Skip to main content
SpringerLink
Log in
Book cover

Advances in Stochastic Models for Reliability, Quality and Safety pp 53–65Cite as

Parameter Estimation in Renewal Processes with Imperfect Repair

  • Chapter

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

Abstract

In this paper we develop statistical methods for a general repair model from Last and Szekli (1995).

For determining the model parameters the maximum likelihood estimator is considered. Special results are obtained by the use of Pareto, Log-linear and Weibull-type intensities. Estimations for the degree of repair in a simple model are developed.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bathe, F. and Franz, J. (1996). Modelling of repairable systems with various degrees of repair, Metrika, 43, 149–164.

    Article  MathSciNet  MATH  Google Scholar 

  2. Baxter, L., Kijima, M. and Tortorella, M. (1996). A point process model for the reliability of a maintained system subject to general repair, Communications in Statistics-Stochastic Models, 12, 37–65.

    MathSciNet  MATH  Google Scholar 

  3. Block, H. W., Langberg, N. and Savits, T. H. (1993). Repair replacement policies, Journal of Applied Probability, 30, 194–206.

    Article  MathSciNet  MATH  Google Scholar 

  4. Brown, M. and Proschan, F. (1983). Imperfect repair, Journal of Applied Probability, 20, 851–859.

    Article  MathSciNet  MATH  Google Scholar 

  5. Gasmi, S. (1995). Statistik der Erneuerungstheorie fr verschiedene Erneuerungsarten, Diplomarbeit.

    Google Scholar 

  6. Kijima, M. (1989). Some results for repairable systems, Journal of Applied Probability, 26, 89–102.

    Article  MathSciNet  MATH  Google Scholar 

  7. Last, G. and Brandt, A. (1995). Marked Point Processes: The Dynamic Approach, New York: Springer-Verlag.

    MATH  Google Scholar 

  8. Last, G. and Szekli, R. (1995). Stochastic comparison of repairable systems by coupling, Bericht 95/11.

    Google Scholar 

  9. Stadje, W. and Zuckerman, D. (1991). Optimal maintenance strategies for repairable systems with general degrees of repair, Journal of Applied Probability, 28, 384–396.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Sofiane Gasmi & Waltraud Kahle

Authors
  1. Sofiane Gasmi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Waltraud Kahle
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Stochastics, Otto-von-Guericke-University Magdeburg, Box 4120, D-39016, Magdeburg, Germany

    Waltraud Kahle

  2. Dept. of Applied Mathematics, University of Würzburg, Sanderring 2, D-97070, Würzburg, Germany

    Elart von Collani

  3. Department of Mathematical Stochastics, Technical University Dresden, Zellescher Weg 12-14, D-01069, Dresden, Germany

    Jürgen Franz

  4. Department of Stochastics, University of Ulm, D-89069, Ulm, Germany

    Uwe Jensen

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Birkhäuser Boston

About this chapter

Cite this chapter

Gasmi, S., Kahle, W. (1998). Parameter Estimation in Renewal Processes with Imperfect Repair. In: Kahle, W., von Collani, E., Franz, J., Jensen, U. (eds) Advances in Stochastic Models for Reliability, Quality and Safety. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2234-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2234-7_4

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7466-7

  • Online ISBN: 978-1-4612-2234-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation