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An Inquiry into the Distributional Properties of Reliability Rate

Received: 24 October 2014     Accepted: 6 November 2014     Published: 20 November 2014
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Abstract

The present paper attempts to model the maximum likelihood estimation of reliability rate and the related statistical properties. Reliability in general refers to the probability that a component or system is able to perform its function satisfactorily during a specific period under normal operating conditions. It is estimated as the fraction of time the unit/system is available for operation. For practical purposes, reliability rate is usually estimated using maximum likelihood estimator (MLE) from sample observations. No study has gone beyond this to analyze the statistical properties of the MLE of reliability rate; the present study is an attempt at such an inquiry. We derive the density function of reliability rate and also the moments; however, it is found that an evaluation of these two moments is very difficult as the series converge very slowly.

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 6)
DOI 10.11648/j.ajtas.20140306.14
Page(s) 197-201
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Reliability, Forced Outage Rate, Maximum Likelihood Estimation, Statistical Properties

References
[1] Bazovsky, Igor (1961) Reliability Engineering and Practice. Prentice hall Space Technological series, Prentice Hall, Englewood Cliffs, NJ.
[2] Pillai, N. Vijayamohanan, (1991), Seasonal Time-of-Day Pricing of Electricity under Uncertainty - A Marginalist Approach to Kerala Power System. Ph. D. Thesis. University of Madras. Ch.4.
[3] Zehna, P. (1966), `Invariance of Maximum Likelihood Estimation', Annals of Mathematical Statistics, Vol. 37, p. 744.
[4] Kendall, M. G., and Stuart, A., (1967), The Advanced Theory of Statistics, Vol. II, 2nd Edition, Hafner, New York. Ch. 18.
[5] Pillai, N. Vijayamohanan (1999) “Reliability Analysis of Power Generation System - A Case Study” Productivity, July – Sept., 1999, Vol 40, No. 2: 310 – 318.
[6] Pillai, N. Vijayamohanan (2002) “Reliability and Rationing Cost in a Power System”, CDS Working Paper No. 325, March. http://cds.edu/download_files/325.pdf
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  • APA Style

    Vijayamohanan Pillai N. (2014). An Inquiry into the Distributional Properties of Reliability Rate. American Journal of Theoretical and Applied Statistics, 3(6), 197-201. https://doi.org/10.11648/j.ajtas.20140306.14

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    ACS Style

    Vijayamohanan Pillai N. An Inquiry into the Distributional Properties of Reliability Rate. Am. J. Theor. Appl. Stat. 2014, 3(6), 197-201. doi: 10.11648/j.ajtas.20140306.14

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    AMA Style

    Vijayamohanan Pillai N. An Inquiry into the Distributional Properties of Reliability Rate. Am J Theor Appl Stat. 2014;3(6):197-201. doi: 10.11648/j.ajtas.20140306.14

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  • @article{10.11648/j.ajtas.20140306.14,
      author = {Vijayamohanan Pillai N.},
      title = {An Inquiry into the Distributional Properties of Reliability Rate},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {3},
      number = {6},
      pages = {197-201},
      doi = {10.11648/j.ajtas.20140306.14},
      url = {https://doi.org/10.11648/j.ajtas.20140306.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140306.14},
      abstract = {The present paper attempts to model the maximum likelihood estimation of reliability rate and the related statistical properties. Reliability in general refers to the probability that a component or system is able to perform its function satisfactorily during a specific period under normal operating conditions. It is estimated as the fraction of time the unit/system is available for operation. For practical purposes, reliability rate is usually estimated using maximum likelihood estimator (MLE) from sample observations. No study has gone beyond this to analyze the statistical properties of the MLE of reliability rate; the present study is an attempt at such an inquiry. We derive the density function of reliability rate and also the moments; however, it is found that an evaluation of these two moments is very difficult as the series converge very slowly.},
     year = {2014}
    }
    

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Author Information
  • Faculty, Centre for Development Studies, Trivandrum – 695 011, Kerala, India

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