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

The Gamma process stands as a prevalent model for monotonic degradation data. However, its statistical inference faces complexity due to the intricate parameter structure within the likelihood function. This paper addresses this challenge by deriving a conjugate prior specifically for the homogeneous gamma process, investigating the properties of this prior distribution. To facilitate posterior inference, three meticulously designed algorithms (Gibbs sampling, discrete grid sampling, and sampling importance resampling) are employed to generate posterior samples of the model parameters. Through extensive simulation studies, these algorithms demonstrate notably high computational efficiency and precise estimation. Extending the conjugate prior to encompass the gamma process with heterogeneous effects, this study enables recursive updates to the posterior distribution of parameters when the inspection time epochs are evenly spaced. An innovative online algorithm is consequently developed, empowering the prediction of remaining useful life for multiple systems. The effectiveness of this online algorithm is demonstrated through comprehensive illustrations from two real‐world cases and a simulated dataset under a high‐frequency monitoring scenario.