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Stochastic models for dependent life lengths induced by common pure jump shock environments

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Haijun Li
Haijun Li*
Affiliation:
Washington State University
*
∗Postal address: Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164, USA. Email address: lih@haijun.math.wsu.edu
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Abstract

The lifelengths of components of a system are usually dependent due to the common random production and operating environments. In this paper, we introduce a multi-variate pure jump Markov process to describe a large class of damage processes on various system components driven by common environmental shocks, and establish some dependence properties (association) for such a process and its multivariate increment process. These strong association properties describe both spatial dependence and temporal dependence of a multivariate pure jump process, and also provide a vehicle to derive some structural properties of component lifelengths of the systems operating in such an environment. Some bounds for the joint survival functions of component lifelengths are also obtained.

Keywords

Survival in random environmentsmultivariate pure jump processhazard rate processassociation of probability measures on partially ordered spacesassociation in timestochastic integral equation

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 453 - 469
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

Supported in part by the NSF grant DMI 9812994.

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