G1-Renewal Process as Repairable System Model

This paper considers a point process model with a monotonically decreasing or increasing ROCOF and the underlying distributions from the location-scale family, known as the geometric process (Lam, 1988). In terms of repairable system reliability analysis, the process is capable of modeling various restoration types including "better-than-new", i.e., the one not covered by the popular G-Renewal model (Kijima & Sumita, 1986). The distinctive property of the process is that the times between successive events are obtained from the underlying distributions as the scale parameter of each is monotonically decreasing or increasing. The paper discusses properties and maximum likelihood estimation of the model for the case of the Exponential and Weibull underlying distributions.