CHAPTER 4 MAINTENANCE STRATEGY SELECTION USING TOPSIS AND FUZZY TOPSIS

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1 59 CHAPTER 4 MAINTENANCE STRATEGY SELECTION USING TOPSIS AND FUZZY TOPSIS 4.1 INTRODUCTION The development of FAHP-TOPSIS and fuzzy TOPSIS for selection of maintenance strategy is elaborated in this chapter. The problem description is presented in section 4.2. The application of FAHP-TOPSIS method for selection of maintenance strategy is detailed in section 4.3. The proposed model for MSS and the stages are explained using illustrative example. Section 4.4 describes the application of fuzzy TOPSIS for MSS. The effect of criterion weights on the decision alternatives are analyzed and reported in section 4.5. The summary of the chapter is presented in section PROBLEM DESCRIPTION In maintenance strategy decision making, there are M alternatives, denoted as A i (for i = 1, 2, 3,, M) and N criteria as C (for = 1, 2, 3,, N) to be considered while choosing among alternatives. The numerical measures to represent the relative importance on performance is referred to as weights W of the criteria A set of K decision makers is involved and listed as E { D1, D2,..., D k }

2 60 A set of m possible maintenance alternatives A { A, A,..., A } ; 1 2 m A set of n criteria, C ( C1, C2,..., C n }, with which maintenance alternatives performances are measured. A set of performance ratings of A ( i 1, 2,..., m ) with respect to criteria C ( 1,2,..., n ) is called X { xi, i 1,2,..., m, 1,2,..., n }. i The fuzzy rating of each decision maker Dk ( k 1,2,..., k ) can be represented as a positive triangle fuzzy number R ( k 1,2,..., k ) with membership function k ˆ ( x ). R A good aggregation method should be evolved for the range of fuzzy rating of each decision maker. The range of aggregated fuzzy rating must include the ranges of fuzzy ratings of all decision makers. Let the fuzzy ratings of all decision makers are modeled as triangular fuzzy numbers Rˆ ( a, b, c ), k 1,2,..., k. k k k k k The obective is to choose an optimum maintenance strategy under fuzzy environment. The problem solving methodologies are detailed in the following sections. 4.3 SOLUTION METHODOLOGY THROUGH FAHP-TOPSIS The proposed evaluation procedure is shown in Figure 4.1. The solution methodology for finding an optimum maintenance strategy is as follows:

3 61 Step 1 - Decision matrix formation: The MCDM problem with m alternatives ( A, A,..., A ) that are evaluated with n criteria ( C, C,..., C ) 1 2 m 1 2 n can be represented as a geometric system with m points in n-dimensional space. An element x i of the matrix indicates the performance rating of each alternative A i with respect to the th criteria, C as below: C C C 1 2 A x x x n A x x x n n A x x x n m1 m 2 mn Identifying the evaluation criteria and maintenance alternatives F e e d b a c k Data collection Establishing decision matrix Establishing normalized decision matrix Computing the ideal and negative ideal solutions Separation of each maintenance strategy FAHP for criteria weights TOPSIS procedure Computing the relative closeness Optimum maintenance strategy selection Figure 4.1 Evaluation framework of proposed FAHP-TOPSIS for MSS

4 62 Step 2 - Calculate the normalized decision matrix: The purpose of normalizing the performance matrix is to unify the unit of matrix entries. The determination of normalized values of alternatives x i is the numerical score of alternative on criterion i. The corresponding normalized value r i is defined as follows: xi ri, i 1,2,..., m; 1,2,..., n m x i 1 2 i (4.1) Step 3 - Calculate the weighted normalized decision matrix: The weighted normalized value v i is calculated as: vi wi * ri 1,2,3,..., i 1,2,3,..., n (4.2) where w i is the weight of the i th criterion. Step 4 - The ideal and negative ideal solutions: The ideal solution (h + ) is defined as the best performance score result of all alternatives on a criterion. On contrary, the negative ideal solution (h ) is determined as the worst performance score results across all alternatives on a criterion. h ( Max vi \ J ), ( Min vi \ J ), i 1,2,..., n (4.3) h ( Min vi \ J), ( Max vi \ J), i 1,2,..., n (4.4) Step 5 - Separation of alternatives: The separation of each alternative from the ideal solution is given as: n 2 ( ), 1,..., J i 1 i D h h n (4.5)

