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Discrete time cold standby repairable system: Combinatorial analysis

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  • Serkan Eryilmaz

Abstract

In this article, we obtain exact expression for the distribution of the time to failure of discrete time cold standby repairable system under the classical assumptions that both working time and repair time of components are geometric. Our method is based on alternative representation of lifetime as a waiting time random variable on a binary sequence, and combinatorial arguments. Such an exact expression for the time to failure distribution is new in the literature. Furthermore, we obtain the probability generating function and the first two moments of the lifetime random variable.

Suggested Citation

  • Serkan Eryilmaz, 2016. "Discrete time cold standby repairable system: Combinatorial analysis," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(24), pages 7399-7405, December.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:24:p:7399-7405
    DOI: 10.1080/03610926.2013.776689
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    Cited by:

    1. Linmin Hu & Rui Peng, 2019. "Reliability modeling for a discrete time multi-state system with random and dependent transition probabilities," Journal of Risk and Reliability, , vol. 233(5), pages 747-760, October.
    2. Cihangir Kan & Serkan Eryilmaz, 2021. "Reliability assessment of a discrete time cold standby repairable system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 613-628, October.

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