Power–Law Nonhomogeneous Poisson Process with a Mixture of Latent Common Shape Parameters

Abstract Rapid developments in information technologies enabled recording big data environments in near real-time. Such big data environments provide an unprecedented opportunity for efficient event detection and therefore effective reliability models, but they also pose interesting challenges. One challenge is modeling the number of recurrent events for heterogeneous subpopulations with limited records. To address this challenge, a power–law nonhomogeneous Poisson process with machine learning capabilities is proposed. The scale parameter of the Poisson process is learned for each individual subpopulation. However, the shape parameter is learned for latent groups that each consists of multiple (internally homogenous) subpopulations. The proposed Poisson process collaboratively models multiple heterogeneous subpopulations; therefore, it allows transferring knowledge between subpopulations and diminishes the chances of overfitting. Simulation and real-life case studies showed the high modeling accuracy of the proposed approach. ACRONYMS: NHPP, nonhomogeneous Poisson process; ALFTM, accelerated lifetime model; NHPP–MSP, nonhomogeneous Poisson process with mixture shape parameters; MCF, mean cumulative function; BIC, Bayesian information criterion; AIC, Akaike information criterion; MOP, month of production