Selection of optimum maintenance strategy based on FAHP integrated with GRA–TOPSIS

Abstract

In today’s competitive environment, industries are required to increase reliability and safety level of their equipment with reasonable cost. Consequently, it is essential to select the appropriate maintenance strategy. In the paper industry, pumping of cooked pulp requires abrasion- and sometimes corrosion-resistant pumps that are able to handle up to 70 % solids content. But the maintenance engineer and supervisor often face failures of the pump. Hence, this article describes the application of multi criteria decision-making (MCDM) technique for the selection of optimum maintenance strategy for pumps used in the paper industry. The proposed hybrid MCDM model comprises fuzzy analytical hierarchy process (FAHP), grey relational analysis (GRA), and technique for order preference by similarity to ideal solution (TOPSIS) technique. The FAHP is used to compute the criteria weights whereas GRA–TOPSIS is used for determining the ranking of alternatives. This study discusses four maintenance strategies: corrective maintenance, predictive maintenance, time-based preventive maintenance, and condition-based maintenance. Four main criteria—safety, cost, added value, and feasibility—have been used to evaluate the optimum maintenance strategy.

Appendices

Appendix 1

1.1 Questionnaire

Read the following questions and put check marks on the pair wise comparison matrices. If a criterion on the left is more important than the matching one on the right, put the check mark to the left of the importance ‘Equal’ under the importance level. If a criterion on the left is less important than the matching one on the right, put your check mark to the right of the importance ‘Equal’ under the importance level.

1.2 Criteria

With respect to safety

• Q1 How important is the safety (C1) when it is compared with cost (C2)?

• Q2 How important is the safety (C1) when it is compared with added value (C3)?

• Q3 How important is the safety (C1) when it is compared with feasibility (C4)?

With respect to cost

• Q4 How important is the cost (C2) when it is compared with added value (C3)?

• Q5 How important is the cost (C2) when it is compared with feasibility (C4)?

With respect to added value

• Q6 How important is the added value (C3) when it is compared with feasibility (C4)?

1.3 Subcriteria

1.3.1 Safety

With respect to personnel

• Q7 How important is the personnel (SC1) when it is compared with facilities (SC2)?

• Q8 How important is the personnel (SC1) when it is compared with environment (SC3)?

With respect to facilities

• Q9 How important is the facilities (SC2) when it is compared with environment (SC3)?

1.4 Cost

With respect to spare part inventories

• Q10 How important is the spare part inventories (SC1) when it is compared with production loss (SC2)?

• Q11 How important is the spare part inventories (SC1) when it is compared with fault identification (SC3)?

With respect to production loss

• Q12 How important is the production loss (SC2) when it is compared with fault identification (SC3)?

1.5 Added value subcriteria

With respect to Hardware

• Q13 How important is the Hardware (SC1) when it is compared with Software (SC2)?

• Q14 How important is the Hardware (SC1) when it is compared with personnel training (SC3)?

• Q15 How important is the Hardware (SC1) when it is compared with Replacement (SC4)?

With respect to Software

• Q16 How important is the Software (SC2) when it is compared with personnel training (SC3)?

• Q17 How important is the Software (SC2) when it is compared with Replacement (SC4)?

With respect to personnel training

• Q18 How important is the personnel training (SC3) when it is compared with Replacement (SC4)?

1.6 Feasibility subcriteria

With respect to Acceptance by labor

• Q19 How important is the Acceptance by labor (SC1) when it is compared with Technique reliability (SC2)?

• Q20 How important is the Acceptance by labor (SC1) when it is compared with procedure (SC3)?

• Q21 How important is the Acceptance by labor (SC1) when it is compared with Maintainability (SC4)?

With respect to Technique reliability

• Q22 How important is the Technique reliability (SC2) when it is compared with procedure (SC3)?

• Q23 How important is the Technique reliability (SC2) when it is compared with Maintainability (SC4)?

