Reliability and performance assessment for fuzzy multi-state elements

A system consisting of a single multi-state element (MSE) with performance rates and transition intensities presented as fuzzy values is considered. In many cases it is very difficult to evaluate the performance rates and transition intensities of MSEs in a multi-state system with a precise value, because of lack, inaccuracy, or fluctuation of data, especially in continuously degrading elements that are usually simplified to an MSE for computational convenience. Fuzzy theory which is a useful methodology to overcome these deficiencies is used to establish reliability models of an MSE. Given the fuzzy transition intensities and performance rates, the state probabilities of an MSE are also fuzzy values. A fuzzy continuous-time Markov model with finite discrete states is proposed to assess the dynamic reliability corresponding to working time. A fuzzy Markov reward model is also introduced to evaluate the dynamic fuzzy performance. In order to obtain the membership functions of the fuzzy reliability and performance, parametric programming technique is employed according to the extension principle. In this paper, the existing approach for fuzzy MSE availability assessment is modified and extended. An example of a power generator is presented to illustrate the proposed models and algorithms.