Component-based perfect replacement optimizations for series and parallel systems consisting of repairable dependent components

In this paper, we consider the preventive perfect replacement and replacement by a new one policies for some arbitrary selected components in the repairable series and parallel systems with dependent components. These policies are also extended to other systems. In fact, regardless of the kind of system, the policies are applied to any system with a survival function that can be calculated as a known function of their component’s survival functions. The dependent structure of these components is formulated regarding copula frameworks. In addition, two optimal maintenance policies in accordance with the maximum expected life for a series and parallel system and minimum/maximum relative risk of a component for a series/parallel system have been provided. The problem issue of finding the optimal relative risk of a component is new and has not been proposed up to now. Although the optimal life extension of a system has been investigated previously, through a replacement policy of the whole system, in this study, the life of a series or parallel system is optimally extended through a replacement policy of some of its dependent components. The existence of the optimal solution has been shown for all copula functions and furthermore, some numerical results are detailed regarding the Gumbel, Frank, Joe, Clayton, FGM, Normal, and AMH copulas.