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Applied Nonparametric Statistics in Reliability pp 121–142Cite as

Systems with Multi-Components

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

Abstract

The main purpose of this chapter is to construct a system structure function based on an observed set of the system output performance and the corresponding performances of its components. To do this, special techniques are proposed by looking at the structure function of a continuous-state system under the scope of a regression model. Multivariate smoothing and isotonic regression methods are adapted to the particular characteristics of the problem at hand.

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References

  1. Aven T (1993) On performance measures for multistate monotone systems. Reliab Eng Syst Safety 41:259–266

    Article  Google Scholar 

  2. Ayer M, Brunk HD, Ewing GM, Reid WT, Silverman E (1955) An empirical distribution function for sampling with incomplete information. Ann Math Stat 26:641–647

    Article  MATH  MathSciNet  Google Scholar 

  3. Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing. Holt, Rinehart and Winston, New York

    Google Scholar 

  4. Baxter LA (1984) Continuum structures I. J Appl Prob 21:802–815

    Article  MATH  MathSciNet  Google Scholar 

  5. Baxter LA (1986) Continuum structures II. Math Proc Cambridge Philos Soc 99:331–338

    Article  MATH  MathSciNet  Google Scholar 

  6. Bowman A (1984) An alternative method of cross validation for the smoothing of density estimates. Biometrika 71:353–360

    Article  MathSciNet  Google Scholar 

  7. Brunelle RD, Kapur KC (1998) Continuous state system reliability: an interpolation approach. IEEE Trans Reliab 47(2):181–187

    Article  Google Scholar 

  8. Brunelle RD, Kapur KC (1999) Review and classification or reliability measures for multistate and continuum models. IIE Trans 31:1171–1180

    Google Scholar 

  9. Burdakow O, Grimwall A, Hussian M (2004) A generalised PAV algorithm for monotonic regression in several variables. COMPSTAT’2004 Symposium

    Google Scholar 

  10. Chen SX (1999) Beta kernel estimators for density functions. Comput Stat Data Anal 31:131–145

    Article  MATH  Google Scholar 

  11. El Neweihi E, Proschan F, Sethuraman J (1978) Multistate coherent systems. J Appl Prob 15(4):675–688

    Article  MATH  MathSciNet  Google Scholar 

  12. Fan J, Gijbels I (1996) Local polynomial modelling and its applications. Monographs on statistics and applied probability. Chapman & Hall, London

    Google Scholar 

  13. Gámiz ML, Martínez-Miranda MD (2010) Regression analysis of the structure function for reliability evaluation of continuous-state system. Reliab Eng Syst 95(2):134–142

    Article  Google Scholar 

  14. González-Manteiga W, Martínez-Miranda MD, Pérez-González A (2004) The choice of smoothing parameter in nonparametric regression through wild bootstrap. Comput Stat Data Anal 47:487–515

    Article  Google Scholar 

  15. Hall P, Hwang LS (2001) Nonparametric kernel regression subject to monotonicity constraints. Ann Stat 29(3):624–647

    Article  MATH  Google Scholar 

  16. Härdle W, Müller M, Sperlich S, Werwatz A (2004) Nonparametric and semiparametric Models. Springer, Berlin

    Book  MATH  Google Scholar 

  17. Kaymaz I, McMahon C (2005) A response surface method based on weighted regression for structural reliability analysis. Prob Eng Mech 20:11–17

    Article  Google Scholar 

  18. Levitin G (2005) The universal generating function in reliability analysis and optimization. Springer, London

    Google Scholar 

  19. Li JA, Wu Y, Lai KK, Liu K (2005) Reliability estimation and prediction of multi state components and coherent systems. Reliab Eng Syst Safety 88:93–98

    Article  Google Scholar 

  20. Lisnianski A (2001) Estimation of boundary points for continuum-state system reliability measures. Reliab Eng Syst Safety 74:81–88

    Article  MATH  Google Scholar 

  21. Lisnianski A, Levitin G (2003) Multi-state system reliability. Assessment, optimization and applications. World Scientific, Singapore

    MATH  Google Scholar 

  22. Meng FC (2005) Comparing two reliability upper bounds for multistate systems. Reliab Eng Syst Safety 87:31–36

    Article  Google Scholar 

  23. Mukarjee H, Stem S (1994) Feasible nonparametric estimation of multiargument monotone functions. J Am Stat Assoc 89:77–80

    Article  MATH  Google Scholar 

  24. Natvig B (1982) Two suggestions of how to define a multistate coherent system. Appl Prob 14:434–455

    Google Scholar 

  25. Pourret O, Collet J, Bon JL (1999) Evaluation of the unavailability of a multistate component system using a binary model. Reliab Eng Syst Safety 64:13–17

    Article  MATH  Google Scholar 

  26. Rackwitz R (2001) Reliability analysis a review and some perspectives. Struct Safety 23:365–395

    Article  Google Scholar 

  27. Rudemo M (1982) Empirical choice of histograms and kernel density estimators. Scand J Stat 9:65–78

    MATH  MathSciNet  Google Scholar 

  28. Ruppert D, Wand MP (1994) Multivariate locally weighted least squares regression. Ann Stat 22:1346–1370

    Article  MATH  MathSciNet  Google Scholar 

  29. Sarhan AM (2002) Reliability equivalence with a basic series/parallel system. Appl Math Comput 132:115–133

    Article  MATH  MathSciNet  Google Scholar 

  30. Turner R (2009) Iso: functions to perform isotonic regression http://CRAN.R-project.org/package=Iso

  31. Wang L, Grandhi RV (1996) Safety index calculations using intervening variables for structural reliability analysis. Comput Struct 59(6):1139–1148

    Article  MATH  Google Scholar 

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Acknowledgments

This chapter is an extension into book-length form of the article Regression analysis of the structure function for reliability evaluation of continuous-state system, originally published in Reliability Engineering and System Safety 95(2), 134–142 (2010).

The authors express their full acknowledgment 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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  4. Prof. Bo Henry Lindqvist
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Corresponding author

Correspondence to M. Luz Gámiz .

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Gámiz, M.L., Kulasekera, K.B., Limnios, N., Lindqvist, B.H. (2011). Systems with Multi-Components. In: Applied Nonparametric Statistics in Reliability. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-118-9_5

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  • DOI: https://doi.org/10.1007/978-0-85729-118-9_5

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  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-117-2

  • Online ISBN: 978-0-85729-118-9

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