An integrated logarithmic fuzzy preference programming based methodology for optimum maintenance strategies selection
Graphical abstract
Introduction
The maintenance activities have become increasingly important as the manufacturers face more advanced and more complex systems in the manufacturing and production process [1], [2]. Maintenance activities improve system availability and performance efficiency through technical actions and management measures [3], [4]. However, the maintenance cost occupies a large proportion in the product life cycle cost which ranges from 15% to 70% [5]. Selecting the optimum maintenance which can retain the system in the normal operating conditions with the lowest possible maintenance loss is one of the main concerns of manufacturing firms [6]. There are varieties of factors that affect maintenance time, cost and quality, such as maintenance technical actions and maintenance strategies selection et al., among which the maintenance strategies selection plays a key role in saving cost, minimizing system mean downtime, increasing system reliability and availability [7], [8].
In the literature, the maintenance is usually divided into three main types: Corrective Maintenance, Preventive Maintenance and Predictive Maintenance [9], [10]. And there are four main popular maintenance strategies: breakdown maintenance, time-based maintenance, condition-based maintenance and predictive maintenance [7], which have numerous applications in various fields. In recent years, many agencies and researchers have managed to develop and select maintenance strategies for port infrastructures [11], naval ships [12], pulse-code modulation circuit switching [13], leased equipment [14], multi-component systems [15], wind turbines [16], mining industries [17], [18], [19] and petroleum pipeline system [20].
Taking many decision goals and comparing criteria into consideration, the optimum maintenance strategies selection is considered as a complex Multiple-Criteria Decision-Making (MCDM) problem [21]. MCDM is a theory that applies several methods to obtain the optimum solution from the possible alternatives (e.g. maintenance strategies) among which decision-makers need to rank or select with the global analysis and evaluation of multiple conflict criteria (e.g. economic, environmental, etc.). From the latter half of the 2000s, the MCDM approach has gained momentum in the field of maintenance strategies selection [22]. However, the literature on the methods of selecting optimum maintenance strategies is limited.
Bertolini and Bevilacqua [23] presented a combined method of “Lexicographic” Goal Programming (GP) and classical Analytic Hierarchy Process (AHP) to define the optimum maintenance strategies for critical centrifugal pumps in an oil refinery. Suresh et al. [24] and Al-Najjar and Alsyouf [25] introduced the fuzzy inference to select the optimum maintenance policy, which developed the classical AHP to fuzzy AHP. Wang et al. [26] used a fuzzy modification of AHP as an evaluation tool to solve the optimization problem with non-linear constraints and consistent or inconsistent fuzzy judgment matrix, and then, to select the optimum maintenance strategies. Pariazar et al. [27] presented an improved AHP method with rough set theory for the maintenance strategy selection. Bashiri et al. [7] presented the interactive fuzzy linear assignment method (IFFLAM) for ranking the maintenance strategies. Hinow and Mevissen [28] introduced the Genetic Algorithm (GA) to handle parameters diversity of Life Cycle Cost (LCC), in order to optimize maintenance strategies for the entire substation system. Uysal and Ömür [29] presented a multi-attribute decision-making methodology—hierarchical fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to define the best-suited selection of computerized maintenance management system (CMMS). Li et al. [30] and Ishizaka et al. [31] developed a new sorting method—Elimination and Choice Expressing Reality Sort (ELECTRE-SORT) to assign more precise and flexible strategies to different machines, which could handle an unlimited number of criteria. Maletič et al. [32] presented AHP to select the most appropriate maintenance policy for the case of Slovenian paper mill company, and used sensitivity analysis to evaluate the stability of the solution. Makinde et al. [33] presented decision making techniques of weighted decision matrix (WDM) and AHP to establish the optimal maintenance strategy for Reconfigurable Vibrating Screen (RVS).
From the literature mentioned above, it is obvious that the AHP method is widely used in the problem of maintenance strategies selection. But in most cases of the problem, it is impossible to provide exact judgments between the criteria for the crisp AHP because of the complexity, vagueness and uncertainty of criteria. Laarhoven and Pedrycz [34] introduced fuzzy set theory to the AHP decision process and allowed decision-makers (DM) to handle the vagueness of meaning of linguistic terms to express their-essentially fuzzy-opinions in fuzzy numbers, and the method provided more realistic results than the original non-fuzzy method. Through comparison studies between fuzzy AHP methods and crisp AHP methods with numerical examples [35], [36], [37], [38], [39], the methods developed with fuzzy AHP have their advantages: (a) better modelling of the uncertainty, imprecision and inconsistence associated with pairwise comparison process; (b) cognitively less demanding on the DM; (c) adequate reflection of the DM’s attitude to risk and their degrees of confidence in the subjective assessments. Fuzzy AHP is more appropriate to be applied instead of crisp AHP in the MCDM problem of optimum maintenance strategies selection.
