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Abstract

We present a marked point process reliability model that is based on failure and degradation data of repairable items operating in a dynamic environment. An item is regarded as failed when degradation reaches a critical threshold level or when a censoring traumatic event occurs. Degradation is modelled by a process with stationary independent increments and is related to external covariates through a random time scale. Traumatic events occur due to a point process with an intensity that may depend on degradation and external covariates. Parametric and semiparametric estimation is considered.

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References

  1. Aven, T. and Jensen, U. (1999). Stochastic Models in Reliability, Springer-Verlag, New York.

    Book  MATH  Google Scholar 

  2. Bagdonavičius, V. (1978). Testing the hypothesis of the additive accumulation of damage, Probability Theory and its Applications, 23, 403–408.

    Google Scholar 

  3. Bagdonavičius, V. and Nikulin, M. S. (2000). Estimation in degradation models with explanatory variables, Lifetime Data Analysis, 7, 85–103.

    Article  Google Scholar 

  4. Kalbfleisch, J. D. and Prentice, R. S. (1980). The Statistical Analysis of Failure Time Data, John Wiley & Sons, New York.

    MATH  Google Scholar 

  5. Last, G. and Brandt, A. (1995). Marked Point Processes on the Real Line, Springer-Verlag, New York.

    MATH  Google Scholar 

  6. Lehmann, A. (2001). A Wiener process based model for failure and degradation data in dynamic environments, Dresdner Schriften zur Mathemat. Stochastik, 4/2001, 35–40.

    Google Scholar 

  7. Singpurwalla, N. D. (1995). Survival in dynamic environments, Statistical Science, 10, 86–103.

    Article  MATH  Google Scholar 

  8. Whitmore, G. A. and Schenkelberg, F. (1997). Modelling accelerated degradation data using Wiener diffusion with a time scale transformation, Lifetime Data Analysis, 3, 27–45.

    Article  MATH  Google Scholar 

  9. Yashin, A. I. and Manton, G. M. (1997). Effects of unobserved and partially observed covariate processes on system failure: A review of models and estimation strategies, Statistical Science, 12, 20–34.

    Article  MATH  MathSciNet  Google Scholar 

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© 2004 Springer Science+Business Media New York

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Lehmann, A. (2004). On a Degradation-Failure Model for Repairable Items. In: Balakrishnan, N., Nikulin, M.S., Mesbah, M., Limnios, N. (eds) Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis, and Quality of Life. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8206-4_5

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  • DOI: https://doi.org/10.1007/978-0-8176-8206-4_5

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6491-0

  • Online ISBN: 978-0-8176-8206-4

  • eBook Packages: Springer Book Archive

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