Interval-valued q-rung orthopair fuzzy FMEA application to improve risk evaluation process of tool changing manipulator

https://doi.org/10.1016/j.asoc.2021.107192Get rights and content

Highlights

  • Introducing the concept of sub-risk factors.

  • Rating risks by using interval-valued q-rung orthoptic fuzzy sets.

  • Conducting a consistency inspection and improvement process with IVq-ROF information.

  • Weighting risk factors/sub-risk factors with the IVq-ROF-DMM.

  • Ranking failures modes with the IVq-ROF-ARAS method.

Abstract

Taking actions to prevent the occurrence of failure in advance, rather than improving reliability through post-mortem testing is crucial for improvement of products’ quality and efficiency. As a typical prevention reliability analysis method, failure mode and effects analysis (FMEA) has an innate advantage in conducting this improvement. However, traditional FMEA also contains some deficiencies in rating risks, weighting risk factors and ranking failure modes. In this paper, a scientific risk evaluation method capable of solving these deficiencies is proposed, which combines interval-valued q-rung orthopair fuzzy-deviation maximization method (IVq-ROF-DMM) with interval-valued q-rung orthopair fuzzy-additive ratio assessment (IVq-ROF-ARAS) method. Moreover, the concept of sub-risk factors is developed to make evaluation results more practical. To make experts’ evaluation information more consistent, a consistency inspection and improvement process is conducted and experts’ evaluation information are fused by IVq-ROF weighted average (IVq-ROFWG) operator and IVq-ROF weighted Maclaurin symmetric mean (IVq-ROFWMSM) operator. Finally, a real case vis-à-vis tool changing manipulator of tool magazine is illustrated, and discussion results indicate that the proposed method is rational and valid.

Introduction

Under the big trend of Industry 4.0 and Made in China 2025, the development of intelligent products with higher reliability and precision is of vital importance for enhancing the competitive strength of an enterprise, industry and even the country, because the quality and reliability of products are the focus of international trade competition, and also the embodiment of national quality and economic strength of a country [1]. Therefore, a number of reliability improvement techniques have been used by manufacturing companies to maintain their market competitiveness, such as FMEA, fault tree analysis (FTA) [2], hazard and operability studies [3], and diagrams and algorithms [4]. As a typical prevention reliability analysis method, FMEA is of great help in improving the reliability and safety of systems, designs, processes and services [5], it’s main functions include identifying all potential risks, ranking failure modes to determine the highest risk, and taking corrective measures to eliminate or alleviate them. The ease of use of FMEA technique has let to the extension of its application in different fields, e.g., the aerospace, automotive, nuclear, and medical industries [6], [7], [8], [9], and so forth.

However, it also remains several deficiencies in the traditional FMEA [10], [11], [12], [13]: (1) Only three risk factors (S, O and D) are taken into account, other important factors such as the economical one are disregarded, and these three risk factors are so highly generalized that experts cannot accurately rate risks; (2) Rating the risks by crisp values, which do not consider the uncertainty and vagueness of experts’ evaluation information; (3) Three risk factors are equally weighted, their weights should not be equal for different risk evaluation cases; (4) Obtaining the risk priority number (RPN) by simply multiplying the three risk factors ratings is irrational, because small variations in one parameter evaluation may lead to significant variations on the resulting RPN; (5) Combination of different evaluation values of three risk factors may lead to the same RPN.

In order to overcome the inherent drawbacks of conventional FMEA method, an increasing number of FMEA method have been proposed. Firstly, due to time pressure and limited knowledge or data, there may be hesitation and uncertainty with respect to experts’ evaluation information. Some fuzzy methods were developed to solve this problem, e.g., triangular/trapezoidal fuzzy sets [14], [15], the intuitionistic fuzzy sets (IFSs) [16], the Pythagorean fuzzy sets (PFSs) [17], and q-rung orthopair fuzzy sets (q-ROFSs) [18], and so forth. Moreover, the interval-valued forms of these fuzzy methods also have a wide range of applications. Liu et al. [5] adopted the interval-valued intuitionistic fuzzy sets (IVIFSs) to rate the risks in the radiation therapy. To increase grades space of experts’ evaluation information, the interval-valued Pythagorean fuzzy sets (IVPFSs) were utilized by Ho et al. [19] to express uncertainty in the multiple criteria decision analysis of stroke rehabilitation treatments. Wang et al. [20] adopted the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) to score green suppliers in green supply chain management. In addition, other methods such as could model [21], matter-element model [22] and so on, were also developed to express the uncertainty. However, there is no study which rates risks by using IVq-ROFSs in FMEA.

Secondly, owing to that experts from different fields have disparate experience and knowledge background, the collected evaluation information of experts may contain some differences. In the current research, there are two main ways to solve this problem, one is consistency method, the other is fusion method.

As for consistency method, it solves the above problem from the source of evaluation information. To this day, many consistency methods have been proposed, these methods can be divided into two categories: One is the iteration-based consistency method. For instance, Xu et al. [23] proposed a two-stage consistency method which included consistency improving stage and consistency reaching stage to evaluate and select suitable location for a shopping center. In the same vein, a two-stage consistency model is constructed by Liu et al. [24] to assist decision makers in achieving a high consensus level by adjusting and improving the probabilistic linguistic preference term sets (PLTRs). Ma et al. [25] proposed a mixed consistency method which included the measurement of group consistency and the improvement of group consistency, and adopted it to an illustrative example of a decision-making problem about investment. All of the above methods are static consistency methods, but in real life, both the consistency process environment and specific parameters of the theoretical model may change. To solve this problem, Pérez et al. [26] developed a dynamic consistency model to represent the dynamic nature of the group decision making problem. Du et al. [27] built a mixed consistency-reaching model for managing noncooperative behaviors, and adopted it to evaluate and select a new production base in one of the countries or regions along the Belt and Road. The other is the optimization-based consistency method. For example, Zha et al. [28] developed an optimization-based consistency model that considered individual bounded confidences and provided decision makers with more acceptable suggestions based on their bounded confidences. Zhang et al. [29] built a novel consistency model for group decision making (GDM) with incomplete linguistic distribution assessments (ILDAs) to evaluate the comprehensive level of football players. Wu et al. [30] proposed some minimum cost consistency models based on implicit trust between individuals and the moderator.

As for fusion method, it solves the above problem from the result of evaluation information. Chen et al. [31] adopted the ordered weighted geometric averaging (OWGA) operator and Choquet integral to aggregate experts’ evaluation information. Zhang et al. [32] built a fuzzy weighted least squares model (WLSM) for aggregating experts judgments to form a consensus group judgment. In addition, Dempster aggregation rule (DAR) [33], D/Z numbers’ integration [34], [35] and so on, are also of help in aggregating evaluation information. However, to the best of our knowledge, there is no study which conducts a consistency and improvement process with IVq-ROF information, and fuses evaluation information by IVq-ROFWG operator and IVq-ROFWMSM operator in FMEA.

Thirdly, for different risk evaluation cases, risk factors’ weights should not be equal. Therefore, a fuzzy best–worst method (FBWM) based on the experts’ opinions was developed by Ghoushchi et al. [36] to measure the weights of risk factors. Ghenai et al. [37] proposed a subjective criteria-weighing method called extended step-wise weight assessment ratio analysis (ESWARA) method to calculate evaluation criteria weights of multi-criteria decision making model. Wu et al. [38] built a linear programming model based on DMM to determine the weights of customer requirements under condition that the weights may be partially known or even completely unknown. In this paper, we combine IVq-ROFSs with DMM to calculate weights of risk factors. Because the DMM is of help in solving the problem that weights are partially known or even completely unknown, it has been widely used to calculate weights. For instance, Li et al. [39] adopted an IVIF-DMM to calculate weights of risk factors. According to information theory, a mean DMM is constructed by Wang et al. to compute the weights of decision-makers objectively. Yi et al. [40] calculated indicator weights using the DMM to highlight the overall difference among the performance values of alternatives. Geng et al. [41] put forward a weight determining method based on the DM principle, which could not only maintain the will of decision makers as much as possible, but also decrease the uncertainty of weights. Li et al. [42] extended the DMM to dynamic situation to calculate indicator weights with the purpose of widening the overall difference of the development of the cities.

Finally, the ranking mechanism of traditional FMEA method is irrational, which ranks failure modes numerically in line with the RPN values. In order to cope with this problem, there are many methods which were proposed to rank failure modes, for instance, the multi-attributive border approximation area comparison (MABAC) method [5], fuzzy multi-attribute ideal real comparative analysis (FMAIRCA) [13], preference ranking organization method for enrichment evaluation (PROMETHEE) approach [10], etc. In this paper, we combine IVq-ROFSs with ARAS method to rank failure modes. The ARAS method was first proposed by Zavadskas [43], which had simple, direct, easy and straightforward steps. The ease of use of this technique has led to the extension of its application in various fields, e.g., Ramezanali et al. [44] proposed a hybrid methodology combining the BWM with ARAS approaches to mineral prospectivity mapping. To select eco-friendly cities in Turkey, the ARAS method was used by Boyac ı [45] to obtain the final ranking of 81 cities. Rajabi [46] proposed a mixed method which combined the fuzzy analytical hierarchy process (FAHP) with fuzzy ARAS (ARAS-F) to identify and prioritize control measures of violence against health care workers. Ghram et al. [47] extended the classical ARAS method to hierarchical ARAS (ARAS-H) method, and adopted it in the case of a hierarchy of criteria. In order to determine optimum scheduled replacement time interval, Emovon et al. [48] proposed a multi-criteria decision making technique combined weighted aggregated sum product assessment (WASPAS) with ARAS. However, to the best of our knowledge, there is no study which carries out risk evaluation combining IVq-ROF-DMM with IVq-ROF-ARAS method in FMEA.

