Analytic Hierarchy Process

(AHP) and its extension for selection of maintenance strategy. The problem

description for selection of maintenance strategy is detailed in section 3.2.

The proposed AHP method for selection of maintenance strategy is detailed in

section 3.3. The proposed Fuzzy AHP (FAHP) models for MSS are described

in section 3.4. The sensitivity analysis on the proposed model is detailed in

section 3.5. The summary of the chapter is presented in section 3.6.

3.2 PROBLEM DESCRIPTION

In decision making problem of maintenance strategy, there are M

strategy alternatives rated on N determining conditions called criteria. The

alternatives are denoted as Ai (for i = 1, 2, 3…, M), criteria as Cj (for j = 1, 2,

3, …, N) and the subcriteria as SCj (for j = 1,2,3,..., N). The A1 denotes

Predictive Maintenance (PM) strategy similarly the A2, A3 and A4 denote

Condition-Based Maintenance (CBM), Preventive Maintenance (PVM) and

32

Reliability-Centered Maintenance (RCM) respectively. The C1 denotes the

main criterion ‘Environmental Conditions’. Similarly C2, C3 and C4 represent

‘Component Failure’, ‘Training Required’ and ‘Flexibility’ respectively for

maintenance strategy evaluation. For each criterion Cj, the decision maker has

to determine its importance, or weight, Wj. The aij denotes the rating of the

ith maintenance strategy on deducting changes in the jth criterion using

suitable measure (expertise) which is determined (for i = 1,2, 3, …, M and

j = 1, 2, 3, …, N); The most preferred alternative is to be found through a

measure of performance of alternative Ai in terms of criterion Cj.

3.3 SOLUTION METHODOLOGY THROUGH AHP

The proposed AHP model for selection of maintenance strategy is

shown in Figure 3.1. The solution methodology for selection of maintenance

strategy is conducted through three stages.

Figure 3.1 Proposed AHP model for MSS

33

Step 1 - Hierarchical structure development: The first step of

AHP is to review the related papers and interview the experts about the

specific domain in order to decompose the problem hierarchically. In the

designing of AHP hierarchical tree, the aim is to develop a framework that

satisfies the needs of the analysis to solve the MSSP. The typical hierarchy

structure of AHP is shown in Figure 3.2. The first level represents the overall

objective of the maintenance problem. The maintenance influencing criteria

and subcriteria are placed in second and third level. The maintenance strategy

alternatives are placed at the bottom.

Figure 3.2 Typical hierarchy structure for the proposed AHP

Step 2 - Pair-wise comparison matrix: A questionnaire based

pair-wise comparison matrix is formulated after the hierarchical structure is

established. Simple pair-wise comparison is used to determine weights and

ratings so that an analyst can concentrate on two factors at one time. The

typical questions are asked like how important is the ‘Component Failure’

criterion with respect to the ‘Training Required’ criterion in maintenance and

the possible responses such as equally important, moderately important are

listed only. These verbal responses are quantified and translated into a score 1

Level 4Maintenancealternative n

Maintenancealternative 1

Maintenancealternative 2

…………

Level 1 Goal: Optimum MSS

Level 2 Criterion 1 Criterion 2 Criterion 3 Criterion n……….

Subcriteria Subcriteria Subcriteria ………. Subcriteria Level 3

34

to 9 point scales developed by Satty (1980). The questionnaire designs are

presented in Appendix 1.

The numerical values representing the judgments of the pair-wise

comparisons are arranged in the upper triangle of the square matrix for

example, aij represents how much criterion ‘Component Failure’ factor (i) is

preferred over ‘training required’ criterion (j). That is iij

j

waw

. Each of its

elements, aij is the ratio of the absolute weight relative to the importance of

criterion i over the absolute weight relative to the importance of criterion j.

The elements in the main diagonal of matrix A will be equal to 1 and the

elements of the down triangle are the inverse of the elements in the upper

triangle (i.e., 1 / 1 / / / )ji ij i j j ia a w w w w . The Pair-wise comparison

matrix is

1 ...

... 1 ...

... 1

i

j

j

i

ww

Aww

(3.1)

The AHP enables an analyst to evaluate the goodness of judgments

with the consistency ratio CR. The judgments can be considered acceptable if

CR <= 0.1. In case of inconsistency, the assessment process for the

inconsistent matrix is immediately repeated.

