On optimal allocation of redundant components for series and parallel systems of two dependent components

In this paper we consider the problem of optimal allocation of a redundant component in the case of series and parallel systems of two components when all the components are dependent. Whereas this problem has been extensively treated for the case of independent components, the case of dependent components has not received too much attention. In this paper we show that for this problem the main tools are the joint stochastic orders introduced by Shanthikumar and Yao (1991).