Evaluating Failure Time Probabilities for Compound Degradation with Linear Path and Mixed Jumps

Many devices may experience nature degradation and mixed jumps simultaneously whose types can be divided into positive jumps and negative jumps, while these complicated performance rules also bring difficulties in lifetime analysis within the concept of the first hitting time. To address this issue, this paper first proposes a compound degradation process, which is characterized by linear path and mixed jumps. Then, by adopting the idea that transforms the positive jumps into the threshold, an approximate lifetime solution is derived. Given the realistic application of furnace wall, numerical verification shows that the proposed method can maintain consistency with Monte Carlo simulation, while conspicuous errors exist for existing methods, demonstrating that the proposed method can be regarded as theoretical support for the future studies.