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Gamma process has been extensively used to model monotone degradation data.Statistical inference for the gamma process is difficult due to the complexparameter structure involved in the likelihood function. In this paper, wederive a conjugate prior for the homogeneous gamma process, and some propertiesof the prior distribution are explored. Three algorithms (Gibbs sampling,discrete grid sampling, and sampling importance resampling) are well designedto generate posterior samples of the model parameters, which can greatly lessenthe challenge of posterior inference. Simulation studies show that the proposedalgorithms have high computational efficiency and estimation precision. Theconjugate prior is then extended to the case of the gamma process withheterogeneous effects. With this conjugate structure, the posteriordistribution of the parameters can be updated recursively, and an efficientonline algorithm is developed to predict remaining useful life of multiplesystems. The effectiveness of the proposed online algorithm is illustrated bytwo real cases.

Online Bayesian prediction of remaining useful life for gamma degradation process under conjugate priors