Summary
In this paper we summarize recent results that have been obtained in Shaked et al. (1994, 1995) on the dynamic modelling of reliability systems in discrete time. Discrete time models of reliability systems are appropriate when the system operates in cycles or the system is monitored at discrete time epochs. On the other hand, discrete failure times arise naturally in several common situations in reliability theory where clock time is not the best scale on which to describe lifetime. Specifically, we model the dynamic behavior of the components of a reliability system by discrete multivariate conditional hazard rates (which is equivalent to specifying the joint life time distribution of the components). But this representation allows one to extend the basic model to incorporate repairs and replacements of components in a natural way. An algorithm to construct sample paths of the dynamics of the components based on the discrete multivariate conditional hazard rate is described. This algorithm can be used to simulate the system behavior and can be used for numerical studies as well as for analytic stochastic comparisons. We use this construction to study stochastic comparison of life times in the hazard rate and other stochastic orderings (of vectors of discrete dependent random lifetimes).
Supported in part by the NSF Grant DMS 9303891
Supported in part by the NSF Grant DMS 9308149
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Shaked, M., Shanthikumar, J.G., Valdez-Torres, J.B. (1996). Dynamic Modelling of Discrete Time Reliability Systems. In: Özekici, S. (eds) Reliability and Maintenance of Complex Systems. NATO ASI Series, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03274-9_5
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DOI: https://doi.org/10.1007/978-3-662-03274-9_5
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