Markov additive processes for degradation with jumps under dynamic environments
Markov additive processes for degradation with jumps under dynamic environments
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DOI：
10.1002/nav.21982
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Y. Shu;Q. Feng;E. P. Kao;D. Coit;Hao Liu
中科院分区：
文献类型：
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作者：
Y. Shu;Q. Feng;E. P. Kao;D. Coit;Hao Liu
我们使用一般的马尔可夫加性过程（马尔可夫调制的Lévy过程）来整体处理退化的复杂性，包括内部诱导和外部诱导的随机特性与复杂的跳跃机制。马尔可夫可加过程的背景分量是定义在有限状态空间上的马尔可夫链;可加分量在一定的背景状态下演化为Lévy从属子，并且可能在背景状态切换时发生瞬时非负跳跃。本文导出了这类马尔可夫调制过程的Fokker-Planck方程，并在此基础上导出了可靠性函数和寿命矩的拉普拉斯表达式，它们用马尔可夫链的无穷小生成矩阵和Lévy从属子的Lévy测度表示。我们的模型的优势是他们的灵活性，在动态环境下的跳跃退化数据建模。数值实验表明，我们的一般模型表现良好。
We use general Markov additive processes (Markov modulated Lévy processes) to integrally handle the complexity of degradation including internally‐induced and externally‐induced stochastic properties with complex jump mechanisms. The background component of the Markov additive process is a Markov chain defined on a finite state space; the additive component evolves as a Lévy subordinator under a certain background state, and may have instantaneous nonnegative jumps occurring at the time the background state switches. We derive the Fokker–Planck equations for such Markov modulated processes, based on which we derive Laplace expressions for reliability function and lifetime moments, represented by the infinitesimal generator matrices of Markov chain and the Lévy measure of Lévy subordinator. The superiority of our models is their flexibility in modeling degradation data with jumps under dynamic environments. Numerical experiments are used to demonstrate that our general models perform well.