Classical Sets and Fuzzy Sets.- Classical and Fuzzy Relations.- Membership Functions.- Defuzzification.- Fuzzy Rule-Based System.- Fuzzy Decision Making.- Applications of Fuzzy Logic.- Fuzzy Logic Projects with Matlab.

Introduction to Fuzzy Logic using MATLAB

Failure mode and effects analysis (FMEA) is a risk assessment tool that mitigates potential failures in systems, processes, designs or services and has been used in a wide range of industries. The conventional risk priority number (RPN) method has been criticized to have many deficiencies and various risk priority models have been proposed in the literature to enhance the performance of FMEA. However, there has been no literature review on this topic. In this study, we reviewed 75 FMEA papers published between 1992 and 2012 in the international journals and categorized them according to the approaches used to overcome the limitations of the conventional RPN method. The intention of this review is to address the following three questions: (i) Which shortcomings attract the most attention? (ii) Which approaches are the most popular? (iii) Is there any inadequacy of the approaches? The answers to these questions will give an indication of current trends in research and the best direction for future research in order to further address the known deficiencies associated with the traditional FMEA.

Review: Risk evaluation approaches in failure mode and effects analysis: A literature review

Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis

Failure mode and effects analysis (FMEA) has been extensively used for examining potential failures in products, processes, designs and services. An important issue of FMEA is the determination of risk priorities of the failure modes that have been identified. The traditional FMEA determines the risk priorities of failure modes using the so-called risk priority numbers (RPNs), which require the risk factors like the occurrence (O), severity (S) and detection (D) of each failure mode to be precisely evaluated. This may not be realistic in real applications. In this paper we treat the risk factors O, S and D as fuzzy variables and evaluate them using fuzzy linguistic terms and fuzzy ratings. As a result, fuzzy risk priority numbers (FRPNs) are proposed for prioritization of failure modes. The FRPNs are defined as fuzzy weighted geometric means of the fuzzy ratings for O, S and D, and can be computed using alpha-level sets and linear programming models. For ranking purpose, the FRPNs are defuzzified using centroid defuzzification method, in which a new centroid defuzzification formula based on alpha-level sets is derived. A numerical example is provided to illustrate the potential applications of the proposed fuzzy FMEA and the detailed computational process of the FRPNs.

https://personalpages.manchester.ac.uk/staff/jian-bo.yang/JB%20Yang%20Journal_Papers/WangChinPoonYang_ESWA.pdf

Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean

Modified failure mode and effects analysis using approximate reasoning

Using fuzzy cognitive maps as a system model for failure modes and effects analysis

The risk priority number (RPN) methodology for prioritizing failure modes is an integral part of the automobile FMECA technique. The technique consists of ranking the potential failures from 1 to 10 with respect to their severity, probability of occurrence, and likelihood of detection in later tests, and multiplying the numbers together. The result is a numerical ranking, called the RPN, on a scale from 1 to 1000. Potential failure modes having higher RPNs are assumed to have a higher design risk than those having lower numbers. Although it is well documented and easy to apply, the method is seriously flawed from a technical perspective. This makes the interpretation of the analysis results problematic. The problems with the methodology include the use of the ordinal ranking numbers as numeric quantities, the presence of holes making up a large part of the RPN measurement scale, duplicate RPN values with very different characteristics, and varying sensitivity to small changes. Recommendations for an improved methodology are also given.

An assessment of RPN prioritization in a failure modes effects and criticality analysis

A failure mode and effects analysis (FMEA) seeks to determine how a system will behave in the event of a device failure. It involves the integration of several expert tasks to select components for analysis, determine failure modes, predict failure effects, propose corrective actions, etc. During an FMEA, numerical values are often not available or applicable and qualitative thresholds and linguistic terms such as high, slightly high, low, etc., are usually more relevant to the design than numerical expressions. Fuzzy set theory and fuzzy cognitive maps provide a basis for automating much of the reasoning required to carry out an FMEA on a system. They offer a suitable technique to allow symbolic reasoning in the FMEA instead of numerical methods, thus providing human like interpretations of the system model under analysis, and they allow for the integration of multiple expert opinions. This paper describes how fuzzy cognitive maps can be used to describe a system, its missions, failure modes, their causes and effects. The maps can then be evaluated using both numerical and graphical methods to determine the effects of a failure and the consistency of design decisions.

Applying fuzzy cognitive-maps knowledge-representation to failure modes effects analysis

The new SAE FAMECA standard goes a long way toward bringing FMECA (failure mode effects and criticality analysis) into line with modern design practices. This is accomplished through three major changes. (1) The new standard describes the FMECA procedure as a process to be used throughout the product development cycle, rather than as a task to be done after the design is complete. It emphasizes the role of functional and interface FMECAs as well as that of the traditional piece part FMECA. (2) The concept of "failure mode equivalence" enables failure modes that have equivalent effects to be analyzed together and reduces much of the duplicative work generated by traditional component-by-component fault analyses. This concept allows the analyses of functional failure modes done early in the design process to be carried over to the effects of interface and piece-part failure modes analyzed later in the design. (3) Criticality is assessed using a Pareto ranking procedure based on the probability and the severity of the failure mode. This is more broadly applicable than the use of criticality numbers as defined in Mil-Std-1629 and it avoids some of the mathematical difficulties of the RPN analysis used in the Automobile FMECA standard, SAE J1739.

J.B. Bowles

Papers

Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis

Using fuzzy cognitive maps as a system model for failure modes and effects analysis

An assessment of RPN prioritization in a failure modes effects and criticality analysis

Applying fuzzy cognitive-maps knowledge-representation to failure modes effects analysis

The new SAE FMECA standard