Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T16:47:43.461Z Has data issue: false hasContentIssue false
  • English
  • Français

A stochastic covariate failure model for assessing system reliability

Part of: Survival analysis and censored data Special processes

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi
Nader Ebrahimi*
Affiliation:
Northern Illinois University
*
∗ Postal address: Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Many failure mechanisms can be traced to an underlying deterioration process, and stochastically changing covariates may influence this process. In this paper we propose an alternative model for assessing a system's reliability. The proposed model expresses the failure time of a system in terms of a deterioration process and covariates. When it is possible to measure deterioration as well as covariates, our model provides more information than failure time for the purpose of assessing and improving system reliability. We give several properties of our proposed model and also provide an example.

Keywords

Damage processdiffusion processhitting timeincreasing failure ratenew better than usedreliabilityItô differential equation

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 761 - 767
Copyright
Copyright © by the Applied Probability Trust 2001 

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.)

References

Barlow, R. E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Cameron, R., and Martin, W. (1944). The Wiener measure of Hilbert neighborhoods in the space of real continuous functions. J. Math. Phys. 23, 195–209.Google Scholar
Myers, L. E. (1981). Survival functions induced by stochastic covariate process. J. Appl. Prob. 18, 523–529.Google Scholar
Woodburg, M. A., and Manton, K. G. (1977). A random walk model of human mortality and aging. Theoret. Popn Biol. 11, 37–48.Google Scholar
Yashin, A. I. (1985). Dynamics in survival analysis: conditional Gaussian property versus Cameron–Martin formula. In Statistics and Control of Stochastic Processes, eds Krylov, N. V., Sh. Lipster, R. and Novikov, A. A. Springer, New York, pp. 466–485.Google Scholar
Yashin, A. I. (1993). An extension of the Cameron–Martin result. J. Appl. Prob. 30, 247–251.Google Scholar
Yashin, A. I., and Manton, K. G. (1997). Effects of unobserved and partially observed covariate processes on system failure: a review of models and estimation strategies. Statist. Sci. 12, 20–34.Google Scholar