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.

1 Introduction

Maintenance system has a vital role in the development and progress of manufacturing and process industries. In general, operation and maintenance are synonymous with high level of availability, reliability, and assets’ operability linking with production and profit of the organization. The minimum cost of maintenance with reliable maintenance actions is ideal for all manufacturers, whereas more maintenance activity will reduce the chances of machine failures but will increase the maintenance cost. However, less maintenance will reduce the cost of maintenance but cause more machine failures (Pourjavad et al. 2013). Improper maintenance of the equipment leads to delay in shipping schedule, loss of profit, loss of opportunity, and increase in the production cost (Zaim et al. 2012). Bevilacqua and Braglia (2000) reported that owing to lack of maintenance operations the maintenance cost varies from 15 to 70 % of total production cost, according to the type of the industry. Maintenance options will vary depending on the equipment and its location. Each equipment design and operation differs, and certain equipment will have a higher probability to undergo failures from different degradation mechanisms than others. To reduce equipment failures, we should consider different maintenance strategies, including preventive maintenance and PM (Ding et al. 2014). The selection of an apt maintenance strategy is important as well as complex in maintenance management, and the output of maintenance is hard to measure and quantify (Mechefske and Wang 2003). The right strategy to counter any type of failure of machines will improve the life-cycle profit or reduce the life-cycle cost (Labib 1998). The evaluation and selection of suitable maintenance strategy involve various conflicting criteria such as safety, cost, added value, and feasibility. Thus, selection of the maintenance strategy is a multicriteria decision-making (MCDM) problem in the presence of many criteria and subcriteria. Numerous research works were carried out during the past few decades in the maintenance management research domain using different MCDM methods (Table 1). Triantaphyllou et al. (1997) stated that analytical hierarchy process (AHP) is the most popular tool among all other MCDM tools. The main advantages of the AHP are based on pair-wise comparison. Also, the AHP calculates the inconsistency index, which is the ratio of the decision-maker’s inconsistency (Önüt and Soner 2008). Even though the AHP is widely used in many decision-making problems, very few authors have listed the limitations of its usage. The conventional AHP cannot reflect the human thinking style (Deng 1999; Cheng et al. 1999; Mikhailov 2003; Chan et al. 2008). Numerical values are exact numbers that are useful only for crisp decision-making applications. To deal with indistinctness of human thoughts, Zadeh (1965) introduced fuzzy set theory to express the linguistic terms in the decision-making process. To overcome the shortcoming of the AHP, the fuzzy linguistic terms are used with AHP and known as fuzzy analytical hierarchy process (FAHP). Many researchers have combined the fuzzy theory into the AHP method to amend its application (Buckley 1985). Chan and Kumar (2007) and Chan et al. (2008) proposed the FAHP to evaluate the supplier selection and to make decisions to solve problems related with advanced manufacturing technology. Shamsuzzaman et al. (2003) proposed to use a fuzzy set and AHP to select the best flexible manufacturing system from a number of feasible alternatives. Ensuring a consistent pair-wise comparison is a challenging task in FAHP method. Moreover, establishing a pair-wise comparison matrix requires $n(n-1)/2$ judgments for a level with $n$ criteria. The number of comparisons increases as the number of criteria increases, thereby leading to inconsistent judgments by the decision-maker.

Table 1 Literature related to maintenance strategy selection

The technique for order preference by similarity to ideal solution (TOPSIS) was first developed by Hwang and Yoon (1981). TOPSIS is relatively simple and fast, with a systematic procedure (Shanian and Savadogo 2006). It is proven as one of the best methods in addressing the rank reversal issue (Ertuğrul and Karakaşoğlu 2009). The basic idea of TOPSIS is that the best decision should be made to be closest to the ideal and far from the nonideal situation. The positive-ideal solution is a solution that maximizes the benefit criteria and minimizes the cost criteria, whereas the negative-ideal solution maximizes the cost criteria and minimizes the benefit criteria (Wang and Elhag 2006). The TOPSIS method is used in this study for four reasons: (i) it is rational and easily understandable; (ii) the computational processes are straightforward; (iii) it allows us to choose the best alternatives for each criterion represented in a simple mathematical form; and (iv) the importance weights are incorporated into the comparison procedures (Wang and Chang 2007). Although the TOPSIS is applied in many fields, it has some limitations. Sanayei et al. (2010) reported that the TOPSIS method introduces two reference points, but it does not consider the relative importance of the distances from these points. Tzeng and Tasur (1994) have reported that the grey relation model and TOPSIS have some similarity in the input and operational procedures. The limitation of TOPSIS is replaced by the definition of grey relation coefficient of grey relation model (Chen and Tzeng 2004). Grey relation refers to the uncertain relations between things, elements of the systems, or between elements and behaviours (Kuo et al. 2007). The reason for using GRA method is to measures the relation among elements based on the degree of similarity or difference of development trends among these elements (Feng and Wang 2000). Grey theory is a possible mathematical method that can be used to deal with inadequate information (Tzeng and Huang 2012).

