Ewma Control Charts For Skewed Dıstrıbutıons

Abstract

The classic Shewhart control charts are generally used for monitoring the process mean and variability in the characteristics of a random quality variable of interest and are based on the normality assumptions. For skewed distributions, in order to demonstrate the changes in the population, non-symmetric control limits need to be used. Methods such as the Weighted Variance (WV) Weighted Standard Deviation (WSD) and Skewness Correction (SC) are used with skewed distributions.

The classic 𝑋� ̅ and R control charts and all their derivatives are generally used to detect large shifts in the process mean hence making them not too reliable in situations where in small shifts are of interest. To solve such problems, the Exponentially Weighted Moving Average (EWMA) control charts is used in this work.

The main aim of this thesis is to apply the Skewness Correction method to the EWMA chart and propose a control limit called Skewness Correction EWMA (SC-EWMA) for skewed distributions. The performances of the newly proposed method are compared and contrasted with those of the Weighted Variance EWMA (WV-EWMA) which was developed by Khoo and Atta (2008), Weighted Standard Deviation EWMA (WSD-EWMA) which was developed by Atta and Ramli (2011) and the classic EWMA control limits based on the degree of skewness and varying smoothing parameters. The comparison is made with respect to their type-Ι errors by using the Monte Carlo simulation technique with data generated from the lognormal, Gamma and Weibull distributions.