ARES Corporation was asked to help analyze the reliability of a subsystem composed only of demand type components ("one-shot" pyrotechnic devices) for a missile defense vehicle. The subsystem was composed of twenty component types and some seventy component instances arranged in various series-parallel blocks. Each component was considered to be only as reliable as indicated by a relatively small set of tests in a relevant environment. ARES formulated a conjugate-pair Bayesian analysis approach, in which each component was associated with a uniform prior distribution on (0,1) - representing no information about reliability - combined with a binomial likelihood function on n tests and f failures. The result is a Beta posterior distribution on component reliability, which can be calculated easily in a spreadsheet. A Monte Carlo analysis on the system logic then derives the probability distribution at the system level. The client required that the testing budget be allocated to maximize the payoff in expected system reliability. The solution was an optimization algorithm which identifies, after each additional test has been added, that component which will yield the largest reliability gain per dollar at the system level given a single additional successful test. The model thus considers both the component reliability and the cost of an additional test on that component when designing a test plan. The current model evaluates the optimum allocation of tests among the various components to prove that the system has a specified reliability at a given confidence level, assuming that no failures occur in the additional tests. This methodology can be extended to account for a non-zero number of failures in additional tests, though at considerable expense in computation time.