The aim of this article was to propose the combination of FAHP integrated with GRA–TOPSIS method is used to rank the alternatives to select a suitable maintenance policy for a pump used in the paper industry. The combination of AHP with fuzzy set theory to overcome the inherent uncertainty and imprecision associated with mapping of the decision-maker’s perception to exact numbers. The TOPSIS method consider the position approximation and whereas GRA helps to measures the relation among elements based on the degree of similarity. Hence, the proposed MCDM model benefits from the advantages of all methods by combining FAHP, GRA and TOPSIS.

The remainder of the paper is organized as follows: the proposed MCDM techniques are detailed in Sect. 2. In Sect. 3, FAHP, fuzzy set theory, and GRA–TOPSIS methodology are summarized. In this section, literature review and methodology for each technique are also given. The numerical application of the proposed model and the evaluation framework of maintenance strategy selection are explained and illustrated in Sect. 4. The obtained results are discussed in Sect. 5. The final section concludes with future research directions.

2 Proposed model

The proposed methodology for the problem related with maintenance strategy combines FAHP and GRA–TOPSIS methods. It consists of four basic stages:

• 1. Identification of criteria for evaluating the alternatives

• 2. Formulation of decision hierarchy

• 3. Computation of FAHP

• 4. Ranking of the alternatives using GRA–TOPSIS

The schematic diagram of the proposed methodology for the selection of alternative maintenance strategy is shown in Fig. 1. In the first and second stages, maintenance strategy alternatives and the evaluation criteria are identified and a decision hierarchy is constructed. The FAHP model is structured such that the objective is at the top level of the hierarchy; criteria are at the second level; subcriteria are at the third level; and the alternative strategies are placed at the fourth level. After the approval of decision hierarchy, criteria used in maintenance selection are assigned with weights using FAHP in the third stage. In the third stage, in order to determine the criteria weights, pair-wise comparison matrices are formed. The experts from the decision-making team make evaluations using the Satty’s scale to determine the values of the elements of pair-wise comparison matrices. The geometric mean of the values obtained from the evaluations is computed. A consensus is arrived at on a final pair-wise comparison matrix formed. On the basis of this final comparison matrix, the weights of the criteria are calculated. These weights are approved by a decision-making team in order to complete this phase. Maintenance strategy ranks are determined by using GRA–TOPSIS method in the fourth stage.

Fig. 1

The proposed evaluation model for maintenance strategy selection

3 Methods

3.1 FAHP method

The analytic hierarchy process (AHP) is a method proposed by Saaty (1980). In the AHP, the decision-making problem is structured hierarchically at different levels with each level consisting of a finite number of elements (Khajeh 2010). It is widely used in many decision-making problems, but very few authors have listed the limitations of its usage. The conventional AHP cannot reflect the human thinking style (Deng 1999). For instance, while doing pair-wise comparison, it is difficult for maintenance engineers to precisely quantify the statements such as what is the relative importance of safety in terms of cost, considering the selection of the suitable maintenance strategy for a pump in the pulp and paper industry. The reply may be “between three to five times more important,” “not three times more important exactly”. To overcome the shortcoming of the AHP, the fuzzy linguistic terms are used with AHP and proposed as FAHP. Laarhoven and Pedrycz (1983) applied fuzzy logic principles in AHP and proposed them as FAHP. As per the published reports, FAHP has been widely applied in many complicated decision-making problems (Table 2).

3.2 Fuzzy set theory

A fuzzy set is a class of objects with grades of membership. It is characterized by a membership function that assigns a grade of membership ranging between 0 and 1 to each object of the class (Zadeh 1965). Fuzzy set theory has the capability of solving real-world problems by providing a wider frame than that of the classic sets theory (Ertuğrul and Tuş 2007). Zadeh (1965) proposed the fuzzy set theory for the scientific environment and later it was been made available to other fields as well. Expressions such as “not very clear,” “probably so,” and “very likely” represent some degree of uncertainty of human thought and are often used in daily life. In our daily life, there are different decision-making problems of diverse intensity and if the fuzziness of human decision-making is not taken into account, the results can be misleading (Tsaur et al. 2002). Fuzzy decision-making turned out to be a rational approach in decision-making problem that takes into account human subjectivity (Ertuğrul and Karakaşoğlu 2009). Bellman and Zadeh (1970) described the decision-making methods in fuzzy environments. The use of fuzzy set theory allows the decision-makers to incorporate uncertain information into decision models (Kulak et al. 2005). The fuzzy set theory resembles human reasoning with the use of approximate information and certainty to make decisions, and it is a better approach to convert linguistic variables to fuzzy numbers under ambiguous assessments. The fuzzy set theory, which is incorporated with AHP, allows a more accurate description of the decision-making process.

