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, 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. © 2024 Elsevier B.V.