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Stochastic Comparisons for Multivariate Shock Models

✍ Scribed by Franco Pellerey

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 125 KB
Volume: 71
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1999.1833

No coin nor oath required. For personal study only.

✦ Synopsis

Consider two devices subjected to shocks arriving according to two identically defined counting processes. Let N 1 and N 2 be the random numbers of shocks until failure of the two devices, respectively, and let T 1 and T 2 be their random lifetimes. Conditions such that stochastic orders between N 1 and N 2 are preserved by T 1 and T 2 have been investigated in recent literature. Here we study this problem in a multivariate setting, considering systems of non-independent components, and we extend some known results to multivariate stochastic orders. Two kinds of multivariate generalizations are considered; the case that each one of the components is subjected to its own fond of shocks and the case that all the components of the same system are subjected to a common font of shocks.

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