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.



Similar content being viewed by others
References
Baxter L et al (1994) Non-parametric confidence intervals for the renewal function and the point availability. Scand J Stat 21:277–287
Baxter LA, Li L (1996) Nonparametric estimation of the limiting availability. Lifetime Data Anal 4(2):391–402
Baxter LA, Li L (2014) Nonparametric estimation of the interval reliability. J Stat Theory Appl 13(4):356–366
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
Bengtsson T, Cavanaugh JE (2006) An improved Akaike information criterion for state-space model selection. Comput Stat Data Anal 50(10):2635–2654
Boukeloua M, Messaci F (2016) Asymptotic normality of kernel estimators based upon incomplete data. J Nonparametric Stat 28(3):1–18
Dinse GE (1982) Nonparametric estimation for partially-complete time and type of failure data. Biometrics 38(2):417–431
Fleming TR, Harrington DP (2011) Counting processes and survival analysis, vol 169. Wiley, New York
Frees EW (1986) Warranty analysis and renewal function estimation. Nav Res Logist Q 33(3):361–372
Grubel R, Pitts SM (1993) Nonparametric estimation in renewal theory I: the empirical renewal function. Ann Stat 21:1431–1451
Hagenimana E et al (2016) Computation of instant system availability and its applications. SpringerPlus 5(1):954
Hagenimana E, Lixin S, Kandege P (2016) Technical application for inspection sampling for repairable systems in an economic system. SpringerPlus 5(1):1955
Harel M, Ocinneide CA, Schneider H (1995) Asymptotics of the sample renewal function. J Math Anal Appl 189(1):240–255
Hellen WW, Edward N (2016) Non-parametric variance estimation using donor imputation method. Am J Theor Appl Stat 5(5):252–259
Høyland A, Rausand M (2009) System reliability theory: models and statistical methods, vol 420. Wiley, New York
Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53(282):457–481
Kumbhakar SC, Park BU, Simar L, Tsionas EG (2007) Nonparametric stochastic frontiers: a local maximum likelihood approach. J Econom 137(1):1–27
Li L (1999) Estimating the point availability with right-censored data. Nav Res Logist (NRL) 46(1):119–127
Li Q, Racine J (2003) Nonparametric estimation of distributions with categorical and continuous data. J Multivar Anal 86(2):266–292
Ouhbi B, Limnios N (2003) Nonparametric reliability estimation of semi-Markov processes. J Stat Plan Inference 109(1):155–165
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
Racine J, Li Q (2004) Nonparametric estimation of regression functions with both categorical and continuous data. J Econom 119(1):99–130
Rausand M, Høyland A (2004) System reliability theory: models, statistical, vol 396. Wiley, New York, p 396
Reyes M, Francisco-Fernández M (2016) Nonparametric kernel density estimation for general grouped data. J Nonparametric Stat 28(2):235–249
Schneider H, Lin B-S, O’Cinneide C (1990) Comparison of nonparametric estimators for the renewal function. Appl Stat 39(1):55–61
Stute W, Wang J-L (1993) The strong law under random censorship. Ann Stat 21(3):1591–1607
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
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
Acknowledgements
The Authors are grateful to the Natural National Science Foundation of China (11371077) for their financial support.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13198-017-0691-8
Keywords
- Instant availability
- Censored data
- Empirical distribution function
- Product limit estimator
- Renewal function
- Nonparametric
- Average availability
- Censored observation