Step 3 - Synthesis and ranking: The weights of components of the

decision hierarchies are calculated and synthesized to rank the scores of

alternative maintenance strategy. Weights are synthesized from the highest

level down by multiplying weights by the weight of their corresponding

parent component in the level above and adding them for each component in a

35

level according to its influencing component. Once the process has been

completed to gauge the effectiveness of the evaluation the feedback

mechanism is introduced. To evaluate and validate the proposed AHP model,

a case study has been done in a textile industry and is explained in the

following sections.

3.3.1 Textile Industry Application

South Indian textile research association found that poor

maintenance was one of the major causes for low yield of yarn. Textile

spinning mill covers blow room, carding, draw frame comber, speed frame,

ring frame, winding, fiber testing and yarn testing. Spinning is the single most

costly step in converting cotton fibers to yarn. The spinning mill is situated in

an area of 15,000 square meter and produces 10,000 kg of yarn per day.

Currently 85% of the world’s yarn is produced with ring-spinning frame. The

investment cost for the ring frame is high in spinning mill. The working

performance and power consumption of the ring frame depends on the lift,

ring diameter and the number of spindles. The company came forward to

adopt a suitable maintenance strategy for a ring frame in order to increase the

productivity and enhance availability of the plant.

The proposed model consists of developing a hierarchical structure

of the MSSP. A four level hierarchical model is proposed and modeled as

shown in Figure 3.3. The objective of the problem is at the first level. The

criteria, subcriteria and alternatives are positioned at the second level, third

level and the last level respectively. The typical main criteria are

Environmental Conditions (EC), Component Failure (CF), Training Required

(TR) and Flexibility (F). The typical subcriteria taken into account for the

evaluation process are namely Moisture (M), Choking (CH), Improper

Sequence (IS), Higher Utilization (HU), Knowledge of Labour (KL), Cost

(C), Difficulty in Training (DT), Difficulty in Implementation (DI) and Ease

36

of Handling (EH). The typical maintenance alternatives are Predictive

Maintenance (PM), Condition-Based Maintenance (CBM), Preventive

Maintenance (PVM) and Reliability-Centered Maintenance (RCM). The

selected criteria and subcriteria are listed in the Table 3.1.

Figure 3.3 Hierarchy for MSS model

Table 3.1 Identified criteria for MSS

Criteria (C) Subcriteria (SC)

Environmental Conditions (EC)Moisture (M)Choking (CH)

Component Failure (CF)Improper Sequence (IS)Higher Utilization (HU)

Training Required (TR)Knowledge of Labour (KL)Cost (C)Difficulty in Training (DT)

Flexibility (F)Ease of Handling (EH)Difficulty in Implementation (DI)

Reliability-centeredMaintenance

PreventiveMaintenance

PredictiveMaintenance

Condition-BasedMaintenance

Knowledge ofLabor

Difficulty inTraining

CostEase of Handling

Difficulty inImplementation

Moisture

Choking

ImproperSequence

HigherUtilization

ComponentFailure

TrainingRequired

FlexibilityEnvironmentalCondition

Goal: Selecting the best maintenance strategy

37

Environmental Condition: Environment condition plays a major

role in textile industry. If the environment condition is not good enough, the

quality of the product will be affected. The relevant factors describing the

Environmental Conditions are Moisture and Choking of material.

Component Failure: Failure of components may occur due to poor

quality of components, higher utilizations of machines and operating

machines at high speed. The subcriteria of Component Failure are Higher

Utilization and Improper Sequence.

Training Required: Maintenance staff can make full use of the

related tools and techniques of maintenance strategies only after sufficient

training. It deals with the level of training required in order to equip the

labour if particular maintenance strategy is implemented. The subcriteria for

the Training Required are Cost, Knowledge of Labour and Difficulty in

Training.

Flexibility: Flexibility of maintenance strategy is considered with

two factors namely Implementation Difficulty and Ease of Handling.

The decision making team completes the task of constructing the

pair-wise comparison matrix by using the Satty’s scale. The pair-wise

comparison matrix, relative weight and the consistency ratio for the main

criterion of the MSS are tabulated in Tables 3.2 and 3.3.