5 63 Similarly, the separation from the negative ideal solution is given as: n 2 J ( ), 1,..., i 1 i D h h n (4.6) where D, D represents the distance between the performance scores of alternatives with respect to all criterion and all the ideal and negative ideal solutions respectively. Step 6 - Calculate the relative closeness to the ideal solution: The relative closeness of the alternative A i with respect to A + is defined as R D D D (4.7) where R denotes the final performance score in TOPSIS method, the chosen alternative which has the maximum value of performance score is expressed as the more prior alternative. To evaluate and validate the proposed model, the case study is conducted in a paper industry is explained in the following section Paper Industry Application A paper industry makes an attempt to identify a suitable maintenance strategy for a boiler in order to increase the productivity. It is the largest bagasse based paper mill, with an installed capacity of Ton Per Annum (TPA). It produces newsprint and writing papers of different varieties and grades. The utility boilers generate steam at a rate of 330 Ton Per Hour (TPH) to process a pulp mill, a soda recovery plant and paper machines. The excess steam is utilized for power generation using four turbo generators. Proposed evaluation framework: The influencing criteria on maintenance strategy is analyzed and fixed by the experts from the industry through questionnaire. Figure 4.2 shows the developed hierarchical structure

6 64 for evaluating maintenance strategy using TOPSIS. After determining the optimum maintenance strategy, the feedback mechanism is introduced to measure the effectiveness of the solution. The criteria for selection of an optimum maintenance strategy are as follows. Personnel safety: Personnel safety is a maor criterion and the failure of certain machines may cause severe inury to the personnel working on site. Facilities safety: Sudden breakdown of certain equipment often affects the performance of the other related accessories. For example, the sudden breakdown of a water-feeding pump can cause a serious damage to the corresponding boiler in a paper mill. Environmental safety: Environmental safety is one of the key norms that every industry must consider. For example, the leakage of any poisonous substance from a container will cause an irreparable damage to the environment. Equipment safety: Some failures will affect the condition of the equipment for example, fire accident will cause a heavy damage to the equipment. Hardware cost: A number of sensors and computers are indispensable in the application of Condition-Based and Predictive Maintenance strategy. Software cost: Some software tools are needed to analyse the data of measured parameters in the application of condition-based maintenance and predictive maintenance strategies. Personnel training cost: It is necessary to train the maintenance staff for adopting any kind of maintenance strategy. That is, only the training on the related tools and techniques of the maintenance will help to reach the maintenance goals. Thus the cost involved in training maintenance staff is also to be considered.

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8 66 Replacement cost: The imperfect or failed part should be replaced while performing maintenance. The total cost of these replaced parts is termed as replacement cost. Spare parts inventories: Generally, the strategy of Corrective Maintenance needs more spare parts than any other maintenance strategy. Spare parts for certain machineries are very expensive. Production loss: The breakdown of any equipment in the production line will directly affect the production and results in severe production loss in terms of quantity, quality or cost. This can be reduced by selecting a suitable maintenance strategy. Fault identification: It refers to how easily and quickly a maintenance strategy can reveal the cause and location of fault occurred to the maintenance engineers by which it reduces the time of maintenance and increases the availability of the machine. Generally, Condition Based and Predictive Maintenance strategies offer a quick fault identification. Acceptance by labour: The acceptance of the persons who are directly involved in maintenance is very important. So the acceptance level and the point of view of these persons should be considered. Generally, they prefer maintenance strategy which can be easily implemented. Technique reliability: Certain maintenance strategy can be easily adapted to certain equipment but it will not be so for some other equipment. For example, predictive maintenance may be difficult for some machines of complicated structure.