With respect to procedure

• Q24 How important is the procedure (SC3) when it is compared with Maintainability (SC4)?

Appendix 2

1.1 Methodology for TOPSIS

TOPSIS was developed by Hwang and Yoon (1981). The procedure of TOPSIS method as follows:

Step 1: Determine 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 $x_{ij}$ is the numerical score of alternative $j$ on criterion n. The corresponding normalized value $r_{ij}$ is defined as follows.

$$\begin{aligned} r_{ij} =\frac{f_{ij} }{\sqrt{\sum \nolimits _{j=1}^J f_{ij}^2 }}j=1,2,3,\ldots , J, \quad i=1,2,3,\ldots ,n \end{aligned}$$

Step 2: Calculate the weighted normalized decision matrix. The weighted normalized value $v_{ij}$ is calculated as:

$$\begin{aligned} v_{ij} =w_i *r_{ij} j=1,2,3,\ldots ,J, \quad i=1,2,3,\ldots ,n, \end{aligned}$$

where $\hbox {w}_\mathrm{i}$ is the weight of the $\hbox {i}^{\mathrm{th}}$ attribute or criterion.

Step 3: The ideal and negative ideal solutions of maintenance alternatives: The ideal solution $\left( {A^{+}} \right)$ is defined as the best performance score result of all alternatives on a criterion. On contrary, the negative ideal solution is $\left( {\hbox {A}^{-}} \right)$ is determined as the worst performance score result across all alternatives on a criterion.

$$\begin{aligned} A^{+}=\left\{ {\hbox {A}_1^+ ,\ldots ,\hbox {A}_\mathrm{n}^+ } \right\} =\left\{ {\left( {\max \limits _j v_{\mathrm{ij}} |\hbox {i}\in \hbox {I}^{{\prime }}} \right) ,\left( {\mathop {\min }\limits _j v_{\mathrm{ij}} |\hbox {i}\in \hbox {I}^{\prime \prime }} \right) } \right\} \\ A^{-}=\left\{ {\hbox {A}_1^{-} ,\ldots ,\hbox {A}_\mathrm{n}^{-} } \right\} =\left\{ {\left( {\mathop {\min }\limits _j v_{\mathrm{ij}} |\hbox {i}\in \hbox {I}^{{\prime }}} \right) ,\left( {\mathop {\max }\limits _j v_{\mathrm{ij}} |\hbox {i}\in \hbox {I}^{\prime \prime }} \right) } \right\} \end{aligned}$$

Where $I^{{{\prime }}}$ a set of is benefit attributes (large value means better performance) and $I^{{{\prime }{\prime }}}$ is a set of cost attributes (smaller value means better performance).

Step 4: Separation of each maintenance alternative for the ideal and negative ideal solution

After determining the ideal solution and negative ideal solution, the distance between the two solutions for each alternative are given as

$$\begin{aligned} D_j +=\sqrt{\sum _{i=1}^n {(v_{ij} -v_i^+ } )^{2}},\quad \hbox {j} = 1,2,3,{\ldots },\hbox {J}.\\ D_j^- =\sqrt{\sum _{i=1}^n {(v_{ij} -v_i^- } )^{2}}, \quad \hbox {j} = 1,2,3,{\ldots },\hbox {J}. \end{aligned}$$

where $\hbox {D}^{+}_{\mathrm{j}}$ and $\hbox {D}^{-}_{\mathrm{j}}$ represents the distance between the performances scores of alternatives with respect to all criteria and all the ideal and negative ideal solutions respectively.

Step 5: Calculation of relative closeness to the ideal solution

$$\begin{aligned} CC_j^+ =\frac{D_j^- }{D_j^+ +D_j^- },\quad \hbox {j} = 1,2,3,{\ldots },\hbox {J}. \end{aligned}$$

where $\hbox {CC}_j^{+}$ denotes the final performance score in TOPSIS method, the chosen alternative has the maximum value of performance score expressed as the more prior alternatives.