Multivariate negative aging in an exchangeable model of heterogeneity

We introduce an exchangeable model, which accounts for heterogeneity and dependence at a time. Based on this model, we show how situations of multivariate negative ageing arise in a natural way from conditions of heterogeneity

A variance-based importance index for systems with dependent components

This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous components. The particular cases of independent components and homogeneous components are also considered. We model the dependence structure among the components by the concept of copula. The proposed measure allows us to provide the best estimation of the system lifetime, in terms of the mean squared error, under the assumption that the lifetime of one of its components is known. We include theoretical results that are useful to calculate a closed-form of our measure and to compare two components of a system. We also provide some procedures to approximate the importance measure by Monte Carlo simulation methods. Finally, we illustrate the main results with several examples

Positive dependence properties of conditionally independent random lifetimes.

Conditions under which conditionally independent random variables are positive dependent are described in this paper. For example, it is shown that if the conditionally independent random variables increase in the hazard rate sense in the condition, then they are WBF (weakened by failures). It is also shown that if the conditionally independent random variables increase in the likelihood ratio sense in the condition, then they are MTP2 (multivariate totally positive of order 2). The results are given for the cases in which the condition is either a random variable or a random vector. Some applications in the areas of imperfect repair, budget allocation, random environments, and discrete-time filtering, illustrate the theory