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Stochastic bounds and dependence properties of survival times in a multicomponent shock model. (English) Zbl 0982.60008
From the authors’ summary: Consider a system that consists of several components. Shocks arrive according to a counting process (which may be nonhomogeneous and with correlated interarrival times) and each shock may simultaneously destroy a subset of the components. Shock models of this type arise naturally in reliability modeling in dynamic environments. The purpose of this paper is to provide a general framework for studying the correlation structure of shock models in the setup of a multivariate, correlated counting process and to systematically develop upper and lower bounds for its joint component lifetime distribution and survival functions. The thrust of the approach is the interplay between a newly developed notion, majorization with respect to weighted trees, and various stochastic orders, especially orthant dependence orders of random vectors and orthant dependence orders of stochastic processes.

60E15 Inequalities; stochastic orderings
60K10 Applications of renewal theory (reliability, demand theory, etc.)
Full Text: DOI
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