Availability evaluation and design optimization of multi-state weighted k-out-of-n systems

The multi-state weighted k-out-of-n system model can illustrate the performance and reliability/availability relationship between components and system so that attracted more and more attentions in recent years. Under the condition that the state probabilities of components are dynamically changing with time, this paper presents a generalized instantaneous availability model for multi-state weighted k-out-of-n systems and an efficient Genetic Algorithm (GA) is proposed to compute optimal reliability and performance design values for components. Firstly, a Universal Generating Function (UGF) approach is developed to efficiently determine the availability of system assuming the state probability distributions of multi-state components follow the non-homogeneous continuous time Markov process. And then, taking into consideration of availability and cost constraints respectively, two design optimization models are set up to obtain the optimal design solutions for component via improved GA. Finally, an example analysis of transportation systems in a naval shipyard is shown to demonstrate effectiveness of the proposed model. Our results show that the improved GA can enhance the applicability of design results and conclusions of our paper can provide clear policy recommendations for design optimization of multi-state weighted k-out-of-n system.