CHAPTER 3 MAINTENANCE STRATEGY SELECTION USING AHP AND FAHP

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 A i (for i = 1, 2, 3, M), criteria as C j (for j = 1, 2, 3,, N) and the subcriteria as SC j (for j = 1,2,3,..., N). The A 1 denotes Predictive Maintenance (PM) strategy similarly the A 2, A 3 and A 4 denote Condition-Based Maintenance (CBM), Preventive Maintenance (PVM) and

32 Reliability-Centered Maintenance (RCM) respectively. The C 1 denotes the main criterion Environmental Conditions. Similarly C 2, C 3 and C 4 represent Component Failure, Training Required and Flexibility respectively for maintenance strategy evaluation. For each criterion C j, the decision maker has to determine its importance, or weight, W j. The a ij denotes the rating of the i th maintenance strategy on deducting changes in the j th 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 A i in terms of criterion C j. 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. Level 1 Goal: Optimum MSS Level 2 Criterion 1 Criterion 2 Criterion 3. Criterion n Level 3 Subcriteria Subcriteria Subcriteria. Subcriteria Level 4 Maintenance alternative 1 Maintenance alternative 2 Maintenance alternative n 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

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, a ij represents how much criterion Component Failure factor (i) is preferred over training required criterion (j). That is a ij wi. Each of its w elements, a ij 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., a ji 1/ aij 1/ wi / wj w j / w i ). The Pair-wise comparison matrix is j A 1...... 1... w w j i... 1 wi w j (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. Goal: Selecting the best maintenance strategy Environmental Condition Component Failure Training Required Flexibility Moisture Choking Improper Sequence Higher Utilization Knowledge of Labor Cost Difficulty in Training Difficulty in Implementation Ease of Handling Predictive Maintenance Condition-Based Maintenance Preventive Maintenance Reliability-centered Maintenance Figure 3.3 Hierarchy for MSS model Table 3.1 Identified criteria for MSS Criteria (C) Environmental Conditions (EC) Component Failure (CF) Training Required (TR) Flexibility (F) Subcriteria (SC) Moisture (M) Choking (CH) Improper Sequence (IS) Higher Utilization (HU) Knowledge of Labour (KL) Cost (C) Difficulty in Training (DT) Ease of Handling (EH) Difficulty in Implementation (DI)

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 Goal Environmental Condition Component Failure Training Required Flexibility Weights Environmental Condition Component Failure 1 2 3 5 0.476 1/2 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 Relative weight Global weight Environmental Conditions Component Failure Training Required 0.476 0.288 0.154 Moisture 0.857 0.407 Choking 0.143 0.067 Improper Sequence 0.833 0.240 Higher Utilization 0.167 0.048 Knowledge of Labour 0.087 0.013 Cost 0.274 0.042 Difficult in Training 0.639 0.099 Ease of Handling 0.125 0.010 Flexibility 0.082 Difficult in Implementation 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.

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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, µ F (x), x R} where x takes its value on the real line R 1 : - < x < + and µ F (x) is a continuous mapping from R 1 to the close interval [0,1]. A triangular fuzzy number can be denoted as M = ( l, m, u). The triangular fuzzy numbers can be represented as follows: A ( x) 0, x, l, x l, m l l x m, u x, u m m x u, 0, 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 M 1 and M 2 are as follows (Kaufmann 1991).

42 Addition M1 M 2 ( l1 l2, m1 m2, u1 u 2) (3.3) Subtraction M1 M 2 ( l1 l2, m1 m2, u1 u 2) (3.4) Multiplication M1M 2 ( l1l2, m1m2, u1u 2) (3.5) M1 l1 m1 u1 Division,, M u m l 2 2 2 2 (3.6) Inverse A 1 1 1 1,, u m l 1 1 1 (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 M 1, M 3, M 5, M 7, M 9 are used to represent the assessment from equally preferred (M 1 ), moderately preferred (M 3 ), strongly preferred (M 5 ), very strongly preferred (M 7 ), extremely preferred (M 9 ) and M 2, M 4, M 6, M 8 are the middle values. The membership function of triangular fuzzy number used for FAHP is shown in Figure 3.5.

