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Generalized Random Sign and Alert Delay models for imperfect maintenance

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Abstract

This paper considers the modelling of the process of Corrective and condition-based Preventive Maintenance, for complex repairable systems. In order to take into account the dependency between both types of maintenance and the possibility of imperfect maintenance, Generalized Competing Risks models have been introduced in “Doyen and Gaudoin (J Appl Probab 43:825–839, 2006)”. In this paper, we study two classes of these models, the Generalized Random Sign and Generalized Alert Delay models. A Generalized Competing Risks model can be built as a generalization of a particular Usual Competing Risks model, either by using a virtual age framework or not. The models properties are studied and their parameterizations are discussed. Finally, simulation results and an application to real data are presented.

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Abbreviations

ABAO:

As Bad As Old

AD:

Alert Delay

AGAN:

As Good As New

ARA:

Arithmetic reduction of age

BP:

Brown–Proschan

CIGCR:

Conditionally Independent Generalized Competing Risks

CM:

Corrective Maintenance

EDF:

Electricité de France

GAD:

Generalized Alert Delay

GCR:

Generalized Competing Risks

GPH:

Generalized Proportional Hazards

GRA:

Generalized Repair Alert

GRS:

Generalized Random Sign

GVA:

Generalized Virtual Age

ICR:

Independent Competing Risks

IPRA:

Intensity Proportional Repair Alert

MSE:

Mean Squared Error

PH:

Proportional Hazards

PM:

Preventive Maintenance

RA:

Repair Alert

RS:

Random Sign

UCR:

Usual Competing Risks

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Authors and Affiliations

  1. Laboratoire de Modélisation et Sûreté des Systémes, Université de Technologie de Troyes, Troyes, France

    Yann Dijoux

  2. Laboratoire Jean Kuntzmann, Université Grenoble Alpes, Grenoble, France

    Olivier Gaudoin

Authors
  1. Yann Dijoux
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  2. Olivier Gaudoin
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Correspondence to Olivier Gaudoin.

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Dijoux, Y., Gaudoin, O. Generalized Random Sign and Alert Delay models for imperfect maintenance. Lifetime Data Anal 20, 185–209 (2014). https://doi.org/10.1007/s10985-013-9249-5

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