Table 2 Literature related to FAHP method

The uncertain comparison ratios are expressed as fuzzy numbers. It is possible to use different fuzzy numbers according to the situation. In general, triangular and trapezoidal fuzzy numbers are used. In common practice, the triangular form of the membership function is used most often (Ding and Liang 2005; Büyüközkan et al. 2004; Ilangkumaran and Thamizhselvan 2010). The reason for using a triangular fuzzy number (TFN) is to make it intuitively easy for the decision-makers to use and calculate. In addition, modelling using TFNs has proved to be an effective way in formulating decision problems where the information available is subjective and imprecise (Yeh et al. 2000; Büyüközkan et al. 2004; Wang and Chang 2007). The evaluation criterion in the judgment matrix and weight vector is represented by TFNs. A fuzzy number is a special fuzzy set $F = \{(x,\mu _\mathrm{F}(x), x$ € $R\}$ where $x$ takes its value on the real line $R_{1}: - \infty < x <+\infty$ and $\mu _\mathrm{F}(x)$ is a continuous mapping from $R_{1}$ to the close interval [0, 1]. A TFN can be denoted as $M = (l, m, u)$. The TFN can be represented as follows:

$$\begin{aligned} \left\{ \begin{array}{ll} 0,&{}x<l, \\ \frac{x-l}{m-l},&{}l<x<m, \\ \frac{u-x}{u-m},&{}m<x<u, \\ 0,&{}x>u \\ \end{array} \right. \end{aligned}$$

According to the nature of TFN, it can be defined as a triplet ($l, m, u)$. The TFN can be represented as $\tilde{A}_{1} = (L, M, U)$ where $L$ and $U$ represent the fuzzy probability between the lower and upper boundaries of evaluation. The two fuzzy numbers $\tilde{A}_{1} = (L_{1}, M_{1}, U_{1})$ and $\tilde{A}_{2}=(L_{2}, M_{2}, U_{2})$ are assumed.

$$\begin{aligned} \tilde{A}_{1} \oplus \tilde{A}_{2}&= (L_{1}, M_{1}, U_{1}) \oplus (L_{2}, M_{2}, U_{2}) = (L_{1} + L_{2}, M_{1} + M_{2}, U_{1}+U_{2})\\ \tilde{A}_{1} - \tilde{A}_{2}&= (L_{1}, M_{1}, U_{1})- (L_{2}, M_{2}, U_{2}) = (L_{1} - L_{2}, M_{1} - M_{2}, U_{1} - U_{2})\\ \tilde{A}_{1} \otimes \tilde{A}_{2}&= (L_{1}, M_{1}, U_{1}) \otimes (L_{2}, M_{2}, U_{2}) = (L_{1} L_{2}, M_{1}M_{2}, U_{1}U_{2})\\ \tilde{A}_{1} \div \tilde{A}_{2}&= (L_{1}, M_{1}, U_{1}) \div (L_{2}, M_{2}, U_{2}) = (L_{1}/L_{2}, M_{1}/M_{2}, U_{1}/U_{2})\\ \tilde{A}_{1}^{-1}&= (L_{1}, M_{1}, U_{1})^{-1 }=(1/U_{1}, 1/M_{1}, 1/L_{1}) \end{aligned}$$

3.2.1 The procedural steps involved in FAHP method are listed below:

Step 1: A complex decision-making problem is structured using a hierarchy. The FAHP initially breaks down a complex MCDM problem into a hierarchy of interrelated decision elements (criteria). With the FAHP, the criteria are arranged in a hierarchical structure similar to a family tree. A hierarchy has at least three levels: overall goal of the problem at the top, multicriteria that define criteria in the middle, and decision criteria at the bottom (Albayrak and Erensal 2004).