The relative weights of each element of levels II and III and the

Consistency Ratio (CR) of each matrix are analyzed as detailed in

Appendix 2. Global weight for the subcriteria is computed by multiplying the

relative weight for the criteria and the relative weight for the subcriteria. The

38

relative weights and the global priority weights for criteria and its subcriteria

are tabulated in Table 3.4.

Table 3.2 Pair-wise comparison matrix for main criteria of AHP

GoalEnvironmental

Condition

Component

Failure

Training

RequiredFlexibility Weights

Environmental

Condition1 2 3 5 0.476

Component

Failure1/2 1 2 4 0.288

Training Required 1/3 1/2 1 2 0.154

Flexibility 1/5 1/4 1/2 1 0.082

Table 3.3 Consistency ratio for the pair-wise comparison matrix of AHP

max 4.02

Consistency index (CI) 0.007

Consistency Ratio (CR) 0.008

39

Table 3.4 Relative Weight and Global Weight of evaluation criteria of

AHP

Criteria Relative weight Subcriteria Relativeweight

Globalweight

Moisture 0.857 0.407EnvironmentalConditions

0.476Choking 0.143 0.067Improper Sequence 0.833 0.240Component

Failure0.288

Higher Utilization 0.167 0.048Knowledge of Labour 0.087 0.013Cost 0.274 0.042

TrainingRequired

0.154

Difficult in Training 0.639 0.099Ease of Handling 0.125 0.010

Flexibility 0.082 Difficult inImplementation 0.875 0.071

The results of the priority weights of criteria, subcriteria and four

maintenance strategies using AHP is tabulated in Table 3.5. The global

weights of the four maintenance alternatives are calculated by multiplying the

relative weight of the criterion, subcriterion and maintenance strategy

alternatives. The final performance ranking value of each maintenance

strategy is tabulated in the last row of the Table 3.5. In this example, the

predictive maintenance is the most preferable maintenance strategy among

four alternatives with the performance ranking value of 0.337. In AHP model

the numerical values are exact numbers and do not reflect an expert choice.

Deterministic scale can produce misleading consequences. For example, some

pessimistic people may not give any point more than four, or very optimistic

people may easily give 5 even if it does not deserve it. Using the integration

of fuzzy set theory with the AHP, the unbalanced scale of judgments and

imprecision in the pair-wise comparison process are reduced. The application

of fuzzy set theory with AHP is detailed in the following sections.

40

41

3.4 FUZZY AHP METHODOLOGY

The AHP is extended by combining it with the fuzzy set theory to

evolve into FAHP. A number of methods have been used to compute the

priority weights of matrices in FAHP. For the proposed model the extent

analysis and eigen vector method are used to evaluate the priority weights of

influencing criteria. These methods are computationally simple and fast.

3.4.1 Fuzzy Logic in AHP

The uncertain comparison ratios are expressed as fuzzy sets (or)

fuzzy numbers. The maintenance criterion in the judgment matrix and weight

vector are represented by triangular fuzzy numbers. A fuzzy number is a

special fuzzy set F = { ( x , µF (x), x € R} where x takes its value on the real

line R1 : - < x < + and µF(x) is a continuous mapping from R1 to the close

interval [0,1]. A triangular fuzzy number can be denoted as M = ( ),, uml . The

triangular fuzzy numbers can be represented as follows:

0, , ,

, ,( )

, ,

0,

A

x lx l l x mm lxu x m x uu m

x u

(3.2)

According to the nature of triangular fuzzy number, it can be

defined as a triplet ( , , )l m u . The parameters such as lower ( l ), middle ( m)

and upper (u ) show that the smallest possible range, the most promising

range and the largest possible range respectively. The main operational laws

for two triangular fuzzy numbers M1 and M2 are as follows (Kaufmann 1991).

42

Addition 1 2 1 2 1 2 1 2( , , )M M l l m m u u (3.3)

Subtraction 1 2 1 2 1 2 1 2( , , )M M l l m m u u (3.4)

Multiplication 1 2 1 2 1 2 1 2( , , )M M l l m m u u (3.5)

Division 1 1 1 1

2 2 2 2

, ,M l m uM u m l

(3.6)

Inverse 1

1 1 1

1 1 1, ,Au m l

(3.7)

The schematic diagram of the proposed FAHP approach is shown

in Figure 3.4. The stages of the model are the hierarchical structure

development, construction of the fuzzy judgment matrix and evaluation of

alternatives.

