Failure mode and effects analysis using a group-based evidential reasoning approach

Abstract

Failure mode and effects analysis (FMEA) is a methodology to evaluate a system, design, process or service for possible ways in which failures (problems, errors, risks and concerns) can occur. It is a group decision function and cannot be done on an individual basis. The FMEA team often demonstrates different opinions and knowledge from one team member to another and produces different types of assessment information such as complete and incomplete, precise and imprecise and known and unknown because of its cross-functional and multidisciplinary nature. These different types of information are very difficult to incorporate into the FMEA by the traditional risk priority number (RPN) model and fuzzy rule-based approximate reasoning methodologies. In this paper we present an FMEA using the evidential reasoning (ER) approach, a newly developed methodology for multiple attribute decision analysis. The proposed FMEA is then illustrated with an application to a fishing vessel. As is illustrated by the numerical example, the proposed FMEA can well capture FMEA team members’ diversity opinions and prioritize failure modes under different types of uncertainties.

Introduction

Failure mode and effects analysis (FMEA) is an engineering technique used to define, identify and eliminate known and/or potential failures, problems, errors and so on from the system, design, process and/or service before they reach the customer [1], [2], [3]. When it is used for a criticality analysis, it is also referred to as failure mode, effects and criticality analysis (FMECA). FMEA has gained wide acceptance and applications in a wide range of industries such as aerospace, nuclear, chemical and manufacturing. A good FMEA can help analysts identify known and potential failure modes and their causes and effects, help them prioritize the identified failure modes and can also help them work out corrective actions for the failure modes. The main objective of FMEA is to allow the analysts to identify and prevent known and potential problems from reaching the customer. To this end, the risks of each identified failure mode need to be evaluated and prioritized so that appropriate corrective actions can be taken for different failure modes. The priority of a failure mode is determined through the risk priority number (RPN), which is defined as the product of the occurrence $(O)$, severity $(S)$ and detection $(D)$ of the failure, namely

$$\mathrm{RPN}=O\times S\times D\text{.}$$

The three factors O, S and D are all evaluated using the ratings (also called rankings or scores) from 1 to 10, as described in Table 1, Table 2, Table 3. The failures with higher RPNs are assumed to be more important and should be given higher priorities.

FMEA has been proven to be one of the most important early preventative initiatives during the design stage of a system, product, process or service. However, the RPN has been extensively criticized for various reasons [4], [5], [7], [8], [9], [10], [11]:

• Different sets of O, S and D ratings may produce exactly the same value of RPN, but their hidden risk implications may be totally different. For example, two different events with values of 2, 3, 2 and 4, 1, 3 for O, S and D, respectively, will have the same RPN value of 12. However, the hidden risk implications of the two events may be very different because of the different severities of the failure consequence. This may cause a waste of resources and time, or in some cases, a high-risk event being unnoticed.

• The relative importance among O, S and D is not taken into consideration. The three factors are assumed to have the same importance. This may not be the case when considering a practical application of FMEA.

• The mathematical formula for calculating RPN is questionable and debatable. There is no rationale as to why O, S and D should be multiplied to produce the RPN.

• The conversion of scores is different for the three factors. For example, a linear conversion is used for O, but a nonlinear transformation is employed for D.

• RPNs are not continuous with many holes and heavily distributed at the bottom of the scale from 1 to 1000. This causes problems in interpreting the meaning of the differences between different RPNs. For example, is the difference between the neighboring RPNs of 1 and 2 the same or less than the difference between 900 and 1000?

• The RPN considers only three factors mainly in terms of safety. Other important factors such as economical aspects are ignored.

• Small variations in one rating may lead to vastly different effects on the RPN, depending on the values of the other factors. For example, if O and D are both 10, then a 1-point difference in severity rating results in a 100-point difference in the RPN; if O and D are equal to 1, then the same 1-point difference results in only a 1-point difference in the RPN; if O and D are both 4, then a 1-point difference produces a 16-point difference in the RPN.

