In the kernel of modelling repairable systems: a goodness of fit test for Weibull-based generalized renewal processes

Statistical modelling has been paramount for the quality control and maintenance of repairable production systems. It allows to reduce costs and to prevent the occurrence of undesirable events - e.g. waste, emissions, losses, and accidents. At the same time, it provides support for enhancing production levels and the longevity of equipments and machines. Generalized Renewal Processes - GRP - are a powerful statistical formalism for modelling repairable systems. They enable one to evaluate the quality of the performed interventions as well as to forecast the time to occur undesirable events. The present paper provides a simple goodness of fit test - GOFT - for the main GRP present in the literature, namely Weibull-based GRP - WGRP. In fact, WGRP researchers are still challenged to offer simple WGRP GOFT. In order to study the performance of the proposed WGRP GOFT in terms of both type I and II error rates, simulated Uniform-based GRP and WGRP realizations are studied. The usefulness of the GOFT is also illustrated by means of real world cases involving offshore, windshield, and transformer facilities. From the simulations, one can conclude that the proposed WGRP GOFT has performance similar to GOFT in general. In turn, the real cases indicate that particular WGRP alternatives might be avoided in some circumstances.