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Measuring Process Capability for Bivariate Non-Normal Process Using the Bivariate Burr Distribution

Measuring Process Capability for Bivariate Non-Normal Process Using the Bivariate Burr Distribution,B. ABBASI,S. AHMAD,M. ABDOLLAHIAN,P. ZEEPHONGSEKUL

Measuring Process Capability for Bivariate Non-Normal Process Using the Bivariate Burr Distribution  
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As is well known, process capability analysis for more than one quality variables is a complicated and sometimes contentious area with several quality measures vying for recognition. When these variables exhibit non-normal characteristics, the situation becomes even more complex. The aim of this paper is to measure Process Capability Indices (PCIs) for bivariate non-normal process using the bivariate Burr distribution. The univariate Burr distribution has been shown to improve the accuracy of estimates of PCIs for univariate non-normal distributions (see for example, (7) and (16)). Here, we will estimate the PCIs of bivariate non-normal distributions using the bivariate Burr distribution. The process of obtaining these PCIs will be accomplished in a series of steps involving estimating the unknown parameters of the process using maximum likelihood estimation coupled with simulated annealing. Finally, the Proportion of Non-Conformance (PNC) obtained using this method will be compared with those obtained from variables distributed under the bivariate Beta, Weibull, Gamma and Weibull-Gamma distributions.
Published in 2007.
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