9 67 Sequence of work: It is the sequence of actions that have to be performed for particular type of maintenance work. It differs from one maintenance strategy to other. Maintainability: The ease and speed with which any maintenance activity can be carried out on a part of equipment may be measured in terms of Mean Time To Repair (MTTR). It is a function of equipment design, and maintenance task design. The implementation of the solution methodology is explained in the following steps: Step 1 - Decision matrix formation for MSS: The identified criteria and maintenance alternatives are listed in Table 4.1. Table 4.1 Identified evaluation criteria and maintenance alternatives for TOPSIS models Evaluation criteria Personnel safety (C 1 ) Software cost (C 6 ) Fault identification (C 11 ) Facilities safety (C 2 ) Personnel training (C 7 ) Environment safety (C 3 ) Replacement (C 8 ) Equipment safety (C 4 ) Spare parts inventories (C 9 ) Acceptance by labour (C 12 ) Technique reliability (C 13 ) Sequence of work (C 14 ) Hardware cost (C 5 ) Production loss (C 10 ) Maintainability (C 15 ) Maintenance strategy alternatives Corrective Maintenance (CM) Time-Based Maintenance (TBM) Condition-Based Maintenance (CBM) Predictive Maintenance (PM)

10 68 The weights are computed using any one of the following methods: AHP, Weighted Sum Method and Weighted Least Square Method. Although some observations are obtained from the examples, the weights of each criterion are similar but weight estimation by FAHP is accurate. The weight inputs for the proposed TOPSIS model are calculated using FAHP as explained in section 3.4 of chapter 3. The decision matrix is formulated and tabulated in Table 4.2. Table 4.2 Decision matrix of maintenance alternatives for TOPSIS CM TBM CBM PM Personnel safety Facilities safety Environment safety Equipment safety Hardware cost Software cost Personnel training Replacement Spare parts inventories Production loss Fault identification Acceptance by labour Technique reliability Sequence of work Maintainability

11 69 Step 2 - The normalized decision matrix is built using equation (4.1) and is tabulated in Table 4.3. Table 4.3 Normalized decision matrix using TOPSIS CM TBM CBM PM Personnel safety Facilities safety Environment safety Equipment safety Hardware cost Software cost Personnel training Replacement Spare parts inventories Production loss Fault identification Acceptance by labour Technique reliability Sequence of work Maintainability Step 3 - The weighted normalized decision matrix is computed using equation (4.2) and tabulated in Table 4.4.

12 70 Table 4.4 Weighted normalized decision matrix using TOPSIS CM TBM CBM PM Personnel safety Facilities safety Environment safety Equipment safety Hardware cost Software cost Personnel training Replacement Spare parts inventories Production loss Fault identification Acceptance by labour Technique reliability Sequence of work Maintainability Step 4 - The computed distance between ideal and negative ideal solution for each maintenance strategy is calculated by using equations (4.3) and (4.4). h {0.065,0.009, 0.021, 0.076,0.009,0.020, 0.008, 0.002, 0.028,0.045,0.007, 0.036,0.068,0.027, 0.017} h {0.003,0.000,0.000, 0.001, 0.000,0.000, 0.000,0.000,0.000, 0,000,0.000,0.000, 0.003, 0.000,0.001,0.000}

13 71 Step 5 - The separation of each alternative for the ideal and negative ideal solutions is computed using equations (4.5) and (4.6) and are tabulated in Table 4.5. Table 4.5 Separation of ideal and negative ideal solution of alternatives using TOPSIS CM TBM CBM PM D D D D D D D D Step 6 - The relative closeness to the ideal solution is determined by using equation (4.7). The results of relative closeness of maintenance strategy alternatives are tabulated in Table 4.6. Table 4.6 Relative closeness to the ideal solution using TOPSIS CM TBM CBM PM CC1 CC2 CC3 CC Based on CC values, the ranking of the maintenance alternatives in descending order are PM > CBM > CM > TBM. The predictive maintenance is the most preferable maintenance strategy with the highest relative closeness value of In TOPSIS, the weights of the maintenance evaluation criterion and the ratings of maintenance alternatives are treated as crisp numerical data. However, under many conditions crisp data are inadequate to model the MSSP. To deal with such uncertain situations fuzzy TOPSIS is proposed and developed.

14 SOLUTION METHODOLOGY THROUGH FUZZY TOPSIS The fuzzy approach is used to assign the relative importance of criterion using fuzzy linguistics instead of precise numbers. The proposed method is suitable for solving the group decision making MSSP under fuzzy environment. The schematic diagram of the proposed fuzzy TOPSIS model is shown in Figure 4.3. Framing a the committee of decision makers Identification of maintenance evaluation criteria Choosing the appropriate linguistic variables Aggregating the fuzzy weight of criterion Construction of fuzzy decision matrix Normalization of fuzzy decision matrix Construction of weighted normalized fuzzy decision matrix Determination of FPIS and FNIS Calculating the distance of each maintenance alternative from FPIS and FNIS Calculation of the closeness coefficient of each maintenance alternative Ranking the maintenance alternatives according to their closeness coefficient Figure 4.3 Steps of the proposed fuzzy TOPSIS model for MSS

15 73 follows: The proposed fuzzy TOPSIS model algorithm is described as Step 1 - In a decision making committee of K decision makers, fuzzy rating of each decision maker D ( k 1, 2,..., k ) is represented as k triangular fuzzy numbers with membership function ( ) a x. Step 2 - Then the evaluation criteria and the appropriate linguistic variables are chosen for evaluating maintenance strategy evaluation criteria and alternatives. as below: Step 3 - The fuzzy multi attribute decision making matrix is created D C C C C A x x x x n A x x x x n A x x x x n n A x x x x n m1 m 2 m3 mn w [ w1, w2,..., w n ] where x, i 1,2,..., m, 1,2,..., n and w, 1,2,..., n are linquistic triangular i fuzzy numbers, xi ( ai, bi, ci ) and w ( w1, w 2, w 3). Note that x i is the performance rating of the i th alternative, A i, with respect to the th criteria, C and w represents the weight of the th criteria, C. Step 4 - The purpose of linear scales transform normalization function used in this study is to preserve the property that the ranges of

16 74 normalized triangular fuzzy numbers to be included in [0, 1]. If R denotes the normalized fuzzy decision matrix, then R [ r ] i 1,2,..., m; 1,2,..., n (4.8) i m n ai bi ci where ri,, * * * c c c C max C * i i Step 5 - Considering the importance of each criterion, the weighted normalized decision matrix can be computed by multiplying the important weights of evaluation criteria and values in the normalized fuzzy decision matrix vi ri (.) w (4.9) Here w represents the importance weight of criterion C according to the weighted normalized fuzzy decision matrix, normalized positive triangular fuzzy numbers can also approximate the elements v i, i,. Step 6 - The Fuzzy Positive Ideal Solution (FPIS A + ) and Fuzzy Negative Ideal Solution (FNIS A ) hence can be defined as A ( v, v, v ) {(max v \ i 1,2,..., m), 1,2,..., n }, (4.10) 1 2 n i i A ( v, v, v ) {(min v \ i 1,2,..., m), 1,2,..., n }, (4.11) 1 2 n i i

17 75 Step 7 - The distance of each maintenance strategy alternatives from FPIS and FNIS can be derived as n * i ( i, ), 1,2,..., 1 d dv v v i m (4.12) n * i ( i, ), 1,2,..., 1 d dv v v i m (4.13) where d v (...) is the distance measurement between two fuzzy numbers, di represents the distance of the alternative A i from FPIS, and distance of the alternative A i from FNIS. di is the Step 8 - The closeness coefficient (CC i ) is defined to rank all possible alternatives. The closeness coefficient represents the distance to the fuzzy positive ideal solution (CC i ) (A + ) and fuzzy negative ideal solution (A - ) simultaneously. The closeness coefficient of each alternative is calculated as di CCi, i 1,2,..., m d d i i (4.14) Step 9 - Rank the preference order. Choose an alternative with maximum CC i. The illustration of the proposed model is explained in the next section Case Study of a Paper Industry A high-technology paper manufacturing company desires to select an optimum maintenance strategy to maintain a critical boiler equipment. There are three decision makers (D1, D2 and D3) are involved in the selection of a suitable maintenance strategy. Fifteen evaluation criteria and four maintenance strategy alternatives have been considered as listed in Table 4.1.

18 76 The snapshot of the fuzzy TOPSIS spreadsheet model is shown in Figure 4.4. The computational procedure of the proposed method is summarized as follows. Calculation of the synthetic important weights of evaluation criteria: The decision makers have to use the linguistic variables to evaluate the importance of criteria and ratings of maintenance alternatives with respect to each criterion. In order to demonstrate the idea of fuzzy linguistics approach in MCDM, the precise values are transformed into seven levels of fuzzy linguistic variables such as Very Low (VL), Low (L), Medium Low (ML), Medium (M), Medium High (MH), High (H) and Very High (VH). The triangular and trapezoidal fuzzy numbers are likely to be the most adaptable one for fuzzy linguistic representation due to their simplicity in modeling and easy interpretation. The triangular fuzzy number can adequately represent the seven-level fuzzy linguistic variables. Based on the interval scale assumptions, a transformation table could be constructed and tabulated in Table 4.7. For example, the fuzzy linguistic variable - Very Low has its associated triangular fuzzy number with minimum of 0, mode of 0.10 and maximum of 0.2. The membership function which is the same definition is applied to other fuzzy variables- low, medium, high and very high. Figure 4.5 illustrates the fuzzy triangular membership functions. Similarly the linguistic variables for alternatives with respect to each criterion are framed and listed in Table 4.8. very low 0, x 0 x 0, x 0.1, 0.2 x, x 0.2 0, x 0.2

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20 78 Table 4.7 Linguistic variables and corresponding fuzzy number for fuzzy TOPSIS Linguistic variables Triangular fuzzy numbers Very low (VL) (0,0,0.2) Low (L) (0.1,0.2,0.3) Medium low (ML) (0.2,0.3,0.5) Medium (M) (0.3,0.5,0.6) Medium high (MH) (0.5,0.6,0.7) High (H) (0.6,0.7,0.8) Very high (VH) (0.7,1,1) VL L ML M MH H VH Figure 4.5 Fuzzy triangular membership functions for corresponding linguistic variables in fuzzy TOPSIS model

21 79 The linguistic variables for rating of maintenance alternative good can be represented as (7, 8, 9), the membership function which is Good 0, x 7 x 7, x 8, 9 x, x 9 0, x 9 Table 4.8 Linguistic variables for ratings of fuzzy TOPSIS Linguistic variables Triangular fuzzy numbers Very poor (VP) (0,0,2) Poor (P) (1,2,3) Medium poor (MP) (2,3.5,5) Fair (F) (4,5,6) Medium good (MG) (5,6.5,8) Good (G) (7,8,9) Very good (VG) (8,10,10) Figure 4.6 illustrates the fuzzy triangular membership functions for importance of maintenance alternatives. The maintenance representatives were requested to express the level of importance for each evaluation criterion in linguistic variables are listed in Table 4.9.

22 80 VP P MP F MG G VG Figure 4.6 Fuzzy triangular membership functions for importance of maintenance alternatives in fuzzy TOPSIS model Table 4.9 Qualitative assessment of criteria weight from decisionmakers for fuzzy TOPSIS Criteria Decision makers D 1 D 2 D 3 Personnel safety VH VH H Facilities safety MH MH VH Environment safety ML MH H Equipment safety H H H Hardware cost VH H MH Software cost VH H VH Personnel training H MH MH Replacement VL L L Spare parts inventories VL L L Production loss M ML ML Fault identification M M M Acceptance by labour L H MH Technique reliability VH M ML Sequence of work MH MH M Maintainability MH MH H

23 81 Construction of the fuzzy decision matrix: The fuzzy linguistic variables are used to express the rating of each maintenance strategy with respect to each evaluation criterion. To evaluate the rating of alternatives, the evaluators have to adopt the linguistic term from Table 4.8. The questionnaire designs are presented in Appendix 4 to evaluate the alternatives of maintenance strategy according to selection criteria. The rating of four maintenance alternatives under 15 criteria are listed in Table The evaluators often may have different understanding for the same evaluation criterion. The fuzzy performance rating of evaluation criterion can be averaged to synthesize the various individual udgments. The fuzzy decision matrix is formed as tabulated in Table Table 4.10 Ratings of the alternatives by decision-makers under various criteria for TOPSIS Decision makers Decision makers Criteria Alternatives Criteria Alternatives D 1 D 2 D 3 D 1 D 2 D 3 CM P MP F CM P MP F C1 C 3 C 5 TBM MG G G TBM F G G C 2 CBM G MG G CBM MG G G PM G G G PM MG G G CM F MP G CM F P P TBM F G G TBM G MG MG C 4 CBM MG G G CBM G G F PM MG G G PM G G MG CM VP VP VP CM P P VP TBM F MG MP TBM P F MG C 6 CBM MG G MG CBM G G MG PM G G G PM VG VG G

