Multivariate reliability modelling based on dependent dynamic shock models

Abstract

• This paper develops new classes of multivariate reliability models with positive dependence. • The developed novel methodology is also used to generate multivariate exponential distributions. • Multivariate dependence and ageing properties of the developed models are discussed. • This paper uses advanced shock models to generate multivariate reliability models. In this paper, we stochastically model positively dependent multivariate reliability distributions based on stochastically dependent dynamic shock models. In the first part, we consider a shock model with delayed failures. This shock model will be used to construct a class of absolutely continuous multivariate reliability distributions. Explicit parametric forms for the multivariate reliability functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. In the second part, we obtain two types of absolutely continuous multivariate exponential distributions based on further generalized shock models.