43 Expert experience Questionnaire and Data analysis Identifying the criteria and subcriteria Constructing the decision model Calculation of criteria/subcriteria weights Fuzzy set theory Calculation of the global weights of subcriteria Ranking of maintenance strategy alternatives 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 ( x 1, x, x 1) for x 3,5,7 9 (7,8,9)

44 1 Equally M 1 Moderately M 32 Strongly M 5 Very Strongly M 7 Extremely M 9 0.5 0 1 2 3 4 5 6 7 8 9 Figure 3.5 Membership functions of triangular fuzzy numbers for FAHP The fuzzy judgment matrix A( a ij) is as follows: A 1 a a a a 12 13 1( n 1) 1n a 1 a a a 21 23 2( n 1) 2n a a a 1 a ( n 1)1 ( n 1)2 ( n 1)3 ( n 1) n a a a a n1 n2 n3 n( n 1) 1 (3.8) 1, where aij 1 1 1 1 1 i j 1,3,5, 7,9 or 1,3,5,7,9, 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.

45 Extent analysis method: Let X = {x 1, x 2, x 3..., x n } represent a set of object, and G = {g 1, g 2, g 3..., g n } 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: M, M,..., M, where 1 2 m gi gi gi i i=1,2,..., m. Where M ( j 1,2,3,..., m ) all are triangular fuzzy numbers. gi 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 Sc 1, Sc 2, Sc 3, Sc 4 and Sc 5. The extent analysis synthesis values of each criterion and subcriterion are calculated. The fuzzy synthetics extent with respect to i th object can be determined by m j n m j i gi i 1 j 1 gi j 1 S M M (3.10) 1 where, m j 1 M j gi is the fuzzy addition operation of m extent analysis values for a particular matrix which can be calculated as m j m m m,, j 1 gi j 1 j j 1 j j 1 j M l m u (3.11) and the value of m m m l, m, u can be obtained j 1 j j 1 j j 1 j 1 j by the fuzzy addition operation of M ( j 1, 2,..., m ) such that gi n m j n m j,, i 1 i 1 gi i 1 i i 1 i i 1 i M l m u (3.12)

46 And the inverse of the above equation is performed as follows 1 1 1,, u m l 1 n m j M i 1 j 1 gi n n n i 1 i i 1 i i 1 i (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 M1 ( l1, m1, u1) and M 2 ( l2, m2, u2) V ( M M ) Sup [min ( ( x)), ( y )] (3.14) 2 1 y x m1 m 2 V ( M M ) hgt ( M M ) ( d ) (3.15) 2 1 1 2 M 2 1, 0, ( l1 u2), ( m u ) ( m l ) 2 2 1 2 if m if l m 2 1 u 1 2 otherwise (3.16) V ( M1 M 2) and V ( M 2 M1) 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 m ( i 1,2,... k ) can be defined by i V ( M M, M,..., M ) min V ( M M ), i 1,2,... k (3.17) 1 2 k i

47 (c) Determine the weight vector The weight vector w is then determined. Assume d( A ) min V ( S S ) for k 1,2,3,..., m 1 i k i then w d A d A d A k 1 T [ ( 1), ( 2)... ( n)] (3.18) where Ai ( i 1,2,..., n ) is n-element (d) Normalize the weight vector w ( d( A ), d( A )..., d( A )) T (3.19) 1 2 n 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 i n j 1 ij 1/ n V a (3.20)