Step 1 - Hierarchical structure development: The procedure for

the development of hierarchical structure is as discussed in section 3.3.

Step 2 - Construction of the fuzzy judgment matrix: The crisp

pair-wise comparison matrix A is fuzzified using the triangular fuzzy number

M = (l, m, u), which fuzzifies the pair-wise comparison matrix and is listed in

Table 3.6. The l and u represent lower and upper bound range that might exist

in the preferences expressed by the maintenance experts. The membership

function of the triangular fuzzy numbers M1, M3, M5, M7, M9 are used to

represent the assessment from equally preferred (M1), moderately preferred

(M3), strongly preferred (M5), very strongly preferred (M7), extremely

preferred (M9) and M2, M4, M6, M8 are the middle values. The membership

function of triangular fuzzy number used for FAHP is shown in Figure 3.5.

43

Figure 3.4 Proposed FAHP model for MSS

Table 3.6 Membership function of fuzzy number for FAHP

Crisp value Fuzzy membership function

1 (1,1,1)

x ( 1, , 1) 3,5,7x x x for x

9 (7,8,9)

Calculation of the global weights ofsubcriteria

Ranking of maintenance strategyalternatives

Calculation of criteria/subcriteriaweights

Fuzzy settheory

Identifying the criteria and subcriteria

Constructing the decision model

Expert experience

Questionnaireand

Data analysis

44

1 3 52 7 94 6 8

ModeratelyM2

StronglyM5

Very StronglyM7

ExtremelyM9

EquallyM1

1

0.5

0

Figure 3.5 Membership functions of triangular fuzzy numbers for

FAHP

The fuzzy judgment matrix ( )ijA a is as follows:

12 13 1( 1) 1

21 23 2( 1) 2

( 1)1 ( 1)2 ( 1)3 ( 1)

1 2 3 ( 1)

11

11

n n

n n

n n n n n

n n n n n

a a a aa a a a

A

a a a aa a a a

(3.8)

where 1 1 1 1 1

1,1,3,5,7,9 1 ,3 ,5 ,7 ,9 ,ij

i ja

or i j(3.9)

Evaluation of criteria weights: The extent analysis and eigen

vector priority weight calculation methods are proposed to determine the

relative weights of criteria and alternatives.

M3

45

Extent analysis method: Let X = {x1, x2, x3 ..., xn} represent a set

of object, and G = {g1, g2, g3 ..., gn} a goal set. Then, extent analysis for each

goal in each object is applied. Thus, totally m extent analysis values for every

object are obtained, with the following signs: 1 2, ,..., mgi gi giM M M ,where

i=1,2, ..., m. Where ( 1,2,3,..., )igiM j m all are triangular fuzzy numbers.

The FAHP based decision making with change’s extent analysis can be

described with the following steps:

(a) Calculate the fuzzy synthetic extent value

The MSS criteria are denoted by Sc1, Sc2, Sc3, Sc4 and Sc5. The

extent analysis synthesis values of each criterion and

subcriterion are calculated.

The fuzzy synthetics extent with respect to ith object can be

determined by

1

1 11

m n mj ji gi gii j

j

S M M (3.10)

where,1

m jgij

M is the fuzzy addition operation of m extent

analysis values for a particular matrix which can be calculated

as

1 1 1 1, ,m m m mj

gi j j jj j j jM l m u (3.11)

and the value of1

1 1 1, ,m m m

j j jj j jl m u can be obtained

by the fuzzy addition operation of ( 1,2,..., )jgiM j m such that

1 1 1 1 1, ,n m n m jj

gi i i ii i i i iM l m u (3.12)

46

And the inverse of the above equation is performed as follows

1

1 1

1 1 1

1 1 1, ,n m jgi n n ni j

i i ii i i

Mu m l

(3.13)

(b) The degree of possibility of two triangular fuzzy numbers

is calculated for each criterion

The degree of possibility of two triangular fuzzy numbers is

defined as if

1 1 1 1( , , )M l m u and 2 2 2 2( , , )M l m u

2 1 1 2( ) [min ( ( )), ( )]y x m mV M M Sup x y (3.14)

2 1 1 2 2( ) ( ) ( )MV M M hgt M M d (3.15)