• The three factors are difficult to precisely determine. Much information in FMEA can be expressed in a linguistic way such as likely, important or very high and so on.

A number of approaches have been suggested in the literature to overcome some of the drawbacks mentioned above. For example, Gilchrist [10] gave a critique of FMEA and proposed an expected cost model. It was formulated as $\mathit{EC}={\mathit{CnP}}_{\mathrm{f}}{P}_{\mathrm{d}}$, where EC is the expected cost to the customer, C the cost per failure, n the items produced per batch or per year, $P_{\mathrm{f}}$ the probability of a failure and $P_{\mathrm{d}}$ the probability of the failure not to be detected. $P_{\mathrm{f}}$ and $P_{\mathrm{d}}$ were assumed to be independent and their product represents the probability that the customer receives a faulty product. The ${\mathit{nP}}_{\mathrm{f}}{P}_{\mathrm{d}}$ is the expected number of failures reaching the customer. The expected cost model was claimed to be more rigorous yet practical than the RPN model and to have great benefit of forcing people to think about quality costs.

Ben-Daya and Raouf [7] argued that the probabilities $P_{\mathrm{f}}$ and $P_{\mathrm{d}}$ in the expected cost model were not always independent and very difficult to estimate at the design stage of a product and the severity was completely ignored by the expected cost model. Based on these arguments, they proposed an improved FMEA model which addressed Gilchrist's criticism and gave more importance to the likelihood of occurrence over the likelihood of detection by raising the ratings for the likelihood of occurrence to the power of 2. The improved FMEA model was combined with the expected cost model to provide a quality improvement scheme for the production phases of a product or service in the way that the former was used to identify the critical failures that require immediate remedial action, whereas the later was used in parallel to estimate the cost of failures reaching the customer and to evaluate the impact of the corrective action taken.

Sankar and Prabhu [5] presented a modified approach for prioritization of failures in a system FMEA, which uses the ranks 1–1000 called risk priority ranks (RPRs) to represent the increasing risk of the 1000 possible severity–occurrence–detection combinations. These 1000 possible combinations were tabulated by an expert in order of increasing risk and can be interpreted as ‘if–then’ rules. The failure having a higher rank was given a higher priority.

Bevilacqua et al. [12] defined RPN as the weighted sum of six parameters which are safety, machine importance for the process, maintenance costs, failure frequency, downtime length and operating conditions, multiplied by the seventh factor, i.e. machine access difficulty, where the relative importance weights of the six parameters were estimated using pairwise comparisons. Monte Carlo simulation was performed as a sensitivity analysis to verify the robustness of the final ranking results.

Braglia [13] developed a multi-attribute failure mode analysis (MAFMA) based on the analytic hierarchy process (AHP) technique, which considers four different factors O, S, D, and expected cost as decision attributes, possible causes of failure as decision alternatives, and the selection of cause of failure as decision goal. The goal, attributes and alternatives formed a three-level hierarchy, where the pairwise comparison matrix was used to estimate attribute weights and the local priorities of the causes with respect to the expected cost attribute, the conventional scores for O, S and D were normalized as the local priorities of the causes with respect to O, S, and D, respectively, and the weight composition technique in the AHP was utilized to synthesize the local priorities into the global priority, based on which the possible causes of failure were ranked. A sensitivity analysis was also conducted to investigate the sensitivity of the priority ranking of the causes to the changes in attribute weights.

Braglia et al. [14] also presented an alternative multi-attribute decision-making approach called fuzzy TOPSIS approach for FMECA, which is a fuzzy version of the technique for order preference by similarity to ideal solution (TOPSIS). The TOPSIS method is a well-known multi-attribute decision-making methodology based on the assumption that the best decision alternative should be as close as possible to the ideal solution and the farthest from the negative-ideal solution. The proposed fuzzy TOPSIS approach allows the risk factors O, S and D and their relative importance to be assessed using triangular fuzzy numbers rather than precise crisp numbers.