48 V a a a a (3.21) 1/ 1 ( 11* 12 * 13 *...* 1 ) n n Eigen vector V i is compounded by the n triangular numbers defined as where V i is a triangular number defined as ( V, V, V ) l m u (b) The eigen vector is to be normalized according to the next relation w i Vl Vm Vu,, 1 1 1 V V V l m u (3.22) T w w w w 1, 2, 3,..., n wi wi wi wi (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. BPN j [( ui li ) ( mi li )] 3 l i (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 Goal Environmental Condition Component Failure Training Required Flexibility 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 Sc 1, Sc 2, Sc 3 and Sc 4. The illustrative calculation of main criterion is as below. By equation (3.10) Sc 1 = (4.33, 6.50, 9) (1/34.50, 1/27.06, 1/20.49) = (0.125, 0.240, 0.439); Sc 2 = (11, 14, 17) (1/34.50, 1/27.06, 1/20.49) = (0.318, 0.517, 0.829); Sc 3 = (1.63, 1.81, 2.17) (1/34.50, 1/27.06, 1/20.49) = (0.047, 0.066, 0.105); Sc 4 = (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 F i over F j (i equations (3.14) to (3.17) j) can be determined by 0.318 0.439 V ( Sc1 Sc2) 0.302 (0.240 0.439) (0.517 0.318) V ( Sc1 Sc3) 1 V ( Sc1 Sc2 ) 1

51 The above calculation procedure is applied to all the subsequent criteria s. The degrees of possibility of criterion are as follows: V ( Sc2 Sc1 ) 1 V ( sc2 Sc3) 1 V ( Sc2 Sc4) 1 Similarly V ( Sc3 Sc1 ) 0 V ( Sc3 Sc2) 0 0.102 0.105 V ( Sc3 Sc4) 0.029 (0.06 0.105) (0.175 0.102) 0.125 0.309 V ( Sc4 Sc1 ) 0.739 (0.175 0.309) (0.240 0.125) V ( Sc4 Sc2 ) 0 V ( Sc4 Sc3 ) 1 Using the equation (3.9) the minimum degree of possibility can be calculated as follows: d (C 1 ) = min (1,0,0.739) = 0 Similarly d (C 2 ) = min (0.302,0,0) = 0 d (C 3 ) = min (1,1,1) = 1 d (C 4 ) = min (1,1,0.029) = 0.029 The weight vectors of the main criteria s are: W = [d (C 1 ), d (C 2 ), d (C 3 ), d (C 4 )] W = (0, 0, 1, 0.029)

52 follows: After the normalization process, the criteria C 1, C 2, C 3 and C 4 are as = (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.

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54 Table 3.9 Pair-wise comparison matrix of Training Required criterion for FAHP Training Required Knowledge of Labour Knowledge of Labour Cost Difficulty in Training Priority (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 in Training (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 comparison matrix 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.

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56 1 0.8 0.6 0.4 0.2 0 Relative weights of subcriteria by means of AHP and FAHP 0.857 0.816 0.184 0.143 0.833 0.856 0.292 0.167 0.274 0.087 0.144 0.079 0.639 0.629 0.125 0.126 M CH IS HU KL C DT EH DI Subcriteria 0.874 0.875 AHP FAHP Figure 3.6 Subcriteria weights of AHP and FAHP Table 3.12 Ranking of maintenance strategies using AHP and FAHP model Maintenance Alternatives AHP Performance values FAHP (Extent analysis) Ranking Performance values FAHP (Eigen vector) Ranking Performance values Ranking PM 0.337 1 0.972 1 0.334 1 CBM 0.203 3 0 4 0.174 4 PVM 0.297 2 0.028 2 0.290 2 RCM 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 Conditions Priority weights Global score of alternatives C 1 C 2 C 3 C 4 PM CBM PVM RCM Main 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 0.196 2 0.159 0.291 0.466 0.085 0.272 0.250 0.266 0.213 3 0.085 0.291 0.159 0.466 0.262 0.327 0.230 0.183 4 0.466 0.159 0.291 0.085 0.327 0.213 0.250 0.211 5 0.466 0.085 0.159 0.291 0.326 0.266 0.211 0.198 6 0.466 0.291 0.085 0.159 0.336 0.186 0.284 0.195 C 1 =Environmental conditions, C 2 =Component failure, C 3 = Training required, C 4 =Flexibility Figure 3.7 Variations of performance values for different conditions through sensitivity analysis

58 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.