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), 2024. Published by Science Publishing Group |
Reliability, Forced Outage Rate, Maximum Likelihood Estimation, Statistical Properties
| [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 |
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
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
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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Download@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}
}
TY - JOUR T1 - An Inquiry into the Distributional Properties of Reliability Rate AU - Vijayamohanan Pillai N. Y1 - 2014/11/20 PY - 2014 N1 - https://doi.org/10.11648/j.ajtas.20140306.14 DO - 10.11648/j.ajtas.20140306.14 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 197 EP - 201 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20140306.14 AB - 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. VL - 3 IS - 6 ER -
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