A Comparison Study on the Performances Of X , EWMA and CUSUM Control Charts for Skewed Distributions Using Weighted Standard Deviations Methods

Abstract

In many statistical process control (SPC) applications, the ease of use of control charts leads to ignoring the fact that the process population of the quality characteristic being measured may be highly skewed. However, in many situations, the normality assumption is usually violated. Among the recent heuristic charts for skewed distributions proposed in the literature are those based on the weighted standard deviation (WSD) method. Thus, this paper compares the performances of certain WSD charts, such as WSD X , WSD Exponential weighted moving Average (WSDEWMA) and WSD Cumulative Sum (WSD-CUSUM) charts for skewed distributions. The skewed distributions being considered are weibull, gamma and lognormal. The false alarm and mean shift detection rates were computed so as to evaluate the performances of the WSD charts. The WSD X chart was found to have the lowest false alarm rate in cases of known and unknown parameters. Moreover, when parameters are known and unknown, the WSD-CUSUM provided the highest mean shift detection rates. The chart with the lowest false alarm and the highest mean shift detection rates for most level of skewness and sample size, n is assumed to be have a better performance.