Exploring the Shift in Symmetry Phenomenon in Exponentially Weighted Moving Average Quality Charts for Statistics Derived from Beta Distribution

Abstract

The Exponential Weighted Moving Average (EWMA) is a statistical method used to create moving averages that assign greater weight to more recent data, frequently used in quality control. This approach, which mitigates asymmetry via the central limit theorem, encounters skewness issues majorly influenced by the lambda parameter ($\lambda$). This research investigates the impact of various EWMA smoothing factors on skewness reduction, utilizing the beta distribution, which can replicate diverse real-world distributions from heavily skewed to nearly symmetric, for data generation. With Matlab, random beta-distributed data was analyzed with the EWMA to observe changes in skewness and kurtosis. This study aids in comprehending data distributions in new or significantly modified processes, assisting in the adjustment of control chart parameters. It identifies a gap in existing literature regarding indeterminate distributions and underscores the need for further investigation in this field.