Reliability Optimization of a System with Sequential k-out-of-n Failure Dependencies

In this paper, a more flexible model for a [Formula: see text]-out-of-[Formula: see text] system called a sequential [Formula: see text]-out-of-[Formula: see text] system is considered. In sequential [Formula: see text]-out-of-[Formula: see text] systems, the dependence structure of the system is taken into consideration, in which the failure of components affects the lifetime of the remaining ones. Redundancy allocation problem (RAP) for the sequential [Formula: see text]-out-of-[Formula: see text] system is also investigated. For the first time, a new mathematical formula based on sequential order statistics is proposed to evaluate the considered system reliability. Moreover, a model is developed to optimize system reliability subject to weight and cost constraints by choosing the number of redundant components between [Formula: see text] and [Formula: see text] for each subsystem. Indeed, the presented work aims to find the best system structure. As RAP belongs to the NP-hard class of optimization problems, an evolutionary algorithm, genetic algorithm (GA), is developed for solving the suggested problem.