24 82 Table 4.10 (Continued) Decision makers Decision makers Criteria Alternatives Criteria Alternatives D 1 D 2 D 3 D 1 D 2 D 3 CM VG G VG CM VG VG VG C 7 C 9 C 11 C 13 C 15 TBM G F G TBM G VG G CBM F P P C 8 CBM P G G PM F VP P PM VP VP P CM G G F CM P P P TBM MG G F TBM MG P MP C 10 CBM MP MP P CBM G F MP PM P P VP PM G MP P CM F P P CM VP P F TBM MG MP P TBM G G F C 12 CBM G MG G CBM MG MG MP PM G MG G PM MG F MP CM P P VP CM F P P TBM MG G F TBM G G F C 14 CBM MG MG G CBM G MG MP PM G MG G PM G F P CM F P VP TBM MG G F CBM MG G F PM MG G MG

25 83 Table 4.11 Fuzzy decision matrix and fuzzy weights of four alternatives using fuzzy TOPSIS CM TBM CBM PM Weight Personnel safety (1,3.5,6) (5,7.5,9) (5,7.5,9) (7,8,9) (0.70,0.93,1) Facilities safety (1,3.5,6) (4,7,9) (5,7.5,9) (5,7.5,9) (0.50,0.77,1) Environment safety (2,5.5,9) (4,7,9) (5,7.5,9) (5,7.5,9) (0.20,0.60,0.9) Equipment safety (1,3,6) (5,7,9) (4,7,9) (5,7.5,9) (0.70,0.80,0.9) Hardware cost (0,0,2) (2,5,8) (5,7,9) (7,8,9) (0.50,0.82,1) Software cost (0,1.33,3) (1,4.5,8) (5,7.5,9) (7,9.33,10) (0.70,0.93,1) Personnel training (7,9.33,10) (4,7,9) (1,3,6) (0,2.33,6) (0.50,0.70,0.9) Replacement (8,10,10) (7,8.67,10) (1,6,9) (0,0.67,3) (0.00,0.13,0.3) Spare parts inventories (4,7,9) (4,6.5,9) (1,3,5) (0,1.33,3) (0.00,0.13,0.3) Production loss (1,2,3) (1,4,8) (2,5.5,9) (1,3.5,6) (0.20,0.40,0.6) Fault identification Acceptance by labour Technique reliability (1,3,6) (1,4,8) (5,7.5,9.) (5,7.5,9) (0.40,0.50,0.6) (0,2.33,6) (4,7,9) (2,5.5,8) (2,4.5,6) (0.10,0.55,0.9) (0,1.33,3) (4,6.5,9) (5,7,9) (5,7.5,9) (0.20,0.62,1) Sequence of work (1,3.0,6) (4,7,9) (2,6,9) (1,5,9) (0.40,0.60,0.8) Maintainability (0,2.33,6) (4,6.5,9) (4,6.5,9) (5,7,9) (0.50,0.70,0.9) Normalization of the fuzzy decision matrix: The normalized triangular fuzzy numbers are included in the interval [0, 1] using the linear scale transform functions. The synthetic fuzzy decision matrix is normalized using equation (4.8) and tabulated in Table 4.12.