Step 2: The crisp pair-wise comparison matrix A is fuzzified using the TFN $M = (l, m, u)$, the $l$ and $u$ represent lower and upper bound range, respectively, that might exist in the preferences expressed by the decision-maker. The membership functions of the TFNs M1, M3, M5, M7, and M9 are used to represent the assessment from equally preferred (M1), moderately preferred (M3), strongly preferred (M5), very strongly preferred (M7), and extremely preferred (M9). This article uses a TFN to express the membership functions of the aforementioned expression values on five scales that are used for FAHP listed in Table 3 and graphically expressed in Fig. 2. For instance, the membership function of cost with respect to feasibility ‘moderate’ can be represented as (2, 3, 4), the membership function which is

$$\begin{aligned} \mu _{moderate} =\left\{ \begin{array}{ll} 0,&{}x\le 2, \\ \frac{x-2}{3-2},&{}2<x<3, \\ \frac{4-x}{4-3},&{}3<x<4, \\ 0,&{}x>4 \\ \end{array} \right. \end{aligned}$$

Let $C=\{C_j |j=1,2,\ldots ,n\}$ be a set of criteria. The result of pair-wise comparison on ‘$n$’ criteria can be summarized in an ($n \times n)$ evaluation matrix $A$ in which every element $a_{ij} (i,j=1,2,\ldots ,n)$ is the quotient of the weights of the criteria, as shown:

$$\begin{aligned} A=\left[ \begin{array}{cccc} {a_{11} }&{} {a_{12} }&{} \cdots &{} {a_{1n} } \\ {a_{21} }&{} {a_{22} }&{} \cdots &{} {a_{2n} } \\ \vdots &{} \vdots &{} \ddots &{} \vdots \\ {a_{n1} }&{} {a_{n2} }&{} \cdots &{} {a_{nn} } \\ \end{array} \right] a_{ii} =1,a_{ij} =1/a_{ji} ,a_{ij} \ne 0. \end{aligned}$$

(1)

Step 3: The mathematical process is commenced to normalize and find the relative weights of each matrix. The relative weights are given by the right Eigen vector $(w)$ corresponding to the largest Eigenvalue $(\lambda )$, as

$$\begin{aligned} \hbox {A}w=\lambda _{\max } w \end{aligned}$$

(2)

It should be noted that the quality of output of FAHP is strictly related to the consistency of the pair-wise comparison judgments. The consistency is defined by the relation between the entries of $A: a_{ij}\times a_{jk}=a_{ik}$. The consistency index (CI) is

$$\begin{aligned} \hbox {CI}=(\lambda _{\max } -n)/(n-1) \end{aligned}$$

(3)

Step 4: The pair-wise comparison is normalized and priority vector is computed to weight the elements of the matrix. The values in these vectors are summed to 1. The consistency of the subjective input in the pair-wise comparison matrix can be determined by calculating a consistency ratio (CR). In general, a CR having the value $<$0.1 is good (Saaty 1980). The CR for each square matrix is obtained from dividing the CI values by random consistency index (RCI) values.

$$\begin{aligned} \hbox {CR}=\hbox {CI}/\hbox {RCI} \end{aligned}$$

(4)

The RCI, which is obtained from a larger number of simulations, runs and varies depending on the order of the matrix. Table 4 lists the value of RCI for matrices of order 1–10 obtained by approximating random indices using a sample size of 500. The acceptable CR range varies according to the size of the matrix. In contrast, if CR is more than the accepted value, inconsistency of judgments within that matrix will occur and the evaluation process should therefore be reviewed, reconsidered, and improved.

Fig. 2

Fuzzy triangular membership function

Table 3 Pair wise comparison scale

Table 4 Average RCI based on matrix size

Step 5: Computation of desirability index: the desirability index is calculated using the following equation:

$$\begin{aligned} D_i =\sum \limits _{j=1}^J \sum \limits _{k=1}^{K_j } P_j A_{kj}^D S_{ikj} \end{aligned}$$

(5)

where $P_j$ is the relative importance weight of criteria $j;A_{kj}^D$ the stabilized relative importance weight for subcriteria $k$ of criteria $j$ for the dependency; $S_{ikj}$the relative impact of strategy alternative i on subcriteria $k$ of criteria $j$ of maintenance strategy selection hierarchy.

3.3 GRA–TOPSIS methodology

The grey relational analysis (GRA), proposed by Deng (1989), is a method that can measure the correlation between the series and belongs to the category of the data analytic method or geometric method. The purpose of the GRA technique is to measure the relation among elements based on the degree of similarity. There are a few studies that applied GRA. Fu et al. (2001) evaluated the effect of environmental factors on corrosion of oil tubes in gas wells and found out the main factors using GRA. Lin and Lin (2002) proposed GRA for the optimization of the electrical discharge machining process with multiple performance characteristics. Chen and Tzeng (2004) solved the problem of choosing the best host country for an expatriate assignment using GRA combined with TOPSIS. Dai et al. (2010) proposed a combined GRA and TOPSIS approach for the integrated water resource security evaluation in Beijing city. Lai et al. (2005) determined the best design combination of product from the elements for matching a given product image represented by a word pair using GRA. Xu et al. (2007) introduced the idea of GRA and proposed a new conflict reassignment approach of belief functions. Lin (2008) proposed a method for electrocardiogram (ECG) heart beat discrimination using GRA to quantify the frequency components among the various ECG beats. Hsu and Wang (2009) proposed GRA for forecast-integrated circuit outputs.

