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On the Survival Time of a Duplex System: A Sokhotski-Plemelj Problem

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  • Edmond J. Vanderperre

Abstract

We analyze the survival time of a renewable duplex system characterized by warm standby and subjected to a priority rule. In order to obtain the Laplace transform of the survival function, we employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we introduce a security interval related to a prescribed security level and a suitable risk criterion based on the survival function of the system. As an example, we consider the particular case of deterministic repair. A computer-plotted graph displays the survival function together with the security interval corresponding to a security level of 90%.

Suggested Citation

  • Edmond J. Vanderperre, 2008. "On the Survival Time of a Duplex System: A Sokhotski-Plemelj Problem," International Journal of Stochastic Analysis, Hindawi, vol. 2008, pages 1-13, December.
    • Handle: RePEc:hin:jnijsa:905721
    DOI: 10.1155/2008/905721
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