On the Statistical Modeling and Analysis of Repairable Systems

TL;DR

This paper reviews statistical models for repairable systems, including imperfect repair, trend-renewal processes, and covariate effects, emphasizing modeling approaches over inference.

Contribution

It introduces a comprehensive framework for modeling repairable system data as marked point processes, integrating various failure and maintenance models with covariates and heterogeneity.

Findings

Inclusion of covariates improves model accuracy.

Marked point process framework unifies failure and maintenance data.

Trend testing methods are discussed for reliability analysis.

Abstract

We review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the nonhomogeneous Poisson process and the renewal process. In the case where several systems of the same kind are observed, we show how observed covariates and unobserved heterogeneity can be included in the models. We also consider various approaches to trend testing. Modern reliability data bases usually contain information on the type of failure, the type of maintenance and so forth in addition to the failure times themselves. Basing our work on recent literature we present a framework where the observed events are modeled as marked point processes, with marks labeling the types of events. Throughout the paper the emphasis is more on modeling than on statistical inference.