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.
- phase-type distribution
- survival function
- shock and wear models
Montoro-Cazorla, D., Perez-Ocon, R., & Segovia Garcia, M. D. C. (2007). Survival probabilities for shock and wear models governed by phase-type distributions. Quality Technology and Quantitative Management , 4(1), 85-94. https://doi.org/10.1080/16843703.2007.11673136