Considering AEWMA control chart applied to Gamma-distributed data with fixed and variable sampling intervals.

Control charts are widely used in manufacturing and quality management to monitor process variability. Although easy to implement, the Shewhart control chart lacks sensitivity to small process shifts. The exponentially weighted moving average (EWMA) control chart is effective in detecting minor shifts, but responds slowly to sudden changes. To enhance the detection capability, this study adopts the adaptive EWMA (AEWMA) control chart, which features dynamic adjustment mechanisms to improve the monitoring performance. This is applicable for skewed process data, particularly those following a Gamma distribution such as lifetime data, waiting times, and current stability indicators in semiconductor manufacturing. The Wilson-Hilferty transformation was applied to approximate the normality before constructing the AEWMA control chart. Monte Carlo simulations were employed to design and evaluate both the fixed sampling interval (FSI) and variable sampling interval (VSI) schemes under various combinations of shapes, