A Fuzzy Inference Method for Multi-State Systems

Reliability is an important measure of performance of products under the severe competition of the market. Traditional reliability theory is based on two elementary assumptions; the probability of component is precise and the system only has two crisp states, success state or failure state. But in some situations, these two assumptions are not suitable. For example, the reliability data is insufficient and fuzzy and the system may be in more than two states. Such situations cannot be modeled with traditional reliability theory. In this paper, we propose a fuzzy reliability expression and a method for fuzzy multi-state systems. First, fuzzy sets theory is used to conduct the fuzzy multi-state system reliability analysis, including the functioning probability values and logic expressions. Then a method to obtain the system functioning probability is proposed using fuzzy inference by following fuzzy operation rules. Finally, we report a case study to demonstrate the feasibility of this method, and conclude that this new modeling method is well-suited to engineering practice.