Chang et al. [15] used fuzzy sets and gray systems theory for FMEA, where fuzzy linguistic terms such as very low, low, moderate, high and very high were used to evaluate the degrees of O, S and D, and gray relational analysis was applied to determine the risk priority of potential causes. To carry out the gray relational analysis, fuzzy linguistic assessment information was defuzzified as crisp values, the lowest level of the three factors O, S and D was defined as a standard series, and the assessment information of the three factors for each potential cause was viewed as a comparative series, whose gray relational coefficients and gray relational degree with the standard series were computed in terms of the gray systems theory [16]. Bigger gray relational degree means smaller effect of potential cause. The increasing order of the gray relational degrees represents the risk priority of the potential problems to be improved. In [9], Chang et al. also utilized the gray system theory for FMEA, but the gray relational degrees were computed using the traditional scores 1–10 for the three factors rather than fuzzy linguistic assessment information.

Seyed-Hosseini et al. [17] proposed a method called decision making trial and evaluation laboratory (DEMATEL) for reprioritization of failure modes in FMEA, which prioritizes alternatives based on severity of effect or influence and direct and indirect relationships between them. Direct relationships were a set of connections between alternatives with a set of connection weights representing severity of influence of one alternative on another. An indirect relationship was defined as a relationship that could only move in an indirect path between two alternatives and meant that a failure mode could be the cause of other failure mode(s). Alternatives having more effect on another were assumed to have higher priority and called dispatcher. Those receiving more influence from another were assumed to have lower priority and called receiver.

Bowles and Peláez [18] described a fuzzy logic-based approach for prioritizing failures in a system FMECA, which uses linguistic terms such as remote, low, moderate, high and very high to describe O, minor, low, moderate, high and very high for S, non-detection, very low, low, moderate, high and very high for D and not-important, minor, low, moderate, important and very important for the riskiness of failure. The relationships between the riskiness and O, S, D were characterized by a fuzzy if–then rule base which was developed from expert knowledge and expertise. Crisp ratings for O, S and D were fuzzified to match the premise of each possible if–then rule. All the rules that have any truth in their premises were fired to contribute to the fuzzy conclusion. The fuzzy conclusion was then defuzzified by the weighted mean of maximum method (WMoM) as the ranking value of the risk priority. Similar fuzzy inference method also appeared in [6], [8], [11], [19], [20], [21], [22], [23], [24], [25].

Fuzzy RPN approaches usually require a large number of rules and it is a tedious task to obtain a full set of rules. The larger the number of rules provided by the users, the better the prediction accuracy of the fuzzy RPN model. Tay and Lim [24] argued that not all the rules were actually required in fuzzy RPN models, eliminating some of the rules did not necessarily lead to a significant change in the model output, but some of the rules might be vitally important and could not be ignored. They thus proposed a guided rules reduction system (GRRS) to simplify the fuzzy logic-based FMEA methodology by reducing the number of rules that need to be provided by FMEA users for fuzzy RPN modeling process.

The above literature review shows that much effort has been paid to the improvement of FMEA by incorporating factor weights, more factors, expert knowledge and/or fuzziness into the analysis, but no or little attention has been paid to the diversity and uncertainty of assessment information. As is known, FMEA is a team function and cannot be performed on an individual basis. In other words, FMEA is a group decision behavior. Different FMEA team members may demonstrate different opinions because of their different expertise and backgrounds [26]. They may provide different assessment information for the same risk factor, some of which may be complete or incomplete, precise or imprecise, known or unknown and certain or uncertain. This diversity and uncertainty of assessment information is sometimes inherent, not easy to eliminate and in need of being considered in FMEA. In this paper we propose a new risk priority model for FMEA using the evidential reasoning (ER) approach. The new model can not only model the diversity and uncertainty of the assessment information in FMEA, but also incorporate the relative importance of risk factors into the determination of risk priority of failure modes in a strict way.

The paper is organized as follows. In Section 2, we develop the risk priority model using the ER approach and incorporate the relative importance weights of risk factors into the determination of risk priority of failure modes. In Section 3, we provide a numerical example to illustrate the potential applications of the new model in FMEA. Section 4 concludes the paper with a summary.