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. 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 characteristic property of the proposed 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. This is similar to the scale parameter transformation in the Accelerated Life Model (Cox & Oakes, 1984). The paper discusses properties and statistical estimation of the proposed model for the case of the Exponential and Weibull underlying distributions.