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Some Models Describing Damage Processes and Resulting First Passage Times

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

Abstract

The system reliability for a shock model with accumulating damages will be described by marked point processes Ф. The likelihood function is determined for different information about Ф. Usually, it depends on unknown parameters. The several resulting maximum—likelihood—estimates are derived for a mixed Poisson process.

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References

  1. Anderson, P., Borgan, Ø., Gill, R. and Keiding, N. (1993). Statistical Models Based on Counting Processes, New York: Springer-Verlag.

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  2. Bremaud, P. (1981). Point Processes and Queues, New York, Berlin, Heidelberg: Springer-Verlag.

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

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© 1998 Birkhäuser Boston

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Wendt, H. (1998). Some Models Describing Damage Processes and Resulting First Passage Times. 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_13

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  • DOI: https://doi.org/10.1007/978-1-4612-2234-7_13

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7466-7

  • Online ISBN: 978-1-4612-2234-7

  • eBook Packages: Springer Book Archive

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