A general repair/proportional hazards framework to model complex repairable systems

by Sofiane Gasmi; Ernie Love; Waltraud Kahle


Preprint series: 98-39, Preprints

60K10 Applications (reliability, demand theory, etc.)
60K05 Renewal theory
62F10 Point estimation


Abstract: In this research we are concerned with the statistical modelling of repairable systems when operating under following two phenomenon. A system (machine) is observed to operate in one of two modes. The most common mode is loaded (or regular) operation. Occasionally the system is placed in an unloaded state. In this latter state, while the system is mechanically still operating, it is assumed that the failure intensity is reduced due to this reduction in operating intensity. To capture this potential reduction in failure intensity due to switching operating modes, a proportional hazards framework is utilized. In either operating condition, maintenance records analyzed indicated that the system was occasionally shut down and either a minor or major repair was undertaken. Furthermore, despite such repairs it was observed that both modes of operation (loaded or unloaded) resulted in failures. On failure, one of three actions were taken; failures were minimally repaired, given a minor repair or given a major repair. Both types of repairs are assumed to impact the intensity following a virtual age process of the general form proposed by Kijima. The issue in this research is to develop a statistical model of such an operating/maintenance environment.

Keywords: repairable systems, imperfect virtual age repair processes, Likelihoodfunction, minimal repair, imperfect repair, Weibull-type intensities.

Notes: This research is supported by NSERC Grant # OCP0197319.

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