On the Statistical Modeling and Analysis of Repairable Systems

Details On the Statistical Modeling and Analysis of Repairable Systems On the Statistical Modeling and Analysis of Repairable Systems

2007-08-02

arxiv.org/abs/0708.0362v1

Statistical Science 2006, Vol. 21, No. 4, 532-551

Statistics

Methodology

Published at http://dx.doi.org/10.1214/088342306000000448 in the Statistical Science (http://www.imstat.org/sts/) by the Insti

Scientific paper

10.1214/088342306000000448

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.

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