Equivalence relations within the failure mode and effects analysis

The reliability and maintainability community has long sought ways to improve the value of the FMEA as a means to influence the final design during early development stages. In addition to eliminating unacceptable single-point failures, provisions for fault detection and fault isolation (FD/FI) provide the most significant areas where the design can be influenced by the FMEA. The most recent gains in this area have been process based. J.B. Bowles' (see Proc. Annual Reliability and Maintainability Symposium, Anaheim, CA, USA, IEEE, p.48-53, 1998) inclusion of a functional FMEA prior to completion of the preliminary design moves the analysis to the beginning of the product development cycle to verify requirements prior to commencing with the detail design. This process change becomes even more significant when this initial analysis can be reused to verify the detail design. This paper examines the mathematical concept of equivalence relations and partitions within the FMEA to (1) influence the FD/FI design, (2) enable the reuse of functional analysis in the subsequent interface and piece part analyses, and (3) improve the quality and cost of the analysis. Set algebra is applied to partition all failure modes and their consequences into disjoint subsets known as fault equivalence classes. Equivalence classes are created as a method for managing all failure mode consequences.