Failure time analysis for compound degradation procedures involving linear path and negative jumps

Failure time analysis for compound degradation process involving abrupt jumps has attracted significant attention in recent years. Particularly, considering the situation of recovery or maintenance, which exists extensively in project reality, degradation process with negative jumps has been increasingly highlighted. However, due to the randomness and the complicated nonmonotonicity aroused by negative jumps, analyzing its first hitting time distribution is a great challenge at current stage. In this paper, aiming at the failure time analysis itself, the concept of invalid epoch is proposed firstly based on the characteristics of this kind of degradation process. Then, a novel analytical solution of lifetime distribution under the concept of the first hitting time is derived in the form of Laplace–Stieltjes transform, and it is further extended to some typical cases. To demonstrate the feasibility and the effectiveness, a series of verifications are carried out comprehensively. Results show that the solution is well-performed under different parameter settings. Finally, the proposed method is applied to a real application of draught fans to illustrate the validity.