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On the Performance of Phase‐I Bivariate Dispersion Charts to Non‐Normality
Authors:Aamir Saghir  Subhabrata Chakraborti  Ishfaq Ahmad
Affiliation:1. Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan;2. Department of Information Systems, Statistics and Management Science, University of Alabama, Tuscaloosa, USA
Abstract:A phase‐I study is generally used when population parameters are unknown. The performance of any phase‐II chart depends on the preciseness of the control limits obtained from the phase‐I analysis. The performance of phase‐I bivariate dispersion charts has mainly been investigated for bivariate normal distribution. However, this assumption is seldom fulfilled in reality. The current work develops and studies the performance of phase‐I |S| and |G| charts for monitoring the process dispersion of bivariate non‐normal distributions. The necessary control charting constants are determined for the bivariate non‐normal distributions at nominal false alarm probability (FAP0). The performance of these charts is evaluated and compared in a situation when samples are generated by bivariate logistic, bivariate Laplace, bivariate exponential, or bivariate t5 distribution. The analysis shows that the proper consideration to underlying bivariate distribution in the construction of phase‐I bivariate dispersion charts is very important to give a real picture of in or out of control process status. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords:false alarm probability  normality/non‐normality  in‐control/out‐of‐control process  process dispersion
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