Lifetime prognostics for multi-phase degradation with random jump at the change point

Due to the environment changing, working state switch, and physical mutation, the degradation process often exhibits multi-phase feather and the random jump usually exists at the change point, which may make traditional lifetime estimation approach for single-stage degradation process unsuitable. In this paper, we concentrate on how to model the multi-phase degradation process and estimate its lifetime. Under this consideration, we firstly formulate a general degradation framework based on the multi-phase Wiener model to describe such the degradation process. Unlike traditional methods, we provide an analytical form of lifetime estimation for two-phase model with fixed jump, and a single integral form for two-phase model with random jump via taking full advantage of the uncertainty of the degradation state at the change point. In addition, we extend these results from two-phase model to multi-phase model and obtain a general result of lifetime estimation. Finally, a numerical case is provided for illustration.