Optimal component-type allocation and replacement time policies for parallel systems having multi-types dependent components

Abstract

In this work, we discuss some challenging open problems and conjectures recently proposed in the literature for parallel systems with dependent components of multiple types. Specifically, we present necessary conditions for the existence of the unique optimal value which minimizes the mean cost rate for two optimization problems. In the first place, the aim is to find the optimal number of components of each type which minimizes the associated mean cost rate, and secondly, to find the optimal replacement time before system failure. In both cases, we consider copulas to model the dependence structure for components whose lifetimes follow any distribution function. Moreover, in order to illustrate the theoretical results, we provide some numerical studies for specific copulas and marginal distribution functions