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

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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[4] N. Balakrishnan, and R. Aggarwala, Progressive Censoring: Theory, Methods and Applications. Boston: Birkhauser Publishers, (2000).
[5] N. Balakrishnan, Progressive censoring methodology: An appraisal. Test 16, (2007), 211--296.
[6] L.G. Johnson, Theory and Technique of Variation Research, Elsevier, Amsterdam, (1964).
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[8] S. J. Wu and S. R. Huang, Progressively first-failure censored reliability sampling plans with cost constraint, Computational Statistics and Data Analysis, 56, (2012), 2018-2030.
[9] A.A. Soliman, A.H. Abd Ellah, N.A. Abou-Elheggag, and A.A. Modhesh, Estimation from Burr type XII distribution using progressive first failure censored data, Journal of Statistical Computation and Simulation, 83,( 2013), 2270-2290
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[11] V.E Kane, Process capability indices, Journal of Quality Technology 18, (1986), 41 52.
[12] L. I. Tong, K. S. Chen, and H. T Chen, Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution, Journal of Quality Reliability Management, vol. 19, (2002), pp. 812--824, .
[13] J.W. Wu, H.M. Lee, and C.L. Lei, Computational testing algorithmic procedure of assessment for lifetime performance index of products with two-parameter exponential distribution, Applied Mathematics and Computation 190, (2007), 116.125
[14] W.C. Lee, J.W. Wu, and C.W. Hong, Assessing the lifetime performance index of products with the exponential distribution under progressively type-II right censored samples, Journal of Computational and Applied Mathematics 231, (2009), 648--656.
[15] M.V. Ahmadi, M. Doostparast and J. Ahmadi, Estimating the lifetime performance index with Weibull distribution based on progressive first-failure censoring scheme, Journal of Computational and Applied Mathematics 239, (2013), 93--102.
[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
[18] M. Ahsanullah Generalized Order Statistics From Exponential Distribution, Journal of Statistical Planning and Inference, 85, (2000), 85--91.
[19] G. Casella, and R.L. Berger, Statistical Inference, second ed., Duxbury, Pacific Grove, CA, (2002).
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Cite This Article
  • 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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    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
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    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
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    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
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Author Information
  • Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

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

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

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

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