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Modelling Recurrent Events for Repairable Systems Under Worse Than Old Assumption

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Advances in Degradation Modeling

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

The objective of the work is to model the failure process of a repairable system under “worse than old”, or harmful repairs, assumption. The proposed model is founded on the counting process probabilistic approach and interprets harmful repairs as the accumulation of failures on the same system. Increase in the conditional intensity is rather induced by the number of previous repair actions than by time contrarily to virtual age models. The LEYP model is defined and some comparison with existing imperfect repair models is given. The explicit form of likelihood function is provided. A covariate-dependent model is defined in order to take the effect of internal or external factors, which may be constant or time dependent, into account. After a description of the estimation procedure for left-truncated and right-censored data using a multiple systems data set, we provide some useful formulae for prediction of the number of failures in a future period. An application to data from the water distribution system of the city of Oslo (Norway) is given.

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Author information

Authors and Affiliations

  1. Cemagref, Cestas Cedex, France

    G. Babykina

  2. IMB, University of Bordeaux, Bordeaux, France

    G. Babykina & V. Couallier

Authors
  1. G. Babykina
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  2. V. Couallier
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Editor information

Editors and Affiliations

  1. Université Victor Segalen Bordeaux 2, I’lnstitut de Mathématiques de Bordeaux, Bordeaux Cedex, 33076, France

    M.S. Nikulin

  2. Département Génie Informatique, Labo. Mathématiques Appliquées Compiègne, Université de Technologie de Compiègne, Compiègne, France

    Nikolaos Limnios

  3. McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, L8S 4K1, Canada

    N. Balakrishnan

  4. Fak. Mathematik, Inst. Mathematische Stochastik, Otto-von-Guericke-Universität, Universitätsplatz 2, Magdeburg, 39106, Germany

    Waltraud Kahle

  5. Laboratoire de Statistique Medicale, Université René Descartes, Paris 5, Paris, 75006, France

    Catherine Huber-Carol

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© 2010 Birkhaüser Boston, a part of Springer Science+Business Media, LLC

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Babykina, G., Couallier, V. (2010). Modelling Recurrent Events for Repairable Systems Under Worse Than Old Assumption. In: Nikulin, M., Limnios, N., Balakrishnan, N., Kahle, W., Huber-Carol, C. (eds) Advances in Degradation Modeling. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4924-1_22

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