  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.