In the summary, the main motivation of this study is as follows: (1) these three risk factors (S, O and D) are so highly generalized that experts cannot accurately rate risks, introducing sub-risk factors can facilitate experts to provide more accurate assessment information; (2) A large quantity of uncertainties may exist in FMEA, IVq-ROFSs have an innate advantage in coping with the uncertainty and vagueness of experts’ evaluation information and provide a parameterized family of aggregation operators such as IVq-ROFWG operator and IVq-ROFWMSM operator; (3) IVq-ROF-DMM is well suited for calculating the relative weights of risk factors from the perspective of relative contrast intensities of risk factors; (4) IVq-ROF-ARAS method has simple, direct, easy and straightforward steps, which can yield reasonable, acceptable and relatively accurate results in ranking failure modes based on their performance concerning selected weighted sub-risk factors.

The major contributions of this paper are summarized up as follows: (1) As an extension of q-ROFSs, IVq-ROFSs score risks using interval value rather than crisp value, which solve the problem that providing exact values of failure modes concerning sub-risk factors for experts is increasingly difficult with the increasing complexity of products and the irrational problem of evaluation information fusion; (2) Introducing the concept of sub-risk factors, which can make risks more concrete and evaluation results more practical; (3) Weighting risk factors/sub-risk factors by IVq-ROF-DMM, which overcomes drawback which risk factors are equally weighted in the traditional FMEA; (4) Ranking failure modes with IVq-ROF-ARAS method, which ranks failure modes numerically in line with the degree of criticality, and overcomes drawback that ranking mechanism is irrational in the traditional FMEA.

The rest of this paper is organized as follows. In Section 2, some critical notions of q-ROFSs, IVq-ROFSs, IVq-ROFWG operator and IVq-ROFWMSM operator are briefly reviewed. The proposed FMEA method which includes risk identification and risk evaluation, consistency inspection and improvement process, weighting risk factors and sub-risk factors with IVq-ROF-DMM and ranking the failure modes with IVq-ROF-ARAS method, is introduced in Section 3. Section 4 presents a real case vis-à-vis tool changing manipulator of tool magazine. In Section 5, a discussion concerning sensitivity analysis, comparison analysis and managerial application is conducted to illustrate the rationality and effectiveness of the proposed FMEA method. The conclusions and future work are given in Section 6.

Section snippets

Preliminaries

To distinguish the self innovation of this paper, in this section, certain critical notions of q-ROFSs, IVq-ROFSs, IVq-ROFWG operator and IVq-ROFWMSM operator that will be utilized in the subsequent research are briefly reviewed.

The proposed FMEA method

To surmount deficiencies of the traditional FMEA method, a model for FMEA based on IVq-ROF-DMM and IVq-ROF-ARAS method is proposed, which includes four phases: risk identification and risk evaluation, consistency inspection and improvement process, weighting risk factors/sub-risk factors with IVq-ROF-DMM and ranking the failure modes with IVq-ROF-ARAS method. Firstly, all potential failure modes are identified based on the previous collected fault tree data, the concepts of cost risk factor and

Background information

In this section, a tool changing manipulator of tool magazine is utilized to demonstrate the implementation process of the proposed FMEA method. Fig. 4 shows the structure diagram of tool magazine, and the numbers 1–6 in the figure represent the six components of the tool magazine, respectively, namely hydraulic motor, tool changing manipulator, auxiliary manipulator, motor, transition tool sleeve and cutter chain. Tool changing manipulator is the core part of tool magazine, its main function

Sensitivity analysis

This paper proposes a model for FMEA based on IVq-ROF-DMM and IVq-ROF-ARAS method, in the proposed FMEA method, q which indicates different decision-making situations and p which indicates different distance measures are two important parameters that may affect the ranking results of failure modes. Therefore, it is necessary for us to analyze how these two parameters affect the failure modes ranking.

Firstly, a sensitivity analysis about parameter q is conducted to explore the influence of

Conclusions and future work

In this paper, a model for FMEA based on IVq-ROF-DMM and IVq-ROF-ARAS method is proposed to conduct risks evaluation. Firstly, the concepts of cost risk factor and sub-risk factors are introduced to make the experts’ evaluation information more practical, and the IVq-ROFSs are utilized to rate risks. Then, a consistency inspection and improvement process is conducted to make experts’ evaluation information more consistent, and the IVq-ROFWG operator and the IVq-ROFWMSM operator are used to fuse

CRediT authorship contribution statement

Chuanxi Jin: Conceptualization, Methodology, Formal analysis, Software, Validation, Investigation, Writing - original draft, Writing - review & editing. Yan Ran: Supervision, Writing - review & editing. Genbao Zhang: Supervision, Project administration.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was financially supported by the National Natural Science Foundation, China (No. 51835001; 51705048); the National Major Scientific and Technological Special Project for “High-grade CNC and Basic Manufacturing Equipment”, China (2018ZX04032-001; 2019ZX04005-001); the State Education Ministry and the Fundamental Research Funds for the Central Universities (2019CDJSK04XK23)”.

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