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Shock models with phase type survival and shock resistance

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  • Marcel F. Neuts
  • Manish C. Bhattacharjee

Abstract

New closure theorems for shock models in reliability theory are presented. If the number of shocks to failure and the times between the arrivals of shocks have probability distributions of phase type, then so has the time to failure. PH‐distributions are highly versatile and may be used to model many qualitative features of practical interest. They are also well‐suited for algorithmic implementation. The computational aspects of our results are discussed in some detail.

Suggested Citation

  • Marcel F. Neuts & Manish C. Bhattacharjee, 1981. "Shock models with phase type survival and shock resistance," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(2), pages 213-219, June.
    • Handle: RePEc:wly:navlog:v:28:y:1981:i:2:p:213-219
    DOI: 10.1002/nav.3800280204
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    Cited by:

    1. Miaomiao Yu & Yinghui Tang, 2024. "Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method," Journal of Risk and Reliability, , vol. 238(2), pages 233-246, April.
    2. Cao, Shihao & Wang, Zhihua & Liu, Chengrui & Wu, Qiong & Li, Junxing & Ouyang, Xiangmin, 2023. "A novel solution for comprehensive competing failure process considering two-phase degradation and non-Poisson shock," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    3. Ranjkesh, Somayeh Hamed & Hamadani, Ali Zeinal & Mahmoodi, Safieh, 2019. "A new cumulative shock model with damage and inter-arrival time dependency," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    4. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach," Mathematics, MDPI, vol. 10(11), pages 1-13, June.
    5. Shamstabar, Yousof & Shahriari, Hamid & Samimi, Yaser, 2021. "Reliability monitoring of systems with cumulative shock-based deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

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