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A discrete‐time model of failure and repair

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  • José M. Rocha‐Martinez
  • Moshe Shaked

Abstract

In this paper the authors introduce and study a model of failures and repairs of units with discrete lifetimes. They suppose that a unit has a sequence of tasks to perform and that its lifetime is measured by the number of tasks performed before its final, fatal failure. Upon a failure the unit may be repaired (with some probability) and then it may attempt again to perform the current task. The unit dies when (with some probability) a repair cannot be completed. We derive some stochastic comparisons of pairs of such models. The stochastic comparisons are then applied for obtaining results regarding the inheritance of several aging properties by the repaired unit. Various examples illustrate the applicability of the model. Some variants of the model of this paper can be viewed as discrete analogues of the notion of imperfect repair.

Suggested Citation

  • José M. Rocha‐Martinez & Moshe Shaked, 1995. "A discrete‐time model of failure and repair," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(2), pages 167-180, June.
    • Handle: RePEc:wly:apsmda:v:11:y:1995:i:2:p:167-180
    DOI: 10.1002/asm.3150110207
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