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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.

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Bakry, S. M., & Mokhlis, N. A. (2019). Exact reliability formula for a linear consecutive k-out-of-n: F system and relayed consecutive systems with a change point for any k?n, with stress-strength application. Pakistan Journal of Statistics and Operation Research, 15(1), 231-247.