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Nonparametric Approach to the Analysis of 1-D Warranty Data

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Book cover Warranty Data Collection and Analysis

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

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Abstract

This chapter discusses the nonparametric approach to the analysis of 1-D warranty data. It explains the nonparametric approach to inference based on the distribution function, renewal function, mean cumulative function, etc., in the context of 1-D warranty data. The estimators depend on the data structures and scenarios discussed in Chap. 5. The chapter deals with the nonparametric approach to deriving estimators for the above quantities based on different data scenarios for the three data structures. Examples using data sets from Appendix F are given to illustrate the methodology.

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Notes

  1. 1.

    These quantities are discussed in Chap. 3, Appendix A, and C. The objectives or goals for analysis are discussed in Sect. 1.6.1.

  2. 2.

    The EDF discussed in Sect. 8.5.1 is based on the nonparametric approach.

  3. 3.

    Some properties of this estimator are discussed in [2], p. 549.

  4. 4.

    A distribution function is said to be arithmetic if its support is on {0, ±d, ±2d, …} for some constant d and otherwise is said to be non-arithmetic, [6].

  5. 5.

    See [7] and ([2] p. 554) for details.

  6. 6.

    Discussed in Sect. 11.3.1.

  7. 7.

    Comparisons between these estimates are given in [5, 6].

  8. 8.

    Estimation of the survival function for censored data also given in Sect. 8.5.1.

  9. 9.

    This is based on a method proposed by [17, 19, 20]. Additional details can be found in ([12], p. 397).

  10. 10.

    The set contains counts of the items working and of the number uncensored just prior to t (k).

  11. 11.

    Detailed derivations can be found in [11, 18], and ([12], p. 398).

  12. 12.

    SPLIDA (S-Plus Life Data Analysis), see, www.public.iastate.edu/~splida.

  13. 13.

    In MINITAB, use Stat ℧ Reliability/Survival ℧ Nonparametric Growth Curve.

  14. 14.

    See MINITAB for details and use Stat ℧ Reliability/Survival ℧ Distribution Analysis (Arbitrary Censoring) ℧ Nonparametric Distribution Analysis.

  15. 15.

    See Sect. 5.12.2 for a graphical view of Structure 2 data.

  16. 16.

    See Chap. 8 for more on plotting procedures.

  17. 17.

    See Sect. 8.5 and Appendix C.

  18. 18.

    This will be investigated further in Chap. 12 by fitting parametric distributions to the data.

  19. 19.

    The survfit function computes an estimate of a survival curve for censored data using either the KaplanᾢMeier or the Fleming and Harrington method and computes the predicted survivor function for a Cox proportional hazards model.

  20. 20.

    For more information, see [4], S-plus (www.insightful.com), and R-language (http://cran.r-project.org).

  21. 21.

    If necessary, the unit “month” can be easily substituted with “week”, “day” and so on [8].

  22. 22.

    See Sect. 5.12.3 for more details of Structure 3 data.

  23. 23.

    Chapter 9 gives general definition and derivation of confidence intervals.

  24. 24.

    Chapter 15 presents a graphical representation of MOPᾢMIS plot.

  25. 25.

    In some cases it can be a shift, if a company operates more than one shift per day.

  26. 26.

    The MOPᾢMIS tables may be of different forms; see Table 11.10 for another form.

  27. 27.

    The detailed data that are required to calculate WCR2(i) for all production months are not given in the book.

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Author information

Authors and Affiliations

  1. 5401 Katherine Avenue, 91401-4922, Sherman Oaks, Los Angeles, CA, USA

    Wallace R. Blischke

  2. Department of Statistics, Rajshahi University, Rajshahi, Bangladesh

    M. Rezaul Karim

  3. School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    D. N. Prabhakar Murthy

Authors
  1. Wallace R. Blischke
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  2. M. Rezaul Karim
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  3. D. N. Prabhakar Murthy
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Correspondence to Wallace R. Blischke .

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Blischke, W.R., Rezaul Karim, M., Prabhakar Murthy, D.N. (2011). Nonparametric Approach to the Analysis of 1-D Warranty Data. In: Warranty Data Collection and Analysis. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-647-4_11

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  • DOI: https://doi.org/10.1007/978-0-85729-647-4_11

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