Availability Analysis and Optimal Design of Multistate Weighted <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math> </inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">${n}$ </tex-math> </inline-formula> Systems With Component Performance Requirements

Abstract

As one of the most typical multistate systems, weighted k-out-of-n system has been extensively studied in recent years. This paper presents a new kind of multistate weighted k-out-of-n system, which simultaneously considers performance requirements of each component and the system performance (cumulative performance threshold of all components). Then, we establish a new dynamic availability model by combining the Markov process and universal generating function. Moreover, an optimal design is proposed to achieve a tradeoff between system reliability/availability and cost. Non-dominated sorting genetic algorithm-II is used to optimize the probability and performance of components in different states. Finally, an example is illustrated to evaluate system availability and optimize component design. The optimization design can be referred as an optimal standard in system update.