On a multivariate IFR and positively dependent lifetime model induced by multiple shot-noise processes

Abstract

In reliability and survival analysis, the shot-noise processes have been intensively employed as a useful tool for modeling the impact of a dynamic environment (in the form of the point process of stresses) on survival characteristics of systems and organisms. However, the studies on the shot-noise processes have been mostly focused on the univariate analysis. In this paper, we develop a class of multivariate stochastic failure models based on a dynamic shock model induced by multiple shot-noise processes and study its properties. Explicit parametric forms for the multivariate survival functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.