Volume 3, Issue 6, November 2014, Page: 167-176
Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme
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
Received: Sep. 21, 2014;       Accepted: Oct. 8, 2014;       Published: Oct. 20, 2014
DOI: 10.11648/j.ajtas.20140306.11      View  2761      Downloads  213
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.
Keywords
Exponentiated Frechet Distribution, Progressive First-Failure Censored Samples, Lifetime Performance Index, Hypothesis Testing, Maximum Likelihood, Bayes Estimates
To cite this article
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, American Journal of Theoretical and Applied Statistics. Vol. 3, No. 6, 2014, pp. 167-176. doi: 10.11648/j.ajtas.20140306.11
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