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Stochastic Models for Dependent Life Lengths Induced by Common Pure Jump Shock Environments

Haijun Li
Journal of Applied Probability
Vol. 37, No. 2 (Jun., 2000), pp. 453-469
Stable URL: http://www.jstor.org/stable/3215720
Page Count: 17
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Stochastic Models for Dependent Life Lengths Induced by Common Pure Jump Shock Environments
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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 multivariate 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.

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