However, the popular existing methods, such as fuzzy preference programming (FPP) based nonlinear priority method and extent analysis method used in fuzzy AHP, may produce multiple, even conflict priority results, leading to distinct conclusions and turn out to be subject to some significant drawbacks [40], such as: firstly, negative membership degree makes no sense; secondly, the model of FPP method produces multiple optimal solutions when there exists strong inconsistency among the fuzzy judgments; thirdly, the priority vectors derived by using the upper and lower triangular elements of a fuzzy pairwise comparison matrix in the FPP method are not the same, even significantly different. Furthermore, when the method is being used in combined forms, it will be complicated and unstable to obtain the optimum solution. In this paper, an integrated Logarithmic Fuzzy Preference Programming (LFPP) based methodology is proposed to solve the optimum maintenance strategies selection problem to obtain the final priorities with AHP, which has the following advantages in contrast with the existing methods:
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The proposed approach can utilize both qualitative and quantitative data, and produce the unique normalized optimal priority vector for fuzzy pairwise comparison matrices;
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The proposed approach applies multiplicative constraints and deviation variables to process the upper and lower triangular fuzzy judgments to obtain the same priorities, which is free from the significant drawbacks of original methods;
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All comparison matrices obtained in AHP of optimum maintenance strategies selection are processed simultaneously and directly in the form of global super-matrix to obtain the final priorities.
The reminder of the paper is organized as follows. Section 2 gives the related theoretical background of alternative maintenance strategies and the evaluation criteria. Section 3 introduces and describes the proposed LFPP method. Section 4 introduces the integrated LFPP based methodology with a two-stage process. In Section 5, comparative results of an example are discussed. Conclusions are offered in Section 6.
Section snippets
Alternative maintenance strategies
As mentioned above, maintenance is usually divided into three types: Corrective Maintenance, Preventive Maintenance and Predictive Maintenance.
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Corrective Maintenance: implemented after the failure occurs. It is a maintenance type resulting from failure.
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Preventive Maintenance: performed before the system failure occurs. It is a maintenance type which implements preventive scheduled activities to detect the error state and repair or replace the fault components.
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Predictive Maintenance: performed
LFPP method
First developed by Satty [46], AHP is a powerful and understandable method that allows groups or individuals to combine qualitative and quantitative factors in decision-making process. It is a MCDM method to solve complicated and unstructured problems, which applies a hierarchical model with levels of goals, criteria, sub-criteria, and alternatives to derive priorities from judgments and make decisions much more accurate.
The following are the steps to apply the AHP to the selection of
Integrated LFPP based methodology
On the basis of logarithmic fuzzy preference programming method proposed above, this section introduces an integrated LFPP based methodology with two-stage process, in order to achieve that all fuzzy comparison matrices of AHP can be processed simultaneously and directly in the form of super-matrix.
Since the LFPP method has the same procedure and produces the same priorities for the upper and lower triangular judgments, the two-stage process for both of the upper and lower triangular judgments
Case study
In this section, a maintenance strategies selection example investigated by Wang et al. [26] is studied. With the criteria discussed in the section 2, we can build the hierarchical structure of the problem, shown in Fig. 1.
In the hierarchical structure, C1, C2, C3 and C4 represent the selected criteria: Safety, Cost, Added-value and Feasibility, and meanwhile, the criteria have their sub-criteria. BM, TBM, CBM and PdM represent the selection alternatives of different potential optimum
Conclusions and discussions
Considering optimum maintenance strategies selection as a problem of MCDM, the paper uses AHP as the hierarchical analysis method and proposes an integrated logarithmic fuzzy preference programming (LFPP) based methodology. The proposed methodology utilizes both qualitative and quantitative data, and applies multiplicative constraints and deviation variables to ensure the same priority rankings for upper and lower triangular judgments with the same fuzzy pairwise comparison matrix, which is
Acknowledgement
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors are grateful to the reviewers for the precious suggestions and feedbacks for improving this paper and to the Editors for their meticulous processing.
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