Some Extended Geometric Processes and Their Estimation Methods

Modelling the failure process of a system is one of the most important problems in the reliability and maintenance research community. The geometric process (GP) is widely used for modelling the failure process because it can describe the phenomenon that the working times after repairs become shorter and shorter. This article reviews the geometric process and its extensions based on existing research. It also reviewd relevant methods for estimating parameters, model performances, and widely used distributions for times to first failures. Future challenges for the GP-like processes will be discussed.