Optimal Replacement Policy for Fuzzy Multi-State Element

In this paper, a system consisting of single multi-state element (MSE) with performance rates and transition intensities presented as fuzzy values is introduced. Due to the lack, inaccuracy or fluctuation of collected data, it is often too difficult to evaluate the performance rates and transition intensities of multi-state element/system with precise value, especially in the continuous degradation element/system which is usually simplified to finite multi-state element/system to avoid “dimension damnation”. To overcome this challenge, fuzzy set theory as a promising methodology to quantify the non-probabilistic uncertainty is employed here to facilitate the multi-state element/system performance assessment. Given the fuzzy transition intensities and performance rates, the state probabilities of multi-state element are fuzzy also. Meanwhile, when considering the replacement policy, fuzzy continuous-time Markov model with finite discrete states is proposed to assess the fuzzy mean time between replacement (MTBR) and the cumulative fuzzy performance reward in each replacement cycle. In order to obtain the membership functions of the fuzzy indices of interest, parametric programming technique is employed based on the Zadeh’s extension principle. The expected fuzzy average profit per unit time is computed under different replacement policy, and then three fuzzy decision making (ordering) methods are adapted to determine the optimal replacement threshold state θ∗ with aim to maximize the expected fuzzy average profit per unit time. The effectiveness of the proposed method is illustrated via an example of multi-state power generator.