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Discrete repairable reliability systems

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  • Moshe Shaked
  • J. George Shanthikumar
  • Haolong Zhu

Abstract

Consider a reliability system consisting of n components. The failures and the repair completions of the components can occur only at positive integer‐valued times k ϵ N++ ϵ (1, 2, …). At any time k ϵ N++ each component can be in one of two states: up (i.e., working) or down (i.e., failed and in repair). The system state is also either up or down and it depends on the states of the components through a coherent structure function τ. In this article we formulate mathematically the above model and we derive some of its properties. In particular, we identify conditions under which the first failure times of two such systems can be stochastically ordered. A variety of special cases is used in order to illustrate the applications of the derived properties of the model. Some instances in which the times of first failure have the NBU (new better than used) property are pointed out. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • Moshe Shaked & J. George Shanthikumar & Haolong Zhu, 1993. "Discrete repairable reliability systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(6), pages 769-786, October.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:6:p:769-786
    DOI: 10.1002/1520-6750(199310)40:63.0.CO;2-B
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    References listed on IDEAS

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    1. Moshe Shaked & J. George Shanthikumar, 1988. "On the First Failure Time of Dependent Multicomponent Reliability Systems," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 50-64, February.
    2. Sheldon M. Ross, 1984. "A model in which component failure rates depend on the working set," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 297-300, June.
    3. Richard E. Barlow & Frank Proschan, 1976. "Theory of Maintained Systems: Distribution of Time to First System Failure," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 32-42, February.
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