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A general shock model for a reliability system

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Georgios Skoulakis
Georgios Skoulakis*
Affiliation:
University of North Carolina
*
∗ Postal address: Department of Finance, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, IL 60208-20001, USA. Email address: g-skoulakis@kellogg.nwu.edu
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Abstract

We study a reliability system subject to shocks generated by a renewal point process. When a shock occurs, components fail independently of each other with equal probabilities that are random numbers drawn from a distribution that may differ from shock to shock. We first consider the case of a parallel system and derive closed expressions for the Laplace-Stieltjes transform and the expectation of the time to system failure and for its density in the case that the distribution function of the renewal process possesses a density. We then treat a more general system structure, which has some very important special cases, such as k-out-of-n:F systems, and derive analogous formulae.

Keywords

System reliabilityshock modelsrandom environmentparallel systemgeneral system

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K37: Processes in random environments
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 925 - 935
Copyright
Copyright © by the Applied Probability Trust 2000 

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