A failure process model with the exponential smoothing of intensity functions

This paper proposes a new model and investigates its special case model, both of which model the failure process of a series system composed of multiple components. We make the following assumption: (1) once the system fails, the failed component can be immediately identified and replaced with a new identical one, and (2) once the system fails, only the time of the failure is recorded; but the component that causes the system to fail is not known. The paper derives a parameter estimation method and compares the performance of the proposed models with nine other models on artificially generated data and fifteen real-world datasets. The results show that the two new models outperform the nine models in terms of the three most commonly used penalised model selection criteria, the Akaike's information criterion (AIC), corrected Akaike's information criterion (AICc) and Bayesian information criterion (BIC), respectively.