Simulated Method for Reliability Evaluation of Multi-State Coherent System

Abstract

Aiming at the reliability evaluation and prediction of multi-state monotone coherent system, a simulated algorithm has been put forward in this paper. First, the multi-state coherent system has been formulated by generalizing the traditional binary reliability theories. Second, generating a random number to the every component and then the system state can be ascertained using minimal path set or minimal cut set. Finally, the proportion of occurring number of each state to the total simulated times can be adopted as the probability that the system is in the specified state. In addition, the prediction of reliability indices for multi-state component has been formulated using Markov chain theory in order to make decision for engineer, such as, the probability that the component will not fail until a specified time or fail before a specified time, the state changing probability from one state to another at certain time, etc. Several examples illustrate the validity of the simulated algorithm and the prediction of reliability indices. Comparing with a k-out-of-n system, the suggested method is of higher precision. These results conclude that the simulated algorithm can be employed as a new substitute for system structure function to accomplish the reliability evaluating of multi-state coherent system.