Stochastic comparisons for multivariate shock models
Consider two devices subjected to shocks arriving according to two respective 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 under which stochastic orders between \(N_1\) and \(N_2\) are preserved by \(T_1\) and \(T_2\) have been investigated in recent literature. The author studies this problem in a multivariate setting, considering systems of non-independent components, and he extends some known results to multivariate stochastic orders. Some of the results of the reviewed paper are generalizations of multivariate results of \textit{T. Wong} [J. Appl. Probab. 34, No. 4, 1009-1020 (1997; Zbl 0899.60075].
scientific article; zbMATH DE number 1369817