A Bayesian approach to diagnosis and prognosis using built-in test

Accounting for the effects of test uncertainty is a significant problem in test and diagnosis, especially within the context of built-in test. Of interest here, how does one assess the level of uncertainty and then utilize that assessment to improve diagnostics? One approach, based on measurement science, is to treat the probability of a false indication [e.g., built-in-test (BIT) false alarm or missed detection] as the measure of uncertainty. Given the ability to determine such probabilities, a Bayesian approach to diagnosis, and by extension, prognosis suggests itself. In the following, we present a mathematical derivation for false indication and apply it to the specification of Bayesian diagnosis. We draw from measurement science, reliability theory, signal detection theory, and Bayesian decision theory to provide an end-to-end probabilistic treatment of the fault diagnosis and prognosis problem.