An adaptive EWMA chart with CUSUM accumulate error-based shift estimator for efficient process dispersion monitoring

Random causes of variation are part of every process and are harmless to product quality characteristics, while special cause variations appear due to a fault in the process and need special attention. The adaptive exponential weighted moving average (EWMA) control chart based on the cumulative sum (CUSUM) accumulation error is proposed in this study. The aim of this study is detecting imbalanced mixed range (different sizes) shifts (special cause) in process dispersion. The Huber and Tukey bi-square functions are used to enhance the proposed chart efficiency to simultaneously detect these small to large shifts. To check the sensitivity of the proposed chart, numerical results are provided through Monto Carlo simulations. The average run length (ARL) for single shift performance and extra quadratic loss (EQL), relative average run length (RARL) and performance comparison index (PCI) measures are used for overall performance evaluation of the proposed chart. The proposed scheme is compared to existing charts in the literature to determine superiority. For practical purposes, the guidelines are provided using real-life data for their practical implementation.