Sequential Diagnosis of K-Out-Of-N Systems with Imperfect Tests

Abstract

A k-out-of-n system configuration requires that, for the overall system to be functional, at least k out of the total of n components must be working. This paper addresses the search for a least-cost diagnosis strategy for k-out-of-n systems when the individual component tests are imperfect, which means that a test can identify a component as working when in reality it is down, and vice versa. The inspection procedure stops when the output accuracy exceeds a given threshold. We underline the importance of the possibility of fixing positive and negative predictive values, we examine different classes of diagnosis policies, we discuss global optimality of each of the classes, and we present a polynomial-time algorithm to find a globally optimal policy.