Availability Analysis of Multi-state Weighted k-out-of-n Systems with Component Performance Requirements

As one of the most typical systems, the k-out-of-n system has been extensively studied in recent years. In this paper, we propose a new kind of multi-state weighted k-out-of-n systems in consideration of performance requirements of component and system, simultaneously. Since the state probability and demand performance of components changes over time, this new system is defined as dynamic weighted k-out-of-n system (DWKNS). Through combining Markov process with universal generating function (UGF) method, the state probability and performance of the components and system are easily obtained. Then, the dynamic instantaneous availability model of DWKNS is established. Finally, taking the power system of ship as an example, the availability of power system is estimated. Besides, influence of components performance requirements on the system availability is studied. In the present paper, we have proposed a dynamic weighted k-out-of-n systems with component performance requirements, which simultaneously considers the performance requirements of component and system. The model of multi-state component is established by using continuous time discrete state Markov model. Then, through combining Markov process and UGF method, the availability model of entire multi-state system is achieved; and also, the state probability and performance of the components and system are obtained. After illustrated the numerical examples, we determined the availability of the system by Markov modeling and UGF. The result shows that the availability decrease over time. In addition, by comparing the performance requirements of components, availability of the system is much less than that the system without component performance requirements. Therefore, the availability of the system varies with changes of component performance requirements. This paper mainly focuses on the system modeling by Markov process and UGF. However, continuously changes of availability over time are not studied, which we plan to discuss further.