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A unified approach for reliability and performability evaluation of semi‐Markov systems

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  • Nikolaos Limnios
  • Gheorghe Oprian

Abstract

The aim of this paper is to give a unified approach for the evaluation of reliability‐ and performability‐related indicators of semi‐Markov systems: reliability, availability, α‐reliable mission time, mean time to failure, performability, throughput availability, maintainability, etc. For a semi‐Markov processes, (Zt; t ∈ ℝ+) say, with an arbitrary state space E, we associate to every state a reward rate (or a performance level), then the accumulated reward until time t, denoted by Wt, is an additive functional of the process. The above‐stated indicators are obtained by some distribution functions of the process (Zt, Wt; t ∈ ℝ+) by means of the Markov renewal theory, as well as the joint distribution of (ZT, WT), where T is the first hitting time of a subset of states. Copyright © 1999 John Wiley & Sons, Ltd.

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  • Nikolaos Limnios & Gheorghe Oprian, 1999. "A unified approach for reliability and performability evaluation of semi‐Markov systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 15(4), pages 353-368, October.
    • Handle: RePEc:wly:apsmbi:v:15:y:1999:i:4:p:353-368
    DOI: 10.1002/(SICI)1526-4025(199910/12)15:43.0.CO;2-2
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    Cited by:

    1. Ji Hwan Cha & Massimiliano Giorgio, 2018. "Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1137-1154, December.

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