Statistical Science

On the Statistical Modeling and Analysis of Repairable Systems

Bo Henry Lindqvist

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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.

Article information

Source
Statist. Sci., Volume 21, Number 4 (2006), 532-551.

Dates
First available in Project Euclid: 23 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177334528

Digital Object Identifier
doi:10.1214/088342306000000448

Mathematical Reviews number (MathSciNet)
MR2369984

Zentralblatt MATH identifier
1129.62092

Keywords
Repairable system preventive maintenance nonhomogeneous Poisson process renewal process marked point process virtual age process trend-renewal process heterogeneity trend competing risks

Citation

Lindqvist, Bo Henry. On the Statistical Modeling and Analysis of Repairable Systems. Statist. Sci. 21 (2006), no. 4, 532--551. doi:10.1214/088342306000000448. https://projecteuclid.org/euclid.ss/1177334528


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