Reliability assessment for fuzzy multi-state systems

Fuzzy multi-state system (FMSS) is defined as a multi-state system (MSS) consisting of multi-state elements (MSE) whose performance rates and transition intensities are presented as fuzzy values. Due to the lack, inaccuracy or fluctuation of data, it is oftentimes impossible to evaluate the performance rates and transition intensities of MSE with precise values. This is true especially in continuously degrading elements that are usually simplified to MSE for computation convenience. To overcome these challenges in evaluating the behaviour of MSS, fuzzy theory is employed to facilitate MSS reliability assessment. Given the fuzzy transition intensities and performance rates, the state probabilities of MSE and MSS are also fuzzy values. A fuzzy continuous-time Markov model with finite discrete states is proposed to assess the fuzzy state probability of MSE at any time instant. The universal generating function with fuzzy state probability function and performance rate is applied to evaluate fuzzy state probability of MSS in accordance with the system structure. A modified FMSS availability assessment approach is introduced to compute the system availability under the fuzzy user demand. In order to obtain the membership functions of the indices of interest, parametric programming technique is employed according to Zadeh's extension principle. The effectiveness of the proposed method is illustrated and verified via reliability assessment of a multi-state power generation system.