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A reliability model based on the gamma process and its analytic theory

Published online by Cambridge University Press:  01 July 2016

Michael L. Wenocur
Michael L. Wenocur*
Affiliation:
Ford Aerospace Corporation
*
∗Postal address: Ford Aerospace Corporation, 280 Henry Ford II Drive, San Jose, CA 94043, USA.
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Abstract

This paper presents a variation of a state-dependent reliability model first proposed in Lemoine and Wenocur [4], [5], and develops some of its corresponding analytical theory. In particular, we develop a reliability model in which system state is a random process satisfying a stochastic differential equation where the driving process is gamma distributed.

Keywords

STATE-DEPENDENT RELIABILITY MODELSTOCHASTIC DIFFERENTIAL EQUATIONINFINITESIMAL OPERATORKAC FUNCTIONALFEYNMAN—KAC EQUATIONMARKOV ANALYTIC THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 899 - 918
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

This research was supported in part by Air Force Office of Scientific Research Contract F49620-86-C-0022.

References

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[3] Friedman, A. (1975) Stochastic Differential Equations and Applications, Vol. 1. Academic Press, New York.Google Scholar
[4] Lemoine, A. J. and Wenocur, M. L. (1985). On failure modeling. Naval Res. Logist. Quart. 32, 497–508.Google Scholar
[5] Lemoine, A. J. and Wenocur, M. L. (1986) A note on shot-noise and reliability modeling. Operat. Res. 34, 320–323.CrossRefGoogle Scholar
[6] Wenocur, M. L. (1986) Brownian motion with quadratic killing and some implications. J. Appl. Prob. 23, 893–903.Google Scholar
[7] Wenocur, M. L. (1988) Diffusion first passage times: approximations and related differential equations. Stoch. Proc. Appl. 27, 159–177.Google Scholar