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Availability of inspected systems subject to shocks - A matrix algorithmic approach


  • Frostig, Esther
  • Kenzin, Moshe


We examine the limiting average availability of a maintained system that deteriorates due to random shock process and as a response to its usage (wear out). System's failures are not self-announcing, hence, failures must be detected via inspection. We consider randomly occurring shocks that arrive according to a Poisson process and cumulatively damage the system. Two models are considered: in Model 1 the shock and wear out processes are independent of the external environment and in Model 2, the shocks arrival rate, the shock magnitudes and the wear out rate are governed by a random environment which evolves as a Markov process. We obtain the system's availability for both models.

Suggested Citation

  • Frostig, Esther & Kenzin, Moshe, 2009. "Availability of inspected systems subject to shocks - A matrix algorithmic approach," European Journal of Operational Research, Elsevier, vol. 193(1), pages 168-183, February.
  • Handle: RePEc:eee:ejores:v:193:y:2009:i:1:p:168-183

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    1. repec:eee:reensy:v:99:y:2012:i:c:p:55-61 is not listed on IDEAS
    2. repec:eee:reensy:v:170:y:2018:i:c:p:137-145 is not listed on IDEAS
    3. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K," European Journal of Operational Research, Elsevier, vol. 235(3), pages 636-642.
    4. repec:eee:apmaco:v:259:y:2015:i:c:p:339-352 is not listed on IDEAS
    5. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2011. "Two shock and wear systems under repair standing a finite number of shocks," European Journal of Operational Research, Elsevier, vol. 214(2), pages 298-307, October.
    6. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.


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