2 1

1 2

1 2

2 2 1 2

1,0,

( ) ,( ) ( )

if m mif l u

l u otherwisem u m l

(3.16)

1 2( )V M M and 2 1( )V M M is needed to compare the

triangular fuzzy numbers. The degree of possibilities for a

convex fuzzy numbers to be greater than k convex fuzzy

numbers ( 1,2,... )im i k can be defined by

1 2( , ,..., ) min ( ), 1,2,...k iV M M M M V M M i k (3.17)

47

(c) Determine the weight vector

The weight vector w is then determined. Assume

11

1 2

( ) min ( ) 1,2,3,...,

[ ( ), ( )....... ( )]i k

Tn

d A V S S for k m

k i then w d A d A d A(3.18)

where ( 1,2,..., )iA i n is n-element

(d) Normalize the weight vector

1 2( ( ), ( )..., ( ))Tnw d A d A d A (3.19)

where w is a non-fuzzy number.

Eigen vector method: The eigenvector method indicates that the

eigenvector corresponding to the largest eigen value of the pair-wise

comparisons matrix provides the relative priorities of the factors, and

preserves ordinal preferences among the maintenance alternatives. This means

that if a maintenance alternative is preferred to another, its eigenvector

component will be larger than that of the other. A vector of weights obtained

from the pair-wise comparisons matrix reflects the relative performance of the

various factors. In the FAHP, triangular fuzzy numbers are utilized to

improve the scaling scheme in the judgment matrices, and an interval

arithmetic is used to solve the fuzzy eigenvector. The computational

procedure of this methodology is summarized as follows:

(a) To estimate the fuzzy eigenvector from a fuzzy comparison

matrix, the equation is used

1/

1

nn

i ijj

V a (3.20)

48

1/1 11 12 13 1( * * *...* ) n

nV a a a a (3.21)

Eigen vector Vi is compounded by the n triangular numbers

defined as

where Vi is a triangular number defined as ( , , )l m uV V V

(b) The eigen vector is to be normalized according to the next

relation

, ,1 1 1l m u

i

l m u

V V VwV V V

(3.22)

31 2, , ,..., n

i i i i

w ww wT w w w w (3.23)

(c) Defuzzification of fuzzy numbers: The result of fuzzy

synthetic decision of each maintenance strategy alternative is a

fuzzy number. It is necessary that the nonfuzzy ranking

method is applied for fuzzy numbers during performance

evaluation of each alternative. Defuzzification is a technique

to convert the fuzzy numbers into crisp real numbers; the

procedure of defuzzification is to locate the Best Nonfuzzy

Performance (BNP) value. There are several methods

available to serve this purpose, the center-of-area method is

used in this research due to its simplicity and does not require

personal judgment of an analyst.

[( ) ( )]3

i i i ij

i

u l m lBPN l (3.24)

49

(d) The consistency of the pair-wise comparison matrix is

determined by calculating the consistency ratio.

Step 3 - Calculate the composite weighted performance of each

maintenance alternative on each criterion by summing up the product of the

performance of each maintenance strategy on each subcriterion and its

relative weight of importance. The application of the proposed model is

illustrated using a case study of textile industry.

3.4.2 Case Study of Textile Industry

The hierarchical structure, criteria, subcriteria and maintenance

strategy alternatives of the problem are same as detailed in section 3.3.1. The

proposed extent analysis of FAHP requires the pair-wise comparisons of the

criteria and subcriteria in order to determine their relative weights. The

pair-wise comparison matrix of the main criteria is tabulated in the Table 3.7.

Table 3.7 Fuzzy evaluation matrix with respect to goal of FAHP

GoalEnvironmental

Condition

Component

Failure

Training

RequiredFlexibility

Environmental

Condition(1,1,1) (1,2,3) (2,3,4) (4,5,6)

Component Failure (1/3,1/2,1) (1,1,1) (1,2,3) (3,4,5)

Training Required (1/4,1/3,1/2) (1/3,1/2,1) (1,1,1) (1,2,3)

Flexibility (1/6,1/5,1/4) (1/5,1/4,1/3) (1/3,1/2,1) (1,1,1)

50

The value of fuzzy synthetic extent with respect to each criterion is

calculated by using the equation (3.10). The different values of extent analysis

synthesis values with respect to main criterion are denoted by Sc1, Sc2, Sc3 and

Sc4. The illustrative calculation of main criterion is as below.

