Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T12:28:06.879Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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

References

[1] Bremáud, P. (1981) Point Processes and Queues: Martingale Dynamics. Springer-Verlag, Berlin.Google Scholar
[2] Çinlar, E. (1977) Shock and wear models and Markov additive processes. In The Theory and Applications of Reliability, Vol. 1, ed. Shimi, I. N. and Tsokos, C. P., Academic Press, New York.Google Scholar
[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