Survival Probabilities for Shock and Wear Models Governed by Phase-Type Distributions

Abstract

A device submitted to shocks arriving randomly and causing damage is considered. The interarrival 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.

Key Words:

• Phase-type distribution
• reliability
• shock and wear model
• survival function

Additional information

Notes on contributors

Delia Montoro-Cazorla

Rafael Pérez Ocón Professor at the University of Granada (Spain). His interests are in the areas of reliability models, matrix-analytic methods, algorithmic probabilities and survival probabilities. His publications have appeared in the areas of engineering and operational research.

Pérez-Ocón Rafael

Delia Montoro Cazorla Ph.D. degree in applied stochastic models in reliability in 2003. She is active in research in performance analysis of stochastic systems, reliability, simulation of complex systems, and optimization problems. She has published several papers about these topics. At the present, she is focused in the algorithmic treatment of matrix-analytic methods for analyzing stochastic systems.

M. Carmen Segovia

Maria del Carmen Segovia Received her BS in Statistics in 2003 and her MD. degree in 2005 at the University of Granada, Spain. She has a grant of the University of Granada. She is working in the applications of reliability and performance analysis of stochastic systems.