TY - JOUR
T1 - On the compound Poisson phase-type process and its application in shock models
AU - Goyal, Dheeraj
AU - Xie, Min
PY - 2024/8/15
Y1 - 2024/8/15
N2 - 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.
AB - 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.
KW - Phase-type distribution
KW - Poisson phase-type process
KW - Reliability
KW - Shock models
UR - http://www.scopus.com/inward/record.url?scp=85186523777&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85186523777&origin=recordpage
U2 - 10.1016/j.cam.2024.115852
DO - 10.1016/j.cam.2024.115852
M3 - RGC 21 - Publication in refereed journal
SN - 0377-0427
VL - 446
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 115852
ER -