The TOPSIS was first developed by Hwang and Yoon (1981). It is proven as one of the best methods in addressing the rank-reversal issue. The basic idea of TOPSIS is that the best decision should be made to be closest to the ideal and far from the nonideal situation. Such ideal and negative-ideal solutions are computed by considering the other overall alternatives according to Ertuğrul and Karakaşoğlu (2009). Many researchers have proposed TOPSIS to solve the MCDM problem. Ho et al. (2010) proposed TOPSIS for supplier evaluation and selection. Kumar and Agrawal (2009) used TOPSIS for electroplating product and plant selection. Alemi et al. (2010) approached TOPSIS to present the best artificial lift method selection for the different circumstances of oil fields. Sezhian et al. (2011) proposed an integrated approach that uses AHP and TOPSIS to assess the performance of three depots of a public-sector bus passenger transport company. Peiyue et al. (2011) applied TOPSIS-based entropy weight to assess the performance of ground-water quality. Rouhani et al. (2012) presented fuzzy TOPSIS for the evaluation of enterprise systems. Although TOPSIS is applied in many fields, it has some limitations. Sanayei et al. (2010) reported that the TOPSIS introduces two reference points, but it does not consider the relative importance of the distances from these points. Tzeng and Tasur (1994) have reported that the grey relation model and TOPSIS have some similarities in the input and operational procedures. The limitation of TOPSIS is replaced through the definition of grey relation coefficient of grey relation model (Chen and Tzeng 2004). In this article, the GRA is integrated with TOPSIS for obtaining the precise ranking of maintenance alternatives. The procedure of GRA–TOPSIS method is as follows:

Step 1: Normalization of the evaluation matrix: this process is to transform different scales and units among various criteria into common measurable units to allow comparisons across the criteria. Assume $f_{ij}$ to be of the evaluation matrix $R$ of alternative $j$ under evaluation criterion $n$, then, an element $r_{ij}$ of the normalized evaluation matrix $R$ can be calculated by many normalization methods to achieve this objective.

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

(6)

Step 2: Determination of the positive- and negative-ideal solutions: The positive ideal solution A$^+$ indicates the most preferable alternative and the negative ideal solution A$^-$ indicate the least preferable alternative.

$$\begin{aligned} A^{+}=\left\{ {A_1^+ ,\ldots ,A_n^+ } \right\} =\left\{ \left( \max \nolimits _j r_{ij} |i\in I^{{\prime }} \right) ,\left( \min \nolimits _j r_{ij} |i\in I^{\prime \prime }\right) \right\} \end{aligned}$$

(7)

$$\begin{aligned} A^{-}=\left\{ {A_1^{-} ,\ldots ,A_n^- } \right\} =\left\{ \left( \min \nolimits _j r_{ij} |i\in I^{{\prime }} \right) ,\left( \max \nolimits _j r_{ij} |i\in I^{\prime \prime } \right) \right\} \end{aligned}$$

(8)

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

Step 3: For taking the positive-and negative-ideal solution as the referential sequence and each of the alternatives to be the comparative sequence, to obtain the grey relation coefficient of each alternative to the ideal $r(A^{+}(j),A(j))$ and the negative ideal solution.

$$\begin{aligned} r(A^{ + } (j),A_{i} (j)) = \frac{\min _{i} \min _{j} |A^{ + } (j) -A_{i} (j)| + \varsigma \max _{i} \max _{j} |A^{ + } (j) - A_{i} (j)|}{|A^{ + } (j) - A_{i} (j)| + \varsigma \max _{i} \max _{j} |A^{ + } (j) - A_{i} (j)|}\end{aligned}$$

(9)

$$\begin{aligned} r(A^{-} (j),A_{i} (j)) = \frac{\min _{i} \min _{j} |A^{ - } (j) - A_{i} (j)| + \varsigma \max _{i} \max _{j} |A^{ - } (j) - A_{i} (j)|}{|A^{ - } (j) - A_\mathrm{i} (j)| + \varsigma \max _{i} \max _{j} |A^{ - } (j) - A_{i} (j)|} \end{aligned}$$

(10)

where ${\varsigma }$ is the distinguished coefficient (${\varsigma }[0, 1])$. Generally, we take ${\varsigma } = 0.5$.

