The failure mode and effect analysis (FMEA) is widely used an effective pre-accident risk assessment tool to identify, eliminate, and assess potential failure modes in different industries for enhancing the safety and reliability of systems, process, services, and products. Therefore, this chapter presents a new approach to rank the failure modes under the interval-valued intuitionistic fuzzy set (IVIFS). For this, a novel measure to measure the fuzziness known as entropy measure is proposed. Some properties and axiom definition of the proposed entropy measure have been presented to show the validity of it. Afterwards, the proposed entropy measure is utilized to obtain the weight of risk factor and developed an approach under the IVIFS environment to determine the risk priority order of failure modes. Finally, a real-life case of FMEA has been discussed to manifest the developed approach, and obtained results are compared with the results obtained by the existing methods for showing the feasibility and validity of the proposed approach.
TopIntroduction
The Failure Mode and effect Analysis (FMEA) method is a risk analyzing method for identifying and removing possible faults, issues and errors to improve system, architecture, process and service efficiency and safety. FMEA first introduced by the United Nations in the 1960s as a formal and systematic approach in aerospace industry of countries with their obvious safety and reliability requirements(Bowles & Peláez, 1995). FMEA’s main purpose is to correct key failure modes instead of fixing them after failures, they reach the customer before. In last decade, FMEA has become a powerful and useful tool that is commonly used in many sectors, including the power, mechanical aerospace, and healthcare industries(Chang & Cheng, 2011; Huang et al., 2017; Li et al., 2019; Song et al., 2013; Vahdani et al., 2015).In typical FMEA, failure modes (FMs) are evaluated with regard to risk factors: occurrence (O), severity (S), and detection (D). The risk priority setting of FMs is determined by calculating its risk priority numbers (RPNs), obtained by multiplying the risk factors O, S and D.
While traditional FMEA is a useful risk assessment tool, it is widely criticized for a number of inconveniences in the literature (H.-C. Liu, 2016; Zhao et al., 2017) which are summarized as follows:
- 1.
The risk factors are di cult to quantify accurately and entirely, due to the uncertainty and vagueness of the decisions of FMEA team members.
- 2.
In conventional FMEA, for the determination of FMs, only three risk factors O, S and D are used, which may ignore other important process or system factors.
- 3.
The relative importance of risk factors, which is not fair in the real case, is not taken into account.
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Using RPNs to assess the probability rating of modes of failure is controversial and debatable.
To overcome the disadvantages of conventional FMEA, scholars have implemented several theories of ambiguity and multi-attribute decision-making (MADM) approaches for tackling the FMEA issues. One of them,Zadeh(1965) introduced the concept of the fuzzy sets (FSs), and after that its extensions intuitionistic FSs (IFSs) (Atanassov, 1986) and interval-valued IFSs (IVIFSs)(Atanassov & Gargov, 1989) have presented as powerful tools to handling the uncertainty. Recently, these theories have been more applied to solve the real world FMEA issues. Song et al.(2013) introduced the FMEA based on the fuzzy TOPSIS. To describe the FMEA information,Vahdani et al.(2015) described a fuzzy structure.
During the decision-making (DM) process in MADM problems the attribute weights play crucial role because fluctuation in the weights can change the ranking of the alternatives. In some MADM problems criteria weights are given by the decision-makers but in some situations decision-makers cannot set the attribute weights due to the fuzziness of the data. Entropy measure is an important method to manage it, which is essentially known as the knowledge measure derived from C.E.Shannon(Shannon, 1948)’s fundamental paper “The Mathematical Theory of Communication.” One of the trusted fields for calculating the degree of uncertainty in the data is information theory. Classical measurements of information, how-ever, deal with information that is detailed in nature. To resolve this, a collection of axioms for fuzzy entropy was suggested in (Deluca A, 1972). Zhang & Jiang(2008) generalized the logarithmic fuzzy entropy measure given in (De Luca & Termini, 1993) for IFSs. Wei et al.(2012) presented a new entropy by using the cosine function for IFS. Wang & Wang(2012) defined cotangent entropy measure for IFS. Verma & Sharma(2013) presented the exponential entropy measure of IFSs. Further, the all above existing entropy measures of IFSs do not contain the degree of hesitancy of IFS. M. Liu & Ren(2014) realized some drawbacks of above existing entropy measures of IFS and presented a new entropy measure by containing the degree of hesitance of IFS. Nguyen(2016) defined the knowledge measure based entropy for IVIFSs.Rashid et al.(2018) defined the distance based entropy measure in context of IVIFSs.Meng & Chen(2016) defined the similarity and entropy measure for IVIFS.