A Reliability Growth Model Involving Dependent Components

Abstract

Earlier papers have shown how to convert competing risk models involving dependent random variables into models involving only independent random variables, while simultaneously preserving the distribution of the minimum and the probabilities of the various failure patterns. In the present paper, we consider a sequence of such conversions occurring at successive points in chronological time in which the independent random variables are becoming stochastically larger. We obtain results which essentially demonstrate that the limiting distributions in the sequence of dependent models "correctly" correspond to the limiting distributions in the sequence of independent models. These results have applications in reliability growth models and in biomedical competing risk models in which the competing risks are increasing with age; in these models dependency is permitted among the random variables.