Step 4: To determine the grade of grey relation of each alternative to the positive- and negative-ideal solutions and its calculation, we can use the following equations:

$$\begin{aligned}&\displaystyle r_i^+ =r(A^{+},A_i )=\sum \limits _{j=1}^n w_j r(A^{+}(j),A_i (j))\end{aligned}$$

(11)

$$\begin{aligned}&\displaystyle r_i^- =r(A^{-},A_i )=\sum \limits _{j=1}^n w_j r(A^{-}(j),A_i (j))\end{aligned}$$

(12)

$$\begin{aligned}&\displaystyle \sum \limits _{j=1}^n w_j =1 \end{aligned}$$

(13)

Step 5: To find the relative closeness degree $(C_i)$ ranges between 0 and 1 which is used as a comprehensive indicator of the maintenance strategy selection, the following equations can be used. A greater value of $C_i$ indicates a higher priority of the alternative.

$$\begin{aligned} c_i =\frac{r_i^+ }{r_i^+ +r_i^- } \end{aligned}$$

(14)

4 Numerical examples of the proposed model

In this section, a numerical example is applied to explain how the maintenance strategy selection decisions are made using the proposed model. This study is applied to a pump in the paper industry located in the southern part of India. The industry is well known for manufacturing of papers in and around India. The manufacturing of papers involves five major steps: mechanical preparation of the wood into wood chips, wood digestion (pulping) to form pulp, pulp whitening (bleaching), pulp stock preparation, and finally, paper formation. By using this process, different variety of papers produced are printing papers, wrapping papers, writing paper, blotting paper, drawing paper, handmade paper, specialty papers, and so on. The critical equipment such as conveyor, digester, motors, pumps, refiners, and rolling stock play an imperative role in paper production. Among these, pumps play a predominant role for sucking and pumping the raw pulp from one place to another. The maintenance engineer and supervisor are often facing failures of the pump due to shaft misalignment and bearing wear, excessive vibration, restricted discharge flow and cavitation, and they are willing to evaluate an optimum maintenance strategy for avoiding the these failures.

4.1 Criteria for selecting an alternative strategy

This study proposes that the evaluation criteria should be identified for selection of optimal maintenance strategies based on an FAHP, as specified by Wang et al. (2007) and other experts in the industry. After the identification of the evaluation criteria, alternative strategies are investigated and decision-making team determines four possible alternatives and the four influencing criteria for the evaluation process. The identified evaluation criteria are described as follows:

• (1) Safety: In many industries, safety is considered at high level, the factors relevant to describing the safety are:

  • (a) Personnel: The failure of the pumps can cause serious injury to personnel, due to vibration, shaft misalignment and so on.

  • (b) Facilities: The sudden failure of reciprocating pump can result in serious damage of other machines in a paper plant.

  • (c) Internal environment: The failure of pumps with inflammable liquid will spread hazardous liquids in the environment.

• (2) Cost: Different maintenance strategies may need different expenditures such as hardware cost, software cost, and personnel training.

  • (a) Hardware: The number of components such as pumps, boilers, and some of monitoring computers are indispensable.

  • (b) Software: It is used to do more complex tasks of organizing and analysing large data sets when using different maintenance strategies.

  • (c) Personnel training: It means training employees on operating procedures and standards. It will make full use of related tools and techniques. It leads to increased employee productivity and knowledge.

  • (d) Replacement: Replacement cost, referred as the price that will have to be paid to replace an existing product with a similar product.

• (3) Added value: Low spare parts inventories, small production loss, and quick fault identification are the parts of added value. It can be induced only by a good maintenance programme.

  • (a) Spare parts inventories: A spare part is a substitutable part kept in an inventory and used for the repair or replacement of failed parts. Some of the machine spare parts are really expensive.

  • (b) Production loss: The failure of important equipment in the production line leads to higher production loss. These losses can be reduced by selecting the appropriate maintenance strategy.

  • (c) Fault identification: It is discovering a failure in hardware or software. Fault detection methods, such as built-in tests, typically log the time when the error occurred and either trigger alarms for manual intervention or initiate automatic recovery. With enterprise networks, network analysers are often attached to the lines to monitor traffic and send an alarm when disruptions are detected.

• (4) Feasibility: Acceptance by labours and technique reliability are the division of feasibility of maintenance strategies.

  • (a) Acceptance by labours: The managers and staff will always prefer the maintenance strategy that is easy to understand.

  • (b) Technique reliability: In some of the production facilities, maintenance strategies such as CM and PM are not applicable.

  • (c) Procedure: A fixed, step-by-step sequence of activities or course of action that must be followed in the same order to perform a task correctly.

  • (d) Maintainability: The ease with which maintenance of a functional unit can be performed in accordance with prescribed requirements.

