论文标题
在线贝叶斯预测在共轭先验下的伽马降解过程中剩余使用寿命
Online Bayesian prediction of remaining useful life for gamma degradation process under conjugate priors
论文作者
论文摘要
伽马过程已广泛用于模拟单调降解数据。由于可能性函数涉及的复杂参数结构，因此很难对伽马过程进行统计推断。在本文中，我们得出了均匀伽马过程的共轭先验，并探讨了先前分布的某些特性。三种算法（Gibbs采样，离散的网格采样和采样重要性重采样）的设计良好，以生成模型参数的后验样本，这可以大大减少后推断的挑战。仿真研究表明，所提出的算法具有较高的计算效率和估计精度。然后将共轭先验扩展到具有异质效应的伽马过程的情况。借助这种共轭结构，可以递归更新参数的后验分布，并开发出有效的在线算法来预测多个系统的剩余使用寿命。两个真实案例说明了拟议的在线算法的有效性。
Gamma process has been extensively used to model monotone degradation data. Statistical inference for the gamma process is difficult due to the complex parameter structure involved in the likelihood function. In this paper, we derive a conjugate prior for the homogeneous gamma process, and some properties of the prior distribution are explored. Three algorithms (Gibbs sampling, discrete grid sampling, and sampling importance resampling) are well designed to generate posterior samples of the model parameters, which can greatly lessen the challenge of posterior inference. Simulation studies show that the proposed algorithms have high computational efficiency and estimation precision. The conjugate prior is then extended to the case of the gamma process with heterogeneous effects. With this conjugate structure, the posterior distribution of the parameters can be updated recursively, and an efficient online algorithm is developed to predict remaining useful life of multiple systems. The effectiveness of the proposed online algorithm is illustrated by two real cases.
