Abstract
In this paper, we consider two coherent systems having shared components. We assume that in the two systems there are three different types of components; components of type one that just belong to the first system, components of type two that lie only in the second system and components of type three that are shared by the two systems. We use the concept of joint survival signature to assess the joint reliability function of the two systems. Using this concept, some representations for the joint reliability function of the system lifetimes are obtained under two different scenarios of component failures. In the first scenario, we assume that the components of the systems fail according to different counting processes such as non-homogeneous Poisson processes. In the second scenario, it is assumed that the component lifetimes of each type are exchangeable while the three types of component lifetimes can be independent or dependent. To illustrate the theoretical results, two systems with shared components are studied numerically and graphically.
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Acknowledgements
We would like to thank the anonymous reviewers for several helpful suggestions. JN was supported in part by Ministerio de Ciencia e Innovación of Spain under grant PID2019-103971GB-I00/AEI/10.13039/501100011033. Asadi’s research work was performed in IPM Isfahan branch and was in part supported by a grant from IPM (No. 98620215).
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Ashrafi, S., Asadi, M. & Navarro, J. Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components. Methodol Comput Appl Probab 24, 1485–1502 (2022). https://doi.org/10.1007/s11009-021-09867-5
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DOI: https://doi.org/10.1007/s11009-021-09867-5