4.2 Possible alternative maintenance strategies

4.2.1 Corrective maintenance

It is also referred as failure-based maintenance, breakdown maintenance, or run-to-failure strategy. It is the original maintenance strategy appeared in industry (Waeyenbergh and Pintelon 2002). This maintenance is not implemented until failure occurs. It is considered as a feasible strategy in the cases where profit margins are larger (Sharma et al. 2005). The failures of equipment do not have a greater impact on the availability or service for productive use of an organization when using this strategy. However, this maintenance may cause serious damage of related facilities, personnel, and environment. The most-effective and reliable maintenance strategies are applied by the maintenance managers for the small profit margin cases and increased global competitions.

4.2.2 Time-based preventive maintenance

According to the reliability characteristic of equipment, maintenance is planned and performed periodically to reduce frequent and sudden failure. It refers to all the tasks of determining the actual condition (inspection) and maintaining the target condition (maintenance) of assets. Every technical asset has a certain service life. If the service life is exhausted, then the maintenance measures must be taken to renew it. Time-based preventive maintenance (TM) is applied widely in industry. In TM, the maintenance tasks are planned and performed, depending on the period specified. In many cases, TMs are used, most machines are maintained with a significant amount of useful life remaining (Mechefske and Wang 2003). This often leads to unnecessary maintenance, even deterioration of machines if incorrect maintenance is implemented.

4.2.3 Condition-based maintenance

This maintenance is performed after one or more indicator shows that equipment is going to fail or that equipment performance is deteriorating. This concept is applicable to mission-critical systems that include active redundancy and fault reporting. It is also applicable to non-mission critical systems that lack redundancy and fault reporting. Maintenance decision is made depending on the measured data from a set of sensor system. Condition-based maintenance (CBM) is based on using real-time data to prioritize and optimize maintenance resources. Ideally, it will allow the maintenance personnel to do only right things, therefore minimizing spare parts cost, system downtime, and time spend on maintenance. This maintenance strategy is often designed for rotating and reciprocating machines, for example, turbine, centrifugal pumps, and compressors. But limitations and deficiency in data coverage and quality reduce effectiveness and accuracy of the CBM strategy (Al-Najjar and Alsyouf 2003).

4.2.4 Predictive maintenance

Predictive maintenance (PM) techniques help determine the condition of in-service equipment to predict when maintenance should be performed. This approach offers cost savings over routine or TM, because tasks are performed only when warranted. The main feature of the PM is to allow convenient scheduling of CM and to prevent unexpected equipment failures. PM attempts to evaluate the condition of equipment by performing periodic or continuous equipment condition monitoring. Fault prognostic is a new technique used by maintenance management, which provides maintenance engineers the option to plan maintenance based on the time of future failure and coincidence maintenance activities with production plans, customers’ orders, and personnel availability. Djurdjanovic et al. (2003) have described an intelligent management system, focusing on fault prognostic techniques and aiming to achieve near-zero-downtime performance of equipment.

4.3 Formation of decision hierarchy

The decision hierarchy diagram is established using identified evaluation criteria, and the alternative strategies are shown in Fig. 3. There are four levels in the decision hierarchy structure in the strategic selection process. The overall goal of the decision process is determined as the selection of alternative strategy at the first level of the hierarchy. The criteria are at the second level; subcriteria are at the third level; and alternative strategies are on the fourth level.

Fig. 3

Hierarchy structure for maintenance strategy selection

4.4 Calculating the weights of criteria using FAHP

After the construction of the hierarchy diagram of the problem as mentioned, the FAHP methodology requires pair-wise comparison of the criteria to determine their relative weights. In the pair-wise comparison process, each criterion is compared with others using Saaty’s nine-point scale. The pair-wise comparison of criteria, subcriteria, and alternatives were calculated and are shown in Tables 5, 6, and 7 respectively. Then CI and CR are calculated to check whether the importance given to the criteria in the pair-wise comparison matrix is correct or not. The weights are approved by a decision-making team towards the completion of this phase. The FAHP computation results are shown in Table 8.

Table 5 Eigen vector of comparison matrix for dependencies in various criteria

Table 6 Eigen vector of comparison matrix of the sub-criteria under criteria ‘safety’

Table 7 Eigen vector of comparison matrix for relative importance of each strategy for sub-criteria ‘personnel’

Table 8 FAHP computation

4.5 Evaluation of maintenance alternatives and determinations of the final rank using GRA–TOPSIS

• Step 1: A company is looking forward to select the best maintenance strategy among the four alternatives, namely CM, TM, CBM, and PM. A committee of three decision-makers D1, D2, and D3 is formed to conduct the evaluation and select the most suitable strategy.

• Step 2: The second step is to define linguistic variables and their corresponding crisp scores. The evaluators are involved in expressing the rating of alternatives with respect to each criterion in linguistic variables.

