带有共享随机效应和累积环境冲击损伤的多元Gamma退化的可靠性与预防性维护
Reliability and Preventive Maintenance for Multivariate Gamma Degradation with Shared Random Effects and Cumulative Environmental Shock Damage
AI总结：
针对多元Gamma退化的相关性、异质性与累积环境损伤问题，提出带共享随机效应和环境退化过程的模型，推导可靠性表达式，开发估计算法与维护优化方法，经模拟与涂层应用验证有效。
摘要：
在工业工程领域，许多高可靠性产品具有多个随时间同时退化的性能特征。由于共同的制造因素和共享的运行环境，这些退化过程通常存在统计相关性。外部环境冲击也可能累积为共同损伤，共同导致系统失效。为刻画此类相关性、单元异质性及累积环境损伤，本研究提出一种带有共享随机效应和共享环境退化过程的多元Gamma退化模型。每个退化过程由一个个体Gamma过程和一个共享Gamma过程组成，随机效应捕捉单元间的潜在异质性并诱导额外相关性。推导了系统可靠性的显式表达式；为进行参数估计，开发了结合变分推断的期望最大化算法，并使用参数自助法进行不确定性量化；进一步建立了预防性维护优化方法。模拟研究和涂层退化应用验证了所提方法的有效性和实用性。
英文摘要：
In industrial engineering, many highly reliable products have multiple performance characteristics that degrade simultaneously over time. Owing to common manufacturing factors and shared operating environments, their degradation processes are often statistically dependent. External environmental shocks may also accumulate into common damage and jointly contribute to system failure. To characterize such dependence, unit heterogeneity, and cumulative environmental damage, this study proposes a multivariate Gamma degradation model with a shared random effect and a shared environmental degradation process. Each degradation process consists of an individual Gamma process and a shared Gamma process, while the random effect captures latent heterogeneity across units and induces additional dependence. An explicit expression for system reliability is derived. For parameter estimation, an expectation maximization algorithm combined with variational inference is developed, and parametric bootstrap is used for uncertainty quantification. A preventive maintenance optimization approach is further established. Simulation studies and a coating degradation application demonstrate the effectiveness and practical applicability of the proposed methods.
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