By equation (3.10)

Sc1 = (4.33, 6.50, 9) (1/34.50, 1/27.06, 1/20.49)

= (0.125, 0.240, 0.439);

Sc2 = (11, 14, 17) (1/34.50, 1/27.06, 1/20.49)

= (0.318, 0.517, 0.829);

Sc3 = (1.63, 1.81, 2.17) (1/34.50, 1/27.06, 1/20.49)

= (0.047, 0.066, 0.105);

Sc4 = (3.53, 4.75, 6.33) (1/34.50, 1/27.06, 1/20.49)

= (0.102, 0.175, 0.309);

The degree of possibility of Fi over Fj (i j) can be determined by

equations (3.14) to (3.17)

1 20.318 0.439( ) 0.302

(0.240 0.439) (0.517 0.318)V Sc Sc

1 3( ) 1V Sc Sc 1 2( ) 1V Sc Sc

51

The above calculation procedure is applied to all the subsequent

criteria’s. The degrees of possibility of criterion are as follows:

2 1 2 3 2 4( ) 1 ( ) 1 ( ) 1V Sc Sc V sc Sc V Sc Sc

Similarly

3 1 3 2( ) 0 ( ) 0V Sc Sc V Sc Sc

3 40.102 0.105( ) 0.029

(0.06 0.105) (0.175 0.102)V Sc Sc

4 10.125 0.309( ) 0.739

(0.175 0.309) (0.240 0.125)V Sc Sc

4 2 4 3( ) 0 ( ) 1V Sc Sc V Sc Sc

Using the equation (3.9) the minimum degree of possibility can be

calculated as follows:

d (C1) = min (1,0,0.739) = 0

Similarly

d (C2) = min (0.302,0,0) = 0 d’(C3) = min (1,1,1) = 1

d (C4) = min (1,1,0.029) = 0.029

The weight vectors of the main criteria’s are:

W = [d (C1), d (C2), d (C3), d (C4)]

W = (0, 0, 1, 0.029)

52

After the normalization process, the criteria C1, C2, C3 and C4 are as

follows:

= (0, 0, 0.972, 0.029)

The results of the main criteria are tabulated in Table 3.8. The

weight of the subcriteria with respect to main criteria and weight of the

alternatives with respect to all the criteria are calculated as discussed above

and the results are listed in the Table 3.8. In this case study, the predictive

maintenance is the most preferable maintenance strategy among the four

alternatives with highest performance value of 0.972. The extent analysis

method in FAHP has a drawback of degenerating to a zero value in some

cases for the criterion environmental condition and component failure.

Alternate method for computing priority weight needs attention.

The pair-wise comparison matrix and consistency ratio are

computed using eigen vector method for the criteria ‘Training Required’ is

tabulated in the Tables 3.9 and 3.10. The pair-wise comparison matrix is

constructed, the relative weights of each element from levels II and III and the

Consistency Ratio (CR) of each matrix are analyzed as detailed in Appendix

3. The normalized global priority weights of the four main criteria and nine

subcriteria are listed in Table 3.11. From second column of

Table 3.11, it is shown that the criterion ‘Environmental Conditions’ has a

weight of 46%, the criterion ‘Component Failure’ has a weight of 29%, the

criterion ‘Training Required’ has a weight of 16% and ‘Flexibility’ 8.5%. The

global priority weight of alternatives are computed by multiplying the local

priority weight of alternatives, weight of criteria and subcriteria. The results

are tabulated in sixth column of Table 3.11.

53

54

Table 3.9 Pair-wise comparison matrix of Training Required criterion

for FAHP

TrainingRequired

Knowledge ofLabour

CostDifficulty in

TrainingPriority

Knowledge ofLabour

(1, 1, 1) (1/5,1/4,1/3) (1/7,1/6,1/5) 0.079

Cost (3, 4, 5) (1, 1, 1) (1/4,1/3,1/2) 0.292

Difficulty inTraining

(5, 6, 7) (2, 3, 4) (1, 1, 1) 0.629

Table 3.10 Consistency ratio for the pair-wise comparison matrix of

FAHP

max 3.0537

Consistency Index (CI) 0.0268

Consistency Ratio (CR) 0.046

Since CR<0.1 Pair-wise comparisonmatrix is accepted

The illustrative example of MSS in textile industry is given using

proposed AHP and FAHP models. The relative weights of subcriteria

computed using both these models are plotted in a graph as shown in

Figure 3.6. The ranking of maintenance strategies through AHP and FAHP

models is tabulated in Table 3.12. The resultant best alternative in the case of

AHP is PM > PVM > CBM > RCM and in case of FAHP is PM > PVM >

RCM > CBM.

