A model based on hidden graphic evaluation and review technique network to evaluate reliability and lifetime of multi-state systems

Abstract

The essence of multi-state system performance degradation is a process of deteriorating state transition. On the basis of hidden Markov model and graphic evaluation and review technique network, this article proposes a new reliability assessment method called hidden graphic evaluation and review technique network model for multi-state system. Specifically, nodes in graphic evaluation and review technique network represent hidden states of a system at different deteriorating times, and they can be expanded through a series of observable sequences. Baum–Welch algorithm in hidden Markov model is introduced to train parameters and when logarithmic likelihood function of the output reaches convergent, we can estimate the most probable output state and obtain the state transition probability eventually. Suppose performance degradation amount between different nodes follows gamma distribution, a method of improved maximum likelihood function is introduced to estimate parameters. According to signal flow graph theory and Mason formula, equivalent transfer function from the initial node to any other nodes can be obtained, then expectation and variance of performance degradation amount can be presented. In the real case study, we compare the reliability assessment method proposed in this article with other two traditional methods, which show the rationality of hidden graphic evaluation and review technique network model.