Abstract
This paper presents exact formulas for the reliability of linear consecutive k-out-of-n: F, and relayed consecutive k-out-of-n: F systems, having a change point at position c, 1 ? c ? n, for any k?n. A change point at position c, means that the components after this point have reliabilities that are different from those before or at position c. The components are assumed to be independent. Practically, the change in the components reliabilities may be due to change in the stress applied. Assuming a change in stress, exact formulas of the stress-strength reliability of the systems are derived, considering two cases. The first case assumed strength and stress having the same form of distributions, while the second case assumed strength and stress having different forms of distributions. Estimation of the stress-strength reliability for both cases is discussed. Application to both cases are considered with numerical illustration.
Highlights
A linear consecutive k-out-of-n: F system consists of n components arranged linearly, the system fails if and only if k or more consecutive components fail
In this paper we study the reliability of a linear consecutive k-out-of-n: F system with a change point at position c, when k could take any possible value i.e., 1 ≤ k ≤ n
R(s:s)(k, n, c), R(s:s)u(k, n, c), and R(s:s)b(k, n, c) are presented when the change in the components reliabilities is due to change in the stress. This means that the components from 1 to c are subjected to a common stress, X1, while the components from c + 1 to n are subjected to a different common stress, X2
Summary
Minimum number of consecutive failed components required for system failure. The number of ways in which j identical balls can be placed in s distinct urns subject to the requirement that at most r balls are placed in any one urn. Position of the change point of the system, 1 ≤ c ≤ n. Linear consecutive k-out-of-n: F system with a change point at position c. Reliability of a L/k/n/c; P, given that the component at position c is working. Reliability of a L/k/n/c; P, given that the component at position c is failed. X, and Reliability of a relayed-unipolar L/k/n/c; P. Stands for a failed, and working component, respectively
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