Abstract
In this article, we investigate the joint reliability signature of a number of k-out-of-n systems. We assume to have n components with independent and identically distributed lifetimes. Each system is composed of all of the components and fails upon the failure of the k-th component, for some . Given an ordering of the failure times, we determine a formula for the joint reliability signature, which is a high-dimensional matrix. Furthermore, we prove a relationship between the joint reliability signature and the order of the failure times and obtain the number of essentially different joint reliability signatures as a function of the number of systems. Moreover, we demonstrate how the joint reliability signature of several k-out-of-n systems is related to their joint signature. A computer program is presented to calculate the joint reliability signature and joint signature, for all permutations of the failure times together.
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