26 84 Table 4.12 Normalized fuzzy decision matrix using fuzzy TOPSIS Personnel safety Facilities safety Environment safety Equipment safety CM TBM CBM PM (0.11,0.39,0.67) (0.56,0.83,1) (0.56,0.83,1) (0.78,0.89,1) (0.11,0.39,0.67) (0.44,0.78,1) (0.56,0.83,1) (0.56,0.83,1) (0.22,0.61,1) (0.44,0.78,1) (0.56,0.83,1) (0.56,0.83,1) (0.11,0.33,0.67) (0.56,0.78,1) (0.44,0.78,1) (0.56,0.83,1) Hardware cost (0,0,0.22) (0.22,0.56,0.89) (0.56,0.78,1) (0.78,0.89,1) Software cost (0,0.13,0.3) (0.1,0.45,0.8) (0.5,0.75,0.9) (0.7,0.93,1) Personnel training (0.7,0.93,1) (0.4,0.7,0.9) (0.1,0.3,0.6) (0,0.23,0.6) Replacement (0.80,1,1) (0.70,0.87,1) (0.1,0.6,0.9) (0,0.07,0.3) Spare parts inventories (0.44,0.78,1) (0.44,0.72,1) (0.11,0.33,0.56) (0,0.15,0.33) Production loss (0.11,0.22,0.33) (0.11,0.44,0.89) (0.22,0.61,1) (0.11,0.39,0.67) Fault identification Acceptance by labour Technique reliability Sequence of work (0.11,0.33,0.67) (0.11,0.44,0.89) (0.56,0.83,1) (0.56,0.83,1) (0,0.26,0.67) (0.44,0.78,1) (0.22,0.61,0.89) (0.22,0.5,0.67) (0,0.15,0.33) (0.44,0.72,1) (0.56,0.78,1) (0.56,0.83,1) (0.11,0.33,0.67) (0.44,0.78,1) (0.22,0.67,1) (0.11,0.56,1) Maintainability (0,0.26,0.67) (0.44,0.72,1) (0.44,0.72,1) (0.56,0.78,1) Formation of the weighted normalized fuzzy decision matrix: The important weights of criteria are different, the weighted normalized fuzzy decision matrix is computed using equation (4.9) and the results are tabulated in Table 4.13.

27 85 Table 4.13 Weighted normalized fuzzy decision matrix using fuzzy TOPSIS Personnel safety Facilities safety Environment safety Equipment safety CM TBM CBM PM (0.08,0.36,0.67) (0.39,0.78,1.00) (0.39,0.78,1.00) (0.54,0.83,1.00) (0.06,0.30,0.67) (0.22,0.60,1.00) (0.28,0.64,1.00) (0.28,0.64,1.00) (0.04,0.37,0.90) (0.09,0.47,0.90) (0.11,0.50,0.90) (0.11,0.50,0.90) (0.08,0.27,0.60) (0.39,0.62,0.90) (0.31,0.62,0.90) (0.39,0.67,0.90) Hardware cost (0.00,0.00,0.22) (0.11,0.45,0.89) (0.28,0.64,1.00) (0.39,0.73,1.00) Software cost (0.00,0.12,0.30) (0.07,0.42,0.80) (0.35,0.70,0.90) (0.49,0.87,1.00) Personnel training (0.35,0.65,0.90) (0.20,0.49,0.81) (0.05,0.21,0.54) (0.00,0.16,0.54) Replacement (0.00,0.13,0.30) (0.00,0.12,0.30) (0.00,0.08,0.27) (0.00,0.01,0.09) Spare parts inventories (0.00,0.10,0.30) (0.00,0.10,0.30) (0.00,0.04,0.17) (0.00,0.02,0.10) Production loss (0.02,0.09,0.20) (0.02,0.18,0.53) (0.04,0.24,0.60) (0.02,0.20,0.60) Fault identification Acceptance by labour Technique reliability Sequence of work (0.04,0.17,0.40) (0.04,0.22,0.53) (0.22,0.42,0.60) (0.22,0.42,0.60) (0.00,0.14,0.60) (0.04,0.43,0.90) (0.02,0.34,0.80) (0.02,0.31,0.80) (0.00,0.16,0.67) (0.09,0.45,1.00) (0.11,0.48,1.00) (0.11,0.51,1.00) (0.04,0.20,0.53) (0.18,0.43,0.80) (0.09,0.40,0.80) (0.04,0.33,0.80) Maintainability (0.00,0.10,0.30) (0.22,0.54,0.90) (0.22,0.51,0.90) (0.28,0.54,0.90) Determination of the fuzzy positive and fuzzy negative ideal solution: Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) are determined using equations (4.10) and (4.11). A (1,1,1), (1,1,1), (0.9,0.9,0.9), (0.9,0.9,0.9), (1,1,1),(1,1,1) (0.9,0.9, 0.9), (0.3, 0.3, 0.3), (0.3, 0.3, 0.3), (0.6, 0.6,0.6), (0.6, 0.6,0.6), (0.9,0.9,0.9),(1,1,1), (0.8,0.8,0.8), (0.9,0.9,0.9)

