Clustering method with axiomatization to support failure mode and effect analysis

Failure Mode and Effect Analysis (FMEA) is a highly structured risk-prevention management process that improves the reliability and safety of a system. This article investigates one of the most critical issues in FMEA practice: Clustering failure modes based on their risks. In the failure mode clustering problem, all identified failure modes need to be assigned to several predefined and risk-ordered categories to manage their risks. We model the clustering of failure modes through multi-expert multiple criteria decision making with an additive value function, and call it the additive N-clustering problem. We begin by proposing six axioms that describe an ideal clustering method in the additive N-clustering problem, and find that the EXogenous Clustering Method (EXCM), where category thresholds can be exogenously provided, is ideal (Exogenous Possibility Theorem), whereas any endogenous clustering method, where the clustering is determined endogenously in the given method, cannot satisfy all six axioms simultaneously (Endogenous impossibility Theorem). In practice, endogenous clustering methods are important, due to the difficulty in providing accurate and reasonable category thresholds of the EXCM. Therefore, we propose the Consensus-based ENdogenous Clustering Method (CENCM) and discuss its axiomatic properties. We also apply the CENCM to the SARS-CoV-2 prevention case and justify the CENCM through axiomatic comparisons and a detailed simulation experiment.