Shock models under a Markovian arrival process

Rafael Pérez-Ocón, Maria del Carmen Segovia

Research output: Contribution to journal › Article

14 Citations (Scopus)

Abstract

A device submitted to shocks arriving randomly and causing damage is considered. Every shock can be fatal or not. The shocks follow a Markovian arrival process. When the shock is fatal, the device is instantaneously replaced. The Markov process governing the shocks is constructed, and the stationary probability vector calculated. The probability of the number of replacements during a time is determined. A particular case in which the fatal shock occurs after a fixed number of shocks is introduced, and a numerical application is performed. The expressions are in algorithmic form due to the use of matrix-analytic methods. Computational aspects are introduced. This model extends others previously considered in the literature.
LanguageEnglish
Pages879-884
Number of pages6
JournalMathematical and Computer Modelling
Volume50
Issue number5-6
Early online date18 May 2009
DOIs
Publication statusPublished - 1 Sep 2009

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Shock Model
Markovian Arrival Process
Shock
Markov processes
Matrix Analytic Methods
Markov Process
Replacement
Damage

Keywords

  • phase-type distribution
  • shock models
  • replacement
  • Markovian arrival process

Cite this

Pérez-Ocón, Rafael ; Segovia, Maria del Carmen. / Shock models under a Markovian arrival process. In: Mathematical and Computer Modelling. 2009 ; Vol. 50, No. 5-6. pp. 879-884.
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Pérez-Ocón, R & Segovia, MDC 2009, 'Shock models under a Markovian arrival process' Mathematical and Computer Modelling, vol. 50, no. 5-6, pp. 879-884. https://doi.org/10.1016/j.mcm.2008.12.020

Shock models under a Markovian arrival process. / Pérez-Ocón, Rafael; Segovia, Maria del Carmen.

In: Mathematical and Computer Modelling, Vol. 50, No. 5-6, 01.09.2009, p. 879-884.

Research output: Contribution to journal › Article

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AU - Pérez-Ocón, Rafael

AU - Segovia, Maria del Carmen

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N2 - A device submitted to shocks arriving randomly and causing damage is considered. Every shock can be fatal or not. The shocks follow a Markovian arrival process. When the shock is fatal, the device is instantaneously replaced. The Markov process governing the shocks is constructed, and the stationary probability vector calculated. The probability of the number of replacements during a time is determined. A particular case in which the fatal shock occurs after a fixed number of shocks is introduced, and a numerical application is performed. The expressions are in algorithmic form due to the use of matrix-analytic methods. Computational aspects are introduced. This model extends others previously considered in the literature.

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Pérez-Ocón R, Segovia MDC. Shock models under a Markovian arrival process. Mathematical and Computer Modelling. 2009 Sep 1;50(5-6):879-884. https://doi.org/10.1016/j.mcm.2008.12.020

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