Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Ahmed Abo-Elmagd Soliman; Essam Al-Sayed Ahmed; Ahmed Hamed Abd Ellah; Al-Wageh Ahmed Farghal

doi:doi:10.11648/j.ajtas.20140306.11

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Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Ahmed Abo-Elmagd Soliman, Essam Al-Sayed Ahmed, Ahmed Hamed Abd Ellah, Al-Wageh Ahmed Farghal

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 6)

Received: 21 September 2014 Accepted: 8 October 2014 Published: 20 October 2014

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Abstract

Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C_L. The MLE and the Bayesian estimators of C_L are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.

Published in	American Journal of Theoretical and Applied Statistics (Volume 3, Issue 6)
DOI	10.11648/j.ajtas.20140306.11
Page(s)	167-176
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

Exponentiated Frechet Distribution, Progressive First-Failure Censored Samples, Lifetime Performance Index, Hypothesis Testing, Maximum Likelihood, Bayes Estimates

References

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[16]	W.C. Lee, J.W. Wu, C.W. Hong, and S.F. Hong, Evaluating the Lifetime Performance Index Based on the Bayesian Estimation for the Rayleigh Lifetime Products with the Upper Record Values, Journal of Applied Mathematics, Volume, (2013), Article ID 547209, 13 pages, http://dx.doi.org/10.1155/2013/547209.
[17]	M.V. Ahmadi, M. Doostparast and J. Ahmadi, Statistical inference for the lifetime performance index based on generalised order statistics from exponential distribution, International Journal of Systems Science, http://dx.doi.org/10.1080/00207721.2013.809611
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APA Style

Ahmed Abo-Elmagd Soliman, Essam Al-Sayed Ahmed, Ahmed Hamed Abd Ellah, Al-Wageh Ahmed Farghal. (2014). Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme. American Journal of Theoretical and Applied Statistics, 3(6), 167-176. https://doi.org/10.11648/j.ajtas.20140306.11

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ACS Style

Ahmed Abo-Elmagd Soliman; Essam Al-Sayed Ahmed; Ahmed Hamed Abd Ellah; Al-Wageh Ahmed Farghal. Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme. Am. J. Theor. Appl. Stat. 2014, 3(6), 167-176. doi: 10.11648/j.ajtas.20140306.11

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AMA Style

Ahmed Abo-Elmagd Soliman, Essam Al-Sayed Ahmed, Ahmed Hamed Abd Ellah, Al-Wageh Ahmed Farghal. Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme. Am J Theor Appl Stat. 2014;3(6):167-176. doi: 10.11648/j.ajtas.20140306.11

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@article{10.11648/j.ajtas.20140306.11,
  author = {Ahmed Abo-Elmagd Soliman and Essam Al-Sayed Ahmed and Ahmed Hamed Abd Ellah and Al-Wageh Ahmed Farghal},
  title = {Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {6},
  pages = {167-176},
  doi = {10.11648/j.ajtas.20140306.11},
  url = {https://doi.org/10.11648/j.ajtas.20140306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140306.11},
  abstract = {Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C_L. The MLE and the Bayesian estimators of C_L are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.},
 year = {2014}
}

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TY  - JOUR
T1  - Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme
AU  - Ahmed Abo-Elmagd Soliman
AU  - Essam Al-Sayed Ahmed
AU  - Ahmed Hamed Abd Ellah
AU  - Al-Wageh Ahmed Farghal
Y1  - 2014/10/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140306.11
DO  - 10.11648/j.ajtas.20140306.11
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  - 167
EP  - 176
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140306.11
AB  - Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C_L. The MLE and the Bayesian estimators of C_L are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.
VL  - 3
IS  - 6
ER  -

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Author Information

Ahmed Abo-Elmagd Soliman

Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
Essam Al-Sayed Ahmed

Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
Ahmed Hamed Abd Ellah

Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
Al-Wageh Ahmed Farghal

Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

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Plain Text BibTeX RIS

APA Style

Ahmed Abo-Elmagd Soliman, Essam Al-Sayed Ahmed, Ahmed Hamed Abd Ellah, Al-Wageh Ahmed Farghal. (2014). Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme. American Journal of Theoretical and Applied Statistics, 3(6), 167-176. https://doi.org/10.11648/j.ajtas.20140306.11

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ACS Style

Ahmed Abo-Elmagd Soliman; Essam Al-Sayed Ahmed; Ahmed Hamed Abd Ellah; Al-Wageh Ahmed Farghal. Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme. Am. J. Theor. Appl. Stat. 2014, 3(6), 167-176. doi: 10.11648/j.ajtas.20140306.11

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AMA Style

Ahmed Abo-Elmagd Soliman, Essam Al-Sayed Ahmed, Ahmed Hamed Abd Ellah, Al-Wageh Ahmed Farghal. Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme. Am J Theor Appl Stat. 2014;3(6):167-176. doi: 10.11648/j.ajtas.20140306.11

Copy | Download

@article{10.11648/j.ajtas.20140306.11,
  author = {Ahmed Abo-Elmagd Soliman and Essam Al-Sayed Ahmed and Ahmed Hamed Abd Ellah and Al-Wageh Ahmed Farghal},
  title = {Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {6},
  pages = {167-176},
  doi = {10.11648/j.ajtas.20140306.11},
  url = {https://doi.org/10.11648/j.ajtas.20140306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140306.11},
  abstract = {Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C_L. The MLE and the Bayesian estimators of C_L are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme
AU  - Ahmed Abo-Elmagd Soliman
AU  - Essam Al-Sayed Ahmed
AU  - Ahmed Hamed Abd Ellah
AU  - Al-Wageh Ahmed Farghal
Y1  - 2014/10/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140306.11
DO  - 10.11648/j.ajtas.20140306.11
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  - 167
EP  - 176
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140306.11
AB  - Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C_L. The MLE and the Bayesian estimators of C_L are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.
VL  - 3
IS  - 6
ER  -

Copy | Download