Reliability optimization of a system with sequential k -out-of- n failure dependencies

In this paper, a more flexible model for a k-out-of-n system called a sequential k-out-of-n system is considered. In sequential k-out-of-n 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 k-out-of-n 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 k and n 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.