28 86 A (0.8,0.8,0.8),(0.6,0.6, 0.6),(0.04,0.04,0.04),(0.08, 0.08,0.08) (0,0,0),(0,0,0),(0,0,0), (0,0,0), (0,0,0), (0.02,0.02,0.02), (0.04,0.04,0.04),(0,0,0),(0,0, 0),(0, 0,0),(0.04,0.04,0.04),(0,0, 0) Calculation of the distance of each maintenance alternatives to FPIS and FNIS: The distance of each alternative from FPIS and FNIS with respect to each criterion is calculated using equations (4.12) and (4.13). d CM A (, ) [(1 0.08) (1 0.36) (1 0.67) ] 0.67 d CM A (, ) [( ) ( ) ( ) ] 0.49 The computed values of each maintenance strategy alternative are listed in Tables 4.14 and Table 4.14 Distance between Ai ( i =1,2,...) and A + with respect to each criterion d(cm, A + ) d(tbm,a + ) d(cbm, A + ) d(pm, A + ) Personnel safety Facilities safety Environment safety Equipment safety Hardware cost Software cost Personnel training Replacement Spare parts inventories Production loss Fault identification Acceptance by labour Technique reliability Sequence of work Maintainability

29 87 Table 4.15 Distance between Ai ( i =1,2,...) and A - with respect to each criterion d(cm, A - ) d(tbm, A - ) d(cbm, A - ) d(pm, A - ) Personnel safety Facilities safety Environment safety Equipment safety Hardware cost Software cost Personnel training Replacement Spare parts inventories Production loss Fault identification Acceptance by labour Technique reliability Sequence of work Maintainability The closeness coefficient for ranking of alternatives: di and di of four maintenance strategy alternatives are calculated using equation (4.13) and the results are tabulated in Table The closeness coefficients of four alternatives are calculated as follows: CC CC CC CC

30 88 Table 4.16 Computation of d +,d - and CC i i i CM TBM CBM PM Ranking order di di CC PM>CBM>TBM>CM The final rank of each maintenance strategy is tabulated in Table The predictive maintenance is the most preferable maintenance strategy among the four alternatives with the performance value of The Condition-based maintenance, Time-based maintenance and Corrective maintenance are ranked as second, third and fourth respectively with performance value of 0.508, 0.490, and To analyze the changes in the ranking of maintenance strategy alternatives under different criteria weights, a sensitivity analysis is conducted and it is explained in the next section. 4.5 SENSITIVITY ANALYSIS The sensitivity analysis is performed by interchanging the weights of the criteria corresponding ranking position of each maintenance alternative. There are ten combinations of weight changes framed and each combination is stated as a condition. The weighted normalized decision matrices and the relative closeness to the ideal solution (CC i ) for each interchange are calculated. The sensitivity analysis results can be seen from Table 4.17 and graphically from Figure 4.7.

31 89

32 Sensitivity analysis CM CBM TBM PM Conditions Figure 4.7 Closeness coefficients of maintenance alternatives through sensitivity analysis The ranking order of the maintenance alternatives for different conditions are PM>CBM>TBM>CM. The fuzzy TOPSIS spread sheet is developed to avoid tedious computation of the relative closeness to the ideal solution (CC i ) for each interchanging criterion weight. 4.6 SUMMARY The integration of consultative FAHP and TOPSIS approaches for MSS are proposed and developed in this research. The FAHP is used to analyze the structure of the MSSP and determine weights of the criteria, the TOPSIS method is used to obtain final ranking. Fuzzy TOPSIS model is proposed and developed to overcome the cumbersome pair-wise comparison process and inconsistency existing in the hierarchical structuring process. The criterion weight is assessed by means of linguistic values. The linguistic ratings are expressed in triangular fuzzy numbers to express the subective udgments of evaluators. The FAHP-TOPSIS and fuzzy TOPSIS models are applied for a paper industry and the steps of decision making process are illustrated. The proposed fuzzy TOPSIS model has significantly increased the efficiency of decision making process in MSS in comparison with FAHP- TOPSIS. A sensitivity analysis is conducted to study the results variation caused by the interchanges of criteria weights.