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

Esther Frostig, Moshe Kenzin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)168-183
Number of pages16
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - 16 Feb 2009


  • Compound poisson
  • Markov additive process
  • Martingale
  • Phase-type distributions
  • Reliability

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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