Comparison between some control panels for the mean of asymmetric distributions with the application

Abstract

The study aims to use two approaches to address the asymmetry of the distribution of the quality characteristic variable; The first approach is the application of a checkerboard for the arithmetic mean after performing Johnson transformations. The other approach is the use of fortified control panels that are not affected by the failure to fulfill the condition of the normal distribution, such as the Weighted Variance (WV) Method and the Scaled Weighted Variance (SWV) Method for quality control. Drinking water in Iraq by taking (120) observations for each of the turbidity variable and the residual chlorine variable and for samples with a size (n = 3,5,8). As for the turbidity variable, we find that the arithmetic mean panel of the weighted contrast method gives a performance that exceeds the performance of the arithmetic mean panels of the other methods, due to its obtaining the largest value for the running length rate, while we find that the average running length of the weighted contrast method measured for a variable. The residual chlorine is a larger value than the average board run-time rates for the other methods, and this indicates that this method is better than the other methods; In the case of average sample sizes (n = 5), we note that the arithmetic mean panel of the measured weighted variance method gives better performance because it has the largest values ​​of run-length rates for both the turbidity variable and the residual chlorine variable; Finally, in the case of large sample sizes (n = 8), we note that Stewart’s mean plate method gives better performance than other methods, by obtaining the largest values ​​for the running length rates for both the turbidity variable and the residual chlorine variable.