Accounting for false indication in a Bayesian diagnostics framework

Accounting for the effects of test uncertainty is a significant problem in test and diagnosis. Specifically, assessment of the level of uncertainty and subsequent utilization of that assessment to improve diagnostics must be addressed. One approach, based on measurement science, is to treat the probability of a false indication (false alarm or missed detection) as the measure of uncertainty. Given the ability to determine such probabilities, a Bayesian approach to diagnosis suggests itself. In the paper, we present a mathematical derivation for false indication and apply it to the specification of Bayesian diagnosis. We draw from measurement science, reliability theory, and the theory of Bayesian networks to provide an end-to-end probabilistic treatment of the fault diagnosis problem.