On the Statistical Modeling and Analysis of Repairable Systems

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 un-observed 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.

Dynamics of an optimal maintenance policy for imperfect repair models

“…Indeed, this representation is quite convenient for IR models (cf. Doyen and Gaudoin, 2004;Lindqvist, 1998). Let F T n+1 |t 1 ,...,tn (t), f T n+1 |t 1 ,...,tn (t), λ T n+1 |t 1 ,...,tn (t), and Λ T n+1 |t 1 ,...,tn (t) be respectively the conditional cdf, pdf, hazard and cumulative hazard functions of T n+1 given that T 1 = t 1 , .…”

Minor maintenance actions and their impact on diagnostic and prognostic CBM models

“…There is also a vast literature concerning the seemingly related field of imperfect repair, recently reviewed in Lindquist (2006), and we would like to distinguish the results in this paper from that field of work. A recent implementation of this methodology appears in Lugtigheid et al (2004) using a repair maintenance indicator estimated from the component repair history.…”

Optimal loading of system with random repair time

“…A repairable system is a system that can be restored to some fully satisfactory performance through maintenance actions (e.g., part adjustment or replacement) after failing to function correctly (Ascher & Feingold, 1984;Lindqvist, 2006;Yang, Zhang, & Hong, 2013). Based on the degree to which the operating condition of a system is restored through the maintenance, three categories or levels of repair models can be identified: perfect repair, general/imperfect repair, and minimal repair (Lindqvist, 2006;Yañez, Joglar, & Modarres, 2002).…”

“…Based on the degree to which the operating condition of a system is restored through the maintenance, three categories or levels of repair models can be identified: perfect repair, general/imperfect repair, and minimal repair (Lindqvist, 2006;Yañez, Joglar, & Modarres, 2002). A perfect repair restores a system to an "as good as new" condition; a minimal repair restores the system to an "as bad as old" condition, i.e., to the same state as it was immediately before its failure; a general repair can bring the system to any condition between the former two cases.…”