G1-Renewal Process as Repairable System Model

TL;DR

This paper introduces a G1-Renewal process model for repairable systems that captures various restoration types, including 'better-than-new', using location-scale family distributions with monotonic ROCOF.

Contribution

It extends renewal process models by incorporating monotonic ROCOF and explores properties and MLE estimation for exponential and Weibull distributions.

Findings

Model can represent 'better-than-new' restorations

Maximum likelihood estimation methods are developed for specific distributions

Properties of the G1-Renewal process are analyzed

Abstract

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.