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Advances in Degradation Modeling pp 59–76Cite as

Shock Models

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Abstract

The standard assumptions in shock models are that the failure (of a system) is related either to the cumulative effect of a (large) number of shocks or that failure is caused by a shock that exceeds a certain critical level. An extension is to consider a mixture, that is, a system breaks down either because of a large shock or as a result of many smaller ones, whichever appears first. In this chapter we survey our results on this problem as well as on a further generalization in which a shock can partly harm the system which implies a lower critical boundary for the following shocks to be fatal. For the cumulative model we also deal with the case in which only the sum of the most recent shocks implies a system failure. In addition we consider the combination of both models with some link functions and briefly discuss an extension of shock models which are based on a Markovian model.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Uppsala University, Uppsala, Sweden

    Allan Gut

  2. Department of Statistics, University of Bern, Bern, Switzerland

    Jürg Hüsler

Authors
  1. Allan Gut
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  2. Jürg Hüsler
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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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Gut, A., Hüsler, J. (2010). Shock Models. 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_5

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