• Step 3: The questionnaire designs are presented in “Appendix 1” to evaluate the alternative maintenance strategy according to selection criteria. The ratings of four alternatives under four criteria, made by three decision-makers, are aggregated by averaging and tabulated.

• Step 4: The GRA–TOPSIS method has been proposed for the selection of a suitable maintenance strategy. According to Eq. 6, the weighted normalized decision matrix is computed and given in Table 9.

• Step 5: The positive- and negative-ideal solutions are calculated using Eqs. 7 and 8, and are given in Table 10.

• Step 6: Then the distance of each alternative from positive-ideal and negative-ideal solutions is computed using Eqs. 9 and 10 and is given in Table 11.

• Step 7: The grade of the grey relation of each alternative to the positive- and negative-ideal solutions is calculated using Eqs. 11 and 12 and given in Table 12.

• Step 8: The computation of the relative closeness degree is done as per Eq. 14 and given in Table 13. Finally, according to the relative closeness degree value, the ranks are preferred to the strategies and the obtained results are given in Table 13.

  Table 9 Normalized decision matrix

  Table 10 Positive ideal solution $(\hbox {A}^{+})$ and negative ideal solution $\hbox {(A}^{-})$

  Table 11 Distance of each alternatives from positive ideal solution (PIS) and negative ideal solution (NIS)

  Table 12 Grade of grey relation of each alternative to the PIS and NIS

Table 13 Results of FAHP GRA–TOPSIS and FAHP TOPSIS

5 Results and discussion

The selection of maintenance strategy is a very important task for engineering industries. The right strategy to counter any mode of failure of machines will improve the lifecycle profit or reduce the lifecycle cost (Labib 1998). Improper selection may adversely affect the operating budget of the company due to unplanned maintenance cost, thereby reducing productivity as well as profitability. In this article, by integrating FAHP, GRA–TOPSIS is proposed to select the appropriate maintenance strategy. The suggested method is used to select an optimal maintenance strategy for pump used in the paper industry. Four maintenance strategies (PM, CBM, TM, and CM) are compared with four criteria (safety, cost, added value, and feasibility) using FAHP integrated with GRA–TOPSIS method to pump used in the paper industry. The suggested model is observed to be quite capable and easy to evaluate the best maintenance strategy among different options. The results of the proposed methodology are given in Table 13.

Predictive maintenance has obtained as the highest performance value of 0.499, which is regarded as the best strategy among the four maintenance strategies using GRA–TOPSIS methodology. CBM, TM, and CM have positioned at the second, third, and fourth ranks with, respectively, 0.496, 0.486, and 0.483 as the final performance values. The ranking order of the alternatives with proposed model is PM $> \hbox {CBM} > \hbox {TM} > \hbox {CM}$. To validate the results of the proposed methodology and to show the impact of GRA–TOPSIS in ranking of maintenance alternatives, we applied FAHP integrated with TOPSIS to the same numerical example and the results obtained are shown in Table 13. The procedural steps of TOPSIS are given in “Appendix 2”. The ranking order of the alternatives with FAHP TOPSIS model is PM $> \hbox {CBM} > \hbox {CM} > \hbox {TM}$. It shows that PM has the best maintenance strategy, and it has the shortest distance from the positive-ideal solution. But the relative importance of the distance from these points is not considered in TOPSIS methodology. The limitation of TOPSIS is replaced through grey relation coefficient of grey relation model. Figure 4 shows the relative closeness degree values using FAHP GRA–TOPSIS and FAHP TOPSIS methods. The result clearly shows PM to be the best by FAHP GRA–TOPSIS method. The results of other researches in maintenance strategy problem in comparison with this study are shown in Table 14. In real case, the paper industry is using TM for maintaining the pumps. However, PM offers cost savings over TM because tasks are performed only when warranted.

Table 14 Maintenance strategy selection related articles and its results

6 Conclusion

The selection of an appropriate maintenance strategy is an important issue and may adversely affect the availability and reliability levels of plant equipment. The total operating budget of the firm is directly influenced by the maintenance policy. Several maintenance strategy alternatives should be considered and evaluated with respect to different influencing criteria under the consideration of subjective data. Therefore, an effective decision-making approach is essential for the selection of maintenance strategy alternatives. The objective of this research was to propose a decision-making approach for maintenance strategy selection through FAHP GRA–TOPSIS. FAHP was used to compute the evaluation criteria weights and GRA–TOPSIS was used to determine the final ranking of maintenance alternatives. The proposed model has been applied to a case study and the steps of the decision-making process are illustrated. The proposed model can help the decision makers to rank the alternatives to select a suitable maintenance strategy. A FAHP–TOPSIS model is also applied in same numerical example to show the validity of the proposed model.

Fig. 4

FAHP GRA–TOPSIS and FAHP TOPSIS scores

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.