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A reliability semi‐Markov model involving geometric processes

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  • Rafael Pérez‐Ocón
  • Inmaculada Torres‐Castro

Abstract

We consider a semi‐Markov process that models the repair and maintenance of a repairable system in steady state. The operating and repair times are independent random variables with general distributions. Failures can be caused by an external source or by an internal source. Some failures are repairable and others are not. After a repairable failure, the system is not as good as new and our model reflects that. At a non‐repairable failure, the system is replaced by a new one. We assume that external failures occur according to a Poisson process. Moreover, there is an upper limit N of repairs, it is replaced by a new system at the next failure, regardless of its type. Operational and repair times are affected by multiplicative rates, so they follow geometric processes. For this system, the stationary distribution and performance measures as well as the availability and the rate of occurrence of different types of failures in stationary state are calculated. Copyright © 2002 John Wiley & Sons, Ltd.

Suggested Citation

  • Rafael Pérez‐Ocón & Inmaculada Torres‐Castro, 2002. "A reliability semi‐Markov model involving geometric processes," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(2), pages 157-170, April.
    • Handle: RePEc:wly:apsmbi:v:18:y:2002:i:2:p:157-170
    DOI: 10.1002/asmb.460
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