55

56

0.857

0.143

0.833

0.1670.087

0.274

0.639

0.125

0.8750.816

0.184

0.856

0.144 0.079

0.292

0.629

0.126

0.874

0

0.2

0.4

0.6

0.8

1

M CH IS HU KL C DT EH DISubcriteria

Relative weights of subcriteria by means of AHP and FAHP

AHP

FAHP

Figure 3.6 Subcriteria weights of AHP and FAHP

Table 3.12 Ranking of maintenance strategies using AHP and FAHP

model

AHP FAHP(Extent analysis)

FAHP(Eigen vector)Maintenance

Alternatives Performancevalues

RankingPerformance

valuesRanking

Performancevalues

Ranking

PM 0.337 1 0.972 1 0.334 1CBM 0.203 3 0 4 0.174 4PVM 0.297 2 0.028 2 0.290 2RCM 0.201 4 0.008 3 0.201 3

3.5 SENSITIVITY ANALYSIS

The aggregate score of maintenance alternatives are highly

dependent on the priority weights of main criteria. The ranking order of

alternatives is influenced by the smaller changes in the criteria weights. To

analyze the impact of criteria weight on maintenance alternatives in the

proposed FAHP model, the sensitivity analysis is conducted. The sensitivity

analysis is done by exchanging each criterion weight with another criterion

weight. The different names are given for each calculation to find the ranking

57

results of each alternative. In this work, six calculations are named as CC*12,

CC*13, CC*14, CC*23, CC*24 and CC*34. Table 3.13 lists the results of

sensitivity analysis. Change of performance values for different conditions

through sensitivity analysis is shown in Figure 3.7.

Table 3.13 Sensitivity analysis results on FAHP Model

Priority weights Global score of alternativesConditions

C1 C2 C3 C4 PM CBM PVM RCMMain 0.466 0.291 0.159 0.085 0.335 0.174 0.290 0.202

1 0.291 0.466 0.159 0.085 0.329 0.167 0.309 0.1962 0.159 0.291 0.466 0.085 0.272 0.250 0.266 0.2133 0.085 0.291 0.159 0.466 0.262 0.327 0.230 0.1834 0.466 0.159 0.291 0.085 0.327 0.213 0.250 0.2115 0.466 0.085 0.159 0.291 0.326 0.266 0.211 0.1986 0.466 0.291 0.085 0.159 0.336 0.186 0.284 0.195

C1=Environmental conditions, C2=Component failure, C3= Trainingrequired, C4=Flexibility

Figure 3.7 Variations of performance values for different conditions

through sensitivity analysis

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The predictive maintenance is the best alternative in most

of the cases for the textile industry under case study. The ranking

of the alternatives under different conditions are PM>PVM>RCM>CBM,

PM>PVM>CBM>RCM, CBM>PM>PVM>RCM and PM>CBM>PVM>RCM.

The decision maker could test different weight combinations as per his

priority and could fix optimal strategy.

3.6 SUMMARY

The evaluation of maintenance strategy is a MCDM problem. The

AHP and FAHP models are proposed and developed for MSS. The proposed

AHP model is used to examine the strengths and weaknesses of the possible

maintenance strategy by comparing them with respect to appropriate criterion.

The AHP model is applied for a textile industry and the steps of decision

making process are illustrated. To eliminate the uncertainty and vagueness of

the decision makers during the pair-wise comparison process, the fuzzy set

theory is integrated with AHP and proposed as FAHP model. The adoption of

fuzzy numbers in AHP model allows the decision maker to have freedom of

estimation of priority weights for the MSS. The pair-wise comparison matrix

and consistency ratio are computed using extent analysis method and eigen

vector method. A numerical example from a textile industry is presented to

exemplify the applicability and performance of the proposed AHP and FAHP

methodologies. The sensitivity analysis is conducted to check the effect of

criteria weights on the decision making of maintenance strategy.