Survival probabilities for shock and wear models governed by phase-type distributions

Delia Montoro-Cazorla, Rafael Perez-Ocon, Maria Del Carmen Segovia Garcia

Research output: Contribution to journalArticlepeer-review


A device submitted to shocks arriving randomly and causing damage is considered. The inter-arrival times follow continuous phase-type distributions. Lifetimes between shocks are affected by the number of cumulated shocks and they follow continuous phase-type distributions. Every shock can be fatal or not, with a probability that follows a discrete phase-type distribution. The device can support a maximum of N shocks. We calculate the distribution of the lifetime of the device in terms of the counting process of the number of shocks, and illustrate the calculations by means of a numerical application. Computational aspects are introduced. This model extends other previously considered in the literature.
Original languageEnglish
Pages (from-to)85-94
Number of pages10
JournalQuality Technology and Quantitative Management
Issue number1
Publication statusPublished - 9 Feb 2007


  • phase-type distribution
  • reliability
  • survival function
  • shock and wear models


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