Belief reliability modeling for the two-phase degradation system with a change point under small sample conditions.

The sparsity of the detection points and the small data size of samples have brought great difficulties in two-phase degradation modeling reliability analysis. This paper adopts belief reliability theory to cope with insufficient data and proposes a new reliability model for systems that display two-phase degradation. The uncertain process is used to model the degradation, thereby the first hitting time distribution and belief reliability of the two-phase degradation are derived. A uncertain variational inference algorithm based on the uncertain maximum likelihood method is also developed to discover the change-point more precisely and efficiently. The proposed method is verified to be more accurate and stable than the two-phase Wiener stochastic process model through the numerical simulation examples and a case of liquid coupling devices.