Building Robust Control Limits for the Mean and Range to Control the Quality of Drinking Water Case of Skewed Distributions

Abstract

In this paper, the problem of the quality characteristic variable asymmetry was addressed by setting non-violable and insensitive control limits for not meeting the normal distribution condition, and using them as an alternative to shewhar s charts for quality control in the event that the data cannot follow a normal distribution, represented by the weighted variance (WV) method and the weighted standard deviation (WSD) method. Monitoring the quality of drinking water in Iraq by taking (120) observations for the free chlorine variable, and depending on the Average Run Length (ARL), it was found that the control charts for the arithmetic mean and the range of the Weighted Variance (WV) method give the best comparative performance in control charts for the mean and range the method of calculation and the Weighted Standard Deviation (WSD) method, by obtaining the largest values of the Averages Run Length (ARL).