On the compound Poisson phase-type process and its application in shock models

In this paper, the compound Poisson phase-type process is defined and analyzed. This paper proves that for a non-negative compound Poisson phase-type process, the compound value for all the arrivals by a given time can be approximated by a phase-type distribution. As an application of this process,...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 446; p. 115852
Main Authors Goyal, Dheeraj, Xie, Min
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.08.2024
Subjects
Phase-type distribution
Poisson phase-type process
Reliability
Shock models
Shock models
Poisson phase-type process
Phase-type distribution
Reliability
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ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2024.115852

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Summary:In this paper, the compound Poisson phase-type process is defined and analyzed. This paper proves that for a non-negative compound Poisson phase-type process, the compound value for all the arrivals by a given time can be approximated by a phase-type distribution. As an application of this process, three different shock models are studied: the cumulative shock model, a degradation-threshold-shock model, and a shock model for the multi-component system. A novel approach is proposed to compute the system’s reliability under the aforementioned shock models for a general counting process. Numerical illustrations are presented.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2024.115852