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Study of nonparametric estimation details of instant system availability average

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Abstract

Interval availability for repairable systems provides the probability measure where the components system are functioning at some delimited time and still working for a particular time of interval. The probability measure is specialized interested in materials equipment. It is operating, performing since there is any particular case happened. The following article considers the study of nonparametric estimation details of instant system availability average, as data collection n have been tested as a complete cycle period for the system operation to be convenient. The given data collection has been considered to be perfect censorship, in addition to this, the procedure has also been taken to be kept up to the limited period T. The application analysis of this article is discussed, and it has been used to get the improvement of nonparametric estimation to the given instant system availability. A present procedure has been demonstrated helped by a mechanical device to the failure collection data.

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References

  • Baxter L et al (1994) Non-parametric confidence intervals for the renewal function and the point availability. Scand J Stat 21:277–287

    MathSciNet  MATH  Google Scholar 

  • Baxter LA, Li L (1996) Nonparametric estimation of the limiting availability. Lifetime Data Anal 4(2):391–402

    Article  MATH  Google Scholar 

  • Baxter LA, Li L (2014) Nonparametric estimation of the interval reliability. J Stat Theory Appl 13(4):356–366

    MathSciNet  Google Scholar 

  • Beaumont J-F, Bocci C (2009) Variance estimation when donor imputation is used to fill in missing values. Can J Stat 37(3):400–416

    Article  MathSciNet  MATH  Google Scholar 

  • Bengtsson T, Cavanaugh JE (2006) An improved Akaike information criterion for state-space model selection. Comput Stat Data Anal 50(10):2635–2654

    Article  MathSciNet  MATH  Google Scholar 

  • Boukeloua M, Messaci F (2016) Asymptotic normality of kernel estimators based upon incomplete data. J Nonparametric Stat 28(3):1–18

    Article  MathSciNet  MATH  Google Scholar 

  • Dinse GE (1982) Nonparametric estimation for partially-complete time and type of failure data. Biometrics 38(2):417–431

    Article  MathSciNet  Google Scholar 

  • Fleming TR, Harrington DP (2011) Counting processes and survival analysis, vol 169. Wiley, New York

    MATH  Google Scholar 

  • Frees EW (1986) Warranty analysis and renewal function estimation. Nav Res Logist Q 33(3):361–372

    Article  MATH  Google Scholar 

  • Grubel R, Pitts SM (1993) Nonparametric estimation in renewal theory I: the empirical renewal function. Ann Stat 21:1431–1451

    Article  MathSciNet  MATH  Google Scholar 

  • Hagenimana E et al (2016) Computation of instant system availability and its applications. SpringerPlus 5(1):954

    Article  Google Scholar 

  • Hagenimana E, Lixin S, Kandege P (2016) Technical application for inspection sampling for repairable systems in an economic system. SpringerPlus 5(1):1955

    Article  Google Scholar 

  • Harel M, Ocinneide CA, Schneider H (1995) Asymptotics of the sample renewal function. J Math Anal Appl 189(1):240–255

    Article  MathSciNet  MATH  Google Scholar 

  • Hellen WW, Edward N (2016) Non-parametric variance estimation using donor imputation method. Am J Theor Appl Stat 5(5):252–259

    Article  Google Scholar 

  • Høyland A, Rausand M (2009) System reliability theory: models and statistical methods, vol 420. Wiley, New York

    MATH  Google Scholar 

  • Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53(282):457–481

    Article  MathSciNet  MATH  Google Scholar 

  • Kumbhakar SC, Park BU, Simar L, Tsionas EG (2007) Nonparametric stochastic frontiers: a local maximum likelihood approach. J Econom 137(1):1–27

    Article  MathSciNet  MATH  Google Scholar 

  • Li L (1999) Estimating the point availability with right-censored data. Nav Res Logist (NRL) 46(1):119–127

    Article  MathSciNet  MATH  Google Scholar 

  • Li Q, Racine J (2003) Nonparametric estimation of distributions with categorical and continuous data. J Multivar Anal 86(2):266–292

    Article  MathSciNet  MATH  Google Scholar 

  • Ouhbi B, Limnios N (2003) Nonparametric reliability estimation of semi-Markov processes. J Stat Plan Inference 109(1):155–165

    Article  MathSciNet  MATH  Google Scholar 

  • Pan W (1999) Extending the iterative convex minorant algorithm to the Cox model for interval-censored data. J Comput Gr Stat 81(1):109–120

    MathSciNet  Google Scholar 

  • Racine J, Li Q (2004) Nonparametric estimation of regression functions with both categorical and continuous data. J Econom 119(1):99–130

    Article  MathSciNet  MATH  Google Scholar 

  • Rausand M, Høyland A (2004) System reliability theory: models, statistical, vol 396. Wiley, New York, p 396

    MATH  Google Scholar 

  • Reyes M, Francisco-Fernández M (2016) Nonparametric kernel density estimation for general grouped data. J Nonparametric Stat 28(2):235–249

    Article  MathSciNet  MATH  Google Scholar 

  • Schneider H, Lin B-S, O’Cinneide C (1990) Comparison of nonparametric estimators for the renewal function. Appl Stat 39(1):55–61

    Article  MathSciNet  MATH  Google Scholar 

  • Stute W, Wang J-L (1993) The strong law under random censorship. Ann Stat 21(3):1591–1607

    Article  MathSciNet  MATH  Google Scholar 

  • Susarla V, Van RJ (1980) Large sample theory for an estimator of the mean survival time from censored samples. Ann Stat 8(5):1002–1016

    Article  MathSciNet  MATH  Google Scholar 

  • Vickers AJ (2005) Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data. BMC Med Res Methodol 5(1):1

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The Authors are grateful to the Natural National Science Foundation of China (11371077) for their financial support.

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Authors and Affiliations

  1. China School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, China

    Emmanuel Hagenimana, Song Lixin & Patrick Kandege

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  1. Emmanuel Hagenimana
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  2. Song Lixin
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  3. Patrick Kandege
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Correspondence to Emmanuel Hagenimana or Song Lixin.

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Hagenimana, E., Lixin, S. & Kandege, P. Study of nonparametric estimation details of instant system availability average. Int J Syst Assur Eng Manag 9, 467–481 (2018). https://doi.org/10.1007/s13198-017-0691-8

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  • DOI: https://doi.org/10.1007/s13198-017-0691-8

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