Abstract
Abstract A parallel redundant system, which is composed of n identical components and fails when all components have failed, is subject to independent and common cause shock failures. Independent failures of one component occur at random times, independently of each other. Common cause shocks are classified into two kinds of shocks: lethal and non-lethal. If a non-lethal shock occurs, each component is assumed to fail, independently of the other components, with probability p, and then the number of failed components is random, with a binomial (n,p) distribution. A lethal shock failure is an event that causes every component in the system to fail. All failures are discovered continuously and minimally repaired or replaced immediately, requiring negligible time. An optimal replacement period for the system based on its average operating cost per unit of time is to be determined, and a necessary and sufficient condition for the existence of such a period is stated. A numerical example is illustrated.
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