Abstract
Consider the lifelengths T 1,…, T k of k components subjected to a randomly varying environment. They are dependent on each other because of their common dependence of the environment. The parameters of the model are the distribution of the random process which describes the environment and a set of rate functions which determine the probability law of T i ,…, T k as a function of the distribution of the environment. We find conditions on the parameters of the model which imply that T 1,…, T k are associated. Other conditions which imply that T 1,…, T k have the multivariate aging properties IHR (increasing hazard rate) and NBU (new better than used) are also described. Also two such models are compared. In particular, we characterize the parameters of these models so that stochastic ordering between the two vectors of resulting lifetimes can be obtained.
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