Statistical Model for a Failure Mode and Effects Analysis and its Application to Computer Fault-Tracing

Abstract

This paper presents a mathematical model of a general statistical approach to a system Failure Mode and Effects Analysis (FMEA). It describes, in particular, the FMEA theory itself, and its application to computer fault-tracing, using a Markov model. The theory yields both a reliability table showing system failure-state probabilities, and a criticality table identifying probable causes of system failure. Computer fault-tracing is implemented by using Markov chains to generate system output-state conditional probabilities. Feedback loop effects are eliminated by using Markov recursive relations for absorption probabilities. This statistical FMEA technique examines individual outputs on every individual component to determine statistically its critical impact on every system output. The fault tracing required is done by computer processing and is exhaustive. The reliability analyst is not required to make any intultive assumptions or simplifications on the complexity of the system block diagram or the effects of feedback loops, and the analyst does not have to decide which components should be examined for criticality. Instead, the analyst's work is shifted to understanding how each component works and relating this understanding to the FMEA technique.