Multi‐Objective Redundancy Allocation Problem for Systems With Weighted k$$ k $$‐Out‐of‐n$$ n $$ Subsystems Formed by Different Types of Multistate Components

ABSTRACT The redundancy allocation problem (RAP) is considered as one of the important problems in reliability theory. In this paper, we consider a series system with several subsystems wherein each subsystem is a weighted ‐out‐of‐ system formed by different types of multi‐state components. The degradation of the performance level (i.e., the probability of changing from a given state to the next state ) of a component of the system is modeled by the Markov process. Then, we study the multi‐objective RAP problem for this system, that is, we determine the optimum number of components of each type in each subsystem so that the maximum system reliability is achieved at minimum cost. Note that the given RAP problem is of NP‐hard type, and consequently, we use the controlled elitism non‐dominated ranked genetic algorithm (CE‐NRGA) to solve this problem. At the end, we illustrate the proposed methodology through a numerical example. Moreover, we discuss a case study to validate the proposed model.