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

被引：0
|
作者：
Goyal, Dheeraj [1 ]
Xie, Min [1 ,2 ]
机构：
[1] Ctr Intelligent Multidimens Data Anal Ltd, Hong Kong Sci Pk, Hong Kong, Peoples R China
[2] City Univ Hong Kong, Dept Syst Engn, Hong Kong, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 446卷
关键词：
Poisson phase-type process; Phase-type distribution; Shock models; Reliability; OPTIMAL REPLACEMENT POLICY; SYSTEMS SUBJECT; POLYA PROCESS; RELIABILITY; FAILURE;
D O I：
10.1016/j.cam.2024.115852
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页数：15
相关论文
共 50 条
  • [1] On Properties of the Phase-type Mixed Poisson Process and its Applications to Reliability Shock Modeling
    Goyal, Dheeraj
    Hazra, Nil Kamal
    Finkelstein, Maxim
    [J]. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2022, 24 (04) : 2933 - 2960
  • [2] On Properties of the Phase-type Mixed Poisson Process and its Applications to Reliability Shock Modeling
    Dheeraj Goyal
    Nil Kamal Hazra
    Maxim Finkelstein
    [J]. Methodology and Computing in Applied Probability, 2022, 24 : 2933 - 2960
  • [3] PRESERVATION OF PHASE-TYPE DISTRIBUTIONS UNDER POISSON SHOCK-MODELS
    MANOHARAN, M
    SINGH, H
    MISRA, N
    [J]. ADVANCES IN APPLIED PROBABILITY, 1992, 24 (01) : 223 - 225
  • [4] Shock and wear models:: The case of phase-type distributions
    Montoro-Cazorla, D.
    Perez-Ocon, R.
    Segovia, M. C.
    [J]. SAFETY AND RELIABILITY FOR MANAGING RISK, VOLS 1-3, 2006, : 1681 - +
  • [5] On the nature of Phase-type Poisson distributions
    Hautphenne, Sophie
    Latouche, Guy
    Nguyen, Giang T.
    [J]. ANNALS OF ACTUARIAL SCIENCE, 2014, 8 (01) : 79 - 98
  • [6] Association of multivariate phase-type distributions, with applications to shock models
    Li, HJ
    [J]. STATISTICS & PROBABILITY LETTERS, 2003, 64 (04) : 381 - 392
  • [7] Reliability assessment for discrete time shock models via phase-type distributions
    Eryilmaz, Serkan
    Kan, Cihangir
    [J]. APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, 2021, 37 (03) : 513 - 524
  • [8] Stochastic shock models for degrading infrastructure systems via Phase-Type distributions
    Riascos-Ochoa, J.
    Sanchez-Silva, M.
    Akhavan-Tabatabaei, Raha
    [J]. SAFETY, RELIABILITY AND RISK ANALYSIS: BEYOND THE HORIZON, 2014, : 1147 - 1155
  • [9] Phase-type Models for Competing Risks
    Lindqvist, Bo H.
    [J]. 2016 SECOND INTERNATIONAL SYMPOSIUM ON STOCHASTIC MODELS IN RELIABILITY ENGINEERING, LIFE SCIENCE AND OPERATIONS MANAGEMENT (SMRLO), 2016, : 37 - 40
  • [10] Using Phase-type Models to Monitor and Predict Process Target Compliance
    McClean, Sally, I
    Stanford, David A.
    Garg, Lalit
    Khan, Naveed
    [J]. ICORES: PROCEEDINGS OF THE 8TH INTERNATIONAL CONFERENCE ON OPERATIONS RESEARCH AND ENTERPRISE SYSTEMS, 2019, : 82 - 90
12345