Abstract
In this paper, we study reliability properties of k-out-of-n system consisting of l(1le lle n) different types of components with discrete, independent lifetimes. We obtain some conditional survival functions of lifetime of a used system. Next, we use them to calculate two conditional failure probabilities of k-out-of-n systems and show that they are equal to unconditional failure probability of a k-out-of-(n-r) system, r<n-k+1. These results are extended versions of the respective ones existing in the literature.
Highlights
A technical system has a k-out-of-n structure if it works when at least k of the n components operate
Two important particular cases of k-out-of-n systems are parallel and series ones corresponding to k = 1 and k = n
Our aim is to extend these results by considering k-out-of-n systems with independent component lifetimes that are of l (1 ≤ l ≤ n) different types and adding some extra information in the conditions of the probabilities
Summary
A technical system has a k-out-of-n structure if it works when at least k of the n components operate. Our aim is to extend these results by considering k-out-of-n systems with independent component lifetimes that are of l (1 ≤ l ≤ n) different types and adding some extra information in the conditions of the probabilities (1) and (2) which concerns failures of these components.
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