Open Access
November 2006 On the Statistical Modeling and Analysis of Repairable Systems
Bo Henry Lindqvist
Statist. Sci. 21(4): 532-551 (November 2006). DOI: 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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Bo Henry Lindqvist. "On the Statistical Modeling and Analysis of Repairable Systems." Statist. Sci. 21 (4) 532 - 551, November 2006.


Published: November 2006
First available in Project Euclid: 23 April 2007

zbMATH: 1129.62092
MathSciNet: MR2369984
Digital Object Identifier: 10.1214/088342306000000448

Keywords: competing risks , Heterogeneity , marked point process , nonhomogeneous Poisson process , preventive maintenance , Renewal process , repairable system , trend , trend-renewal process , virtual age process

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.21 • No. 4 • November 2006
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