Bayesian methods for evaluating discrete reliability growth

Abstract

Bayesian estimation procedures are derived herein that may be utilized to evaluate reliability growth of discrete-use systems, such as guns, rockets, missile systems, torpedoes, etc. One advantage of these Bayesian procedures is that they directly quantify the epistemic uncertainties in model parameters, i.e., the shape parameters of the beta distribution, as well as several reliability growth metrics of basic interest to program management. These metrics include: (1) the initial system reliability; (2) the projected reliability following failure mode mitigation; (3) reliability growth potential, i.e., the theoretical upper-limit on reliability achieved by finding and fixing all failure modes via a specified level of effectiveness; (4) the expected number of failure modes observed during testing; (5) the probability of observing a new failure mode and; (6) the fractional contribution of correctable failure modes to the initial probability of failure. These metrics and associated model equations give reliability practitioners the means to: (1) assess reliability achievement of discrete-use systems undergoing development; (2) address model goodness-of-fit concerns and; (3) quantify programmatic risk, and system maturity.