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Models for Perfect Repair

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Applied Nonparametric Statistics in Reliability

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

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Abstract

In this chapter, we begin with the study of repairable systems. Specifically, we study probabilistic models for systems which after failure are replaced by a new one exactly. We say then that the system operating state is restored to “as good as new” conditions after failure. In the first approach to this kind of systems, we assume that the system is repaired (replaced) and put into new operation immediately after the failure. The sample information that we analyze consist of a sequence of random variables independent and identically distributed, which represent the time between two consecutive failures. The model that we consider in this situation is a Renewal Process, and the main purpose is to present and compare several ways of nonparametrically estimate the renewal function, that is, the expected number of failures occurring in the system up to a given time t. When the repair times are of interest, the data collected consist of a sequence of alternating up and down periods. The modeling tool indicated in this case is the Alternating Renewal Process, and we will concentrate on estimating the availability function (the probability that the system is functioning at a given time) using nonparametric techniques.

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Notes

  1. 1.

    Sometimes one may let “operating time” be the time parameter; or possibly “number of cycles” or “number of kilometers” (for cars). Then, repair times are 0 in these time axes.

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Acknowledgments

Section 2.3 of this chapter is an extension into book-length form of the article Nonparametric estimation of the availability in a general repairable system, originally published in Reliability Engineering and System Safety93 (8), 1188–11962 (2008).

The authors express their full acknowledgement of the original publication of the paper in the journal cited above, edited by Elsevier.

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Authors and Affiliations

  1. Facultad Ciencias, Depto. Estadistica e Investigacion Operativa, Universidad Granada, Campus Univ. Fuentenueva, 18071, Granada, Spain

    Assoc. Prof. M. Luz Gámiz

  2. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634-1907, USA

    Prof. K. B. Kulasekera

  3. Centre de Recherches de Royallieu, Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, BP 20529 , 60205, Compiègne, France

    Prof. Nikolaos Limnios

  4. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Prof. Bo Henry Lindqvist

Authors
  1. Assoc. Prof. M. Luz Gámiz
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  2. Prof. K. B. Kulasekera
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  3. Prof. Nikolaos Limnios
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Correspondence to M. Luz Gámiz .

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Gámiz, M.L., Kulasekera, K.B., Limnios, N., Lindqvist, B.H. (2011). Models for Perfect Repair. In: Applied Nonparametric Statistics in Reliability. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-118-9_2

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  • DOI: https://doi.org/10.1007/978-0-85729-118-9_2

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