Improved failure mode and effect analysis with interval-valued intuitionistic fuzzy rough number theory
Introduction
As a systematic and powerful risk assessment and identification methodology, failure mode and effect analysis (FMEA) has been regarded as an important and effective reliability management technique to extract and prioritize known or potential failures, errors, and problems influencing the quality and safety of products or systems (Liu et al., 2019b). FMEA is usually conducted through a cross-functional team of FMEA experts with different backgrounds to assist risk engineers to determine failure modes’ risk orders and crucial failures that should be improved for the reliability and performance of the overall system (Lo et al., 2019). Its main goal is to investigate and analyze all failure modes, list their causes and effects from bottom to top in the product or system, and then develop corrective measures to eliminate and reduce the crucial ones before they occur. Due to its flexibilities and advantages, FMEA method has been widely applied and presented a remarkable contribution in lots of industries, e.g., aerospace (Gargama and Chaturvedi, 2011, Li et al., 2019d), trucking industry (Dadsena et al., 2019), air conditioning system (Kim and Zuo, 2018), and healthcare system (Liu et al., 2019b).
In the classical FMEA model, the risk priority number (RPN) is applied to reflect the risk level of each failure mode, which is calculated by the arithmetic product of the crisp evaluation values of three RPN elements (risk elements) under corresponding failure mode, i.e., occurrence (O), severity (S), and detection (D). A 10-point scale is employed to quantify each RPN element’s risk. The higher the score of RPN means the stronger the influence level of the corresponding failure mode to the system. Based on RPN results, the risk order rankings of all failure modes are identified, and then rational control actions are developed to maintain the quality and reliability of the subject system. As an important early preventive technique, FMEA has been frequently used to provide valuable risk information. However, the conventional RPN method has been criticized for numerous inherent limitations that weaken its effectiveness. The most crucial ones are presented as follows (Catelani et al., 2018, Huang et al., 2017, Liu et al., 2017a, Liu et al., 2019a, Wang et al., 2018b): (1) The accurate and crisp ratings of three RPN elements are difficult to be determined. (2) The relative weights of RPN elements and FMEA experts are not considered. (3) Different evaluation sets of RPN elements may yield the same RPN result. For example, the RPN elements’ evaluations of two failure modes are 2, 1, 9, and 3, 2, 3, respectively, their RPN is the same, i.e., 18. However, their real risk levels are different. (4) Only the three RPN elements are considered, which may not make a precise depiction of a system’s risk. (5) The arithmetical formula of RPN is too simplistic and is strongly sensitive to assessments’ variations.
Recently, numerous positive approaches have been proposed by related researchers to conquer the limitations of the classical FMEA technique and to enhance the performance and precision of risk evaluations. Considering the vagueness of human cognition, it is usually difficult for experts to assess failure modes by exact numbers. Fuzzy set (FS) theory is a useful technique for linguistic computation and can reflect the vagueness and uncertainty of qualitative notions (Lakshmi and Baskar, 2019). Over the last decade, the extended FMEA methods based on FS theory have been the most popular method (Li et al., 2019a). Plenty of previous FMEA approaches employ FS theory to conduct the conversion between quantitative numbers and qualitative notions for coping with risk assessments under uncertain environment, e.g., FMEA based on D-number (Bian et al., 2018), linguistic distribution assessment (Liu et al., 2019a), 2-tuple linguistic terms (Liu et al., 2016), and triangular fuzzy number (Panchal et al., 2019). However, the weaknesses of FS theory may weaken the precision and credibility of the final risk orders, such as (1) Neglecting the subjective and hesitation of membership ratings (Wang et al., 2018a); (2) The suitable membership functions are often hard to determine, which is complicated; (3) There is no mechanism of handling consensus of experts, i.e., group uncertainty (Li et al., 2019a). In addition, the relative weights of both RPN elements and experts in related studies are either lose sight of calculation or determined by using subjective weighting approach or through applying objective weighting approach, and many improved FMEA methods potentially consider the assessments given by experts are total reliable. These may lead to information loss and precision decrease of the real importance of RPN elements or experts. Maintenance (M) is an important criterion that can reflect real risk levels of failure modes, and a few pieces of research considered it. Most of the previous methods only consider the three classical RPN elements (O, D, and D) to determine failure modes’ risk levels, which may not capture failures’ real risk information. Finally, failure mode priority is a process of multiple criteria group decision-making (MCGDM) (Baghery et al., 2018). The technique for order performance by similarity to ideal solution (TOPSIS) method can give valuable quantitative information that concurrently considers the best solution and the worst solution in all alternatives. However, the conventional TOPSIS model cannot manipulate vagueness and subjectivity and is also not suitable for multidimensional and hierarchical decision-making problems. Hence, it is necessary to develop a comprehensive risk assessment model to overcome these issues.
