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Pure jump shock models in reliability

Published online by Cambridge University Press:  01 July 2016

James W. Drosen
James W. Drosen*
Affiliation:
The Pennsylvania State University
*
∗Postal address: Division of Management Science, College of Business Administration, The Pennsylvania State University, 310 Business Administration Building, University Park, PA 16802, USA.
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Abstract

There are many examples of a device suffering damage from random environmental shocks. We model the damage level of such a device as a pure jump Markov process, where the incremental damage caused by a shock depends both on the magnitude of the shock and on the damage level just before the shock. We also look at the time until failure of the device, which occurs when the damage level exceeds a random threshold. The distribution of the failure time and the failure rate are examined, and conditions for the failure rate to be increasing or to have an increasing average are found.

Keywords

STOCHASTIC INTEGRAL EQUATIONSJUMP PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 2 , June 1986 , pp. 423 - 440
Copyright
Copyright © Applied Probability Trust 1986 

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