The uncertainty in reliability analysis of complex multi-state system may be due to the complexity of system structures

the limited test samples

and the insufficient reliability data. A new reliability analysis method for complex uncertainty system based on non-deterministic membership functions and interval characteristic quantities is proposed by introducing the fuzzy mathematics and grey system theory into the Bayesian network model. The influences of human subjective factors on the selection of membership function can be effectively avoided and the failure states of components and systems can be defined accurately by using the variable membership function to describe the failure states of component and system. The uncertain failure logic relationship between component and system can be effectively expressed by substituting the exact value in the conditional probability table with the interval grey number. A parameter planning model of the system reliability characteristic quantity is constructed

and the system reliability characteristic quantity is expressed in the form of an interval. The proposed method is applied in the reliability analysis of the satellite propulsion system. The results show that the method can be used to analyze the system reliability and component importance under fuzzy uncertain conditions

and the calculation amount is controllable. It is an effective reliability analysis method for complex uncertainty systems. Key