Inspired by the above discussions, a novel extended FMEA method that unites the merits of interval-valued intuitionistic fuzzy set (IVIFS) theory, rough number, and hierarchical TOPSIS approach is extended in this study to effectively and precisely prioritize the risk levels of all failures. The main contributions of the developed risk assessment model are summed up as follows: (1) A novel integrated linguistic computation model, namely interval-valued intuitionistic fuzzy rough number (IVIFRN), is developed to manipulate risk assessments given FMEA experts, which can manipulate diverse uncertainties, i.e., vagueness, hesitation, and subjectivity. The mathematical construction form, operating properties, and integration operators of IVIFRN are presented; (2) M is added into the three classical RPN elements (O, S, and D) as a new risk aspect, and thus to build a risk evaluation structure containing four dimensions and eight RPN elements by dividing the O, S, D, and D into eight different parameters, respectively; (3) The bounded rationality of experts and the overall weights of RPN elements are computed by the two synthetic weighting methods developed in this study that simultaneously consider subjective and objective aspects, which can fully express their relative importance levels and make the risk rankings of all failure modes more reliable; (4) An integrated hierarchical TOPSIS based on IVIFRN is presented to identify the risk rankings of all failure modes; (5) To demonstrate the developed model’s feasibility and effectiveness, a real risk assessment case of a rotary turntable is conducted together with a comparison to current approaches.
The rest of this study is presented as follows: Section 2 introduces the related studies regarding the improvement of FMEA systematically. Section 3 outlines IVIFS theory and some related notions; Based on them, the new hybrid linguistic computation method of IVIFRN is developed in Section 4, and some arithmetic operations of IVIFRN are also presented. In Section 5, the novel proposed FMEA model is displayed on the basis of IVIFRN and hierarchical TOPSIS mentioned above, whose feasibility and effectiveness are demonstrated by a real application case in Section 6. Finally, Section 7 remarks on the conclusions and future researches.
Section snippets
A literature review of the improved FMEA
The inherent deficiencies of the conventional FMEA model often lead to imprecise and undependable risk assessment results in practical situations, especially when superintendents meet with uncertain and vague information in the decision making processes (Zhou and Thai, 2016). In the past years, numerous extended FMEA methods have been developed to conquer the weaknesses of the classical RPN approach and to enhance the precision and effectiveness of failures’ risk evaluations. In this section,
IVIFSs theory
The concept of IVIFS is first introduced by Atanassov based on the classical fuzzy set method and interval theory (Jiang et al., 2010), in which the membership and non-membership function of each assessment elements are reflected as an interval value rather than the crisp number. Due to its complete flexibility and effectiveness in dealing with vagueness and hesitation of human cognition, IVIFS has been used in a variety of fields. The basic concepts of IVIFS are presented as follows:
Definition 1 Let X {Jiang et al., 2010, Liu et al., 2019b
Interval-valued intuitionistic fuzzy rough numbers (IVIFRNs)
Based on the rough set theory without the ability to handle vague information, the concept of rough number is first developed by Zhai et al. (2009) to manipulate subjectivity and incompleteness of customers’ preference information in quality function deployment. It applies three concepts, i.e., upper approximation, lower approximation, and boundary interval, to express decision-makers’ assessment roughness. One of its prominent characteristics is that subjectivity and imprecision are stemmed
Developed FMEA model
In this section, an integrated risk evaluation method is developed to assess the risk orders of failure modes. The developed approach employs IVIFRN theory to handle various uncertainties, where the risk evaluation values are provided by FMEA experts in linguistic variables, and then applies the hierarchical TOPSIS approach to rank failure modes. The implementation process of the developed FMEA model is depicted in Fig. 1, which contains five main stages.
Stage 1: Evaluation of failure modes and
Application example
In this section, a real illustrative case assessing failure modes’ risk orders for a rotary turntable is presented to demonstrate the feasibility and effectiveness of the newly developed FMEA model.
Conclusions, limitations, and future works
A newly integrated risk assessment model by combining IVIFRN theory and hierarchical TOPSIS method is proposed to assess and prioritize identified failure modes in FMEA. It enhances the precision of FMEA team members’ assessments to make risk ranking results closer to practical situations. A real application example regarding a rotary turntable to demonstrate the effectiveness of the developed risk model is performed and the same case is also conducted by other existing FMEA approaches to
CRediT authorship contribution statement
Guangquan Huang: Conceptualization, Methodology, Writing - original draft. Liming Xiao: Methodology, Writing - review & editing. Genbao Zhang: Project administration, Writing - review & editing.
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 supported in part by the National Natural Science Foundation of China under Grant 51705048, and in part by the National Major Science and Technology Projects of China under Grant 2018ZX04032-001.
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