Fuzzy Failure Modes and Effects Analysis

At the University of California in 1965, Prof. L Zadeh (1965) introduced fuzzy logic by extending possibility theory where its basis was formed from a fuzzy set (Riahi et al., 2012). Zadeh designed the theory to deal with the fuzziness of human judgment. Fuzzy logic allowed a mathematical approach to be applied for identifying fuzzy information, knowledge, and concepts (Riahi et al., 2012). In other words, in probability theory the values are indicated by numbers; however, in possibility theory the values are indicated by words, in natural or artificial language, to deal with uncertainty. Thus probability theory and possibility theory are distinct. Negligible, moderately likely, and highly unlikely are a sample of description variables that may be used for defining situations (Pillay and Wang, 2003; Sii, et al., 2001). These linguistic variables allow imprecise possibility statements to be mathematically described within fuzzy algorithms. From the beneficial characteristics of the linguistic

variables to the possibility theory, the technique developed in the 1960s (i.e. fuzzy logic) became one of the most widely known approaches in expert knowledge.

According to Liu et al. (2004), fuzzy knowledge base/rule base is the core fuzzy logic structure. A fuzzy knowledge base/rule base is constructed by using experts’ knowledge and expertise about the failure in the form of fuzzy IF-THEN rules (Yang et al., 2008). A simple example of a fuzzy IF-THEN rule is as follows (Liu et al., 2004):

𝐼𝐹 𝑥 𝑖𝑠 𝐴 𝑇ℎ𝑒𝑛 𝑦 𝑖𝑠 𝐵 4.2

where 𝐴 and 𝐵 represent the linguistic grades for rules 𝑥 and 𝑦 respectively. The first part of the fuzzy IF-THEN rule (i.e. the IF part) is known as the antecedent or premise, whilst the second part of the rule (i.e. the THEN part) is known as the consequence or conclusion (Liu et al., 2004).

In a fuzzy rule base FMEA, the L, C, and P are represented in the IF, whilst the THEN represents the risk. An example of a fuzzy IF-THEN rule for safety analysis is as follows (Liu et al., 2004):

Rule: IF the Failure Rate (FR) is frequent and the Consequence Severity (CS) is catastrophic and the Failure Consequence Probability (FRP) is likely, THEN the Safety Level (S) is poor

Incompleteness is another type of uncertainty. This type of uncertainty occurs when the experts are incapable of creating a strong correlation between the IF and the THEN. In other words, it occurs when there is not enough available evidence, or when the experts’ belief in a particular hypothesis is not 100% certain, but only to a certain degree of belief (Liu et al., 2004). An example of a fuzzy IF-THEN rule with degree of belief for multiple possible consequence terms is as follows (Yang et al., 2008):

Rule: IF Likelihood (L) is Very Low, Consequence severity (C) is Negligible and chance of failure being undetected (P) is Reasonably Unlikely, THEN S is Good with 0.91, Average with 0.09, Fair with 0 and Poor with 0

where [(Good 0.91), (Average 0.09), (Fair 0), and (Poor 0)] is the expert degree of belief, which means that the experts are 91% sure that the safety level is Good, and 9% sure that the safety level is Average.

The representation of knowledge and reasoning with rules-based structures is widely used in risk assessment due to the following factors (Rahman, 2012; Liu et al., 2004; John et al. 2014a):

 The modularity of each rule, which can be seen as one unit of knowledge

 The expressed knowledge in the rule, which is represented with the same formation

 The natural formation of the rules in knowledge expression

 The easiness and clarity of the expressed knowledge

The incorporation of fuzzy logic and FMEA for enhancing the performance of FMEA has been widely applied. For example, an alternative multi-attribute decision-making method was proposed by Braglia et al. (2003), who termed the method the fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. This decision-making method considers the three risk attributes (i.e. L, C, and P) as criteria, and the failure mode as an alternative.

A fuzzy method and grey theory were proposed by Chang et al. (1999). To evaluate the risk attributes L, C, and P, the researchers applied fuzzy linguistic variables. However, the grey theory was used for determining the risk priority of potential failure. Pillay and

Wang (2003) developed a fuzzy rule-based approach that does not require a utility function for defining the risk factors and avoids using the traditional use of RPN. The linguistic variables in Pillay and Wang’s (2003) study that represented the three FMEA attributes were directly evaluated within this method. Other studies have assigned relative weighting coefficients using the grey theory to achieve an RPN. Similar studies, such as Sharma et al. (2008, 2007) and Chang et al. (2001), applied the fuzzy method and grey theory for ranking the failure mode in FMEA.

A critical risk assessment approach was presented by Puente et al. (2002). The approach is qualitative rule-based, which provides a risk ranking for potential failures. Depending on the presented knowledge about the three risk factors (failure detection, frequency, and severity), a risk priority ranking is assigned to each failure cause in an FMEA. A total of 125 rules are then structured by using the IF-THEN rule formation in FMEA. All the rules are presented in a three-dimensional graph. Liu et al. (2015) combined interval 2-tuple linguistic variables with grey relational analysis to improve the effectiveness of the traditional FMEA in medical services. Jiang et al. (2017) developed an advance risk ranking method based on fuzzy evidential theory in a Micro-Electro- Mechanical System (MEMS). Tazi et al. (2017) integrated cost factors to traditional FMEA to improve system design reliability of wind turbine systems.

Among the developments in FMEA, a fuzzy rule-based Bayesian reasoning (FuRBaR) approach was developed by Yang et al. (2008) to prioritise failures in FMEA without compromising the simplicity of the traditional RPN approach. The researchers developed this hybrid technique to deal with some of the FMEA drawbacks regarding the use of conventional fuzzy rule-based methods. The connection between the L, C, and P parameters is established in a fuzzy IF-THEN rule with the degree of belief structure in FuRBaR defined by using domain experts’ knowledge. The approach

applies the mechanism of Bayesian reasoning to rank the potential failure modes through aggregating the relevant rules.

For the purpose of this research, the technique of fuzzy rule-based Bayesian reasoning (FRBBR) is adopted. This hybrid technique analyses the risks associated with PTSs and provides a risk-ranking technique that is useful for decision-makers in uncertain situations. Therefore, it is important to understand the Bayesian Network (BN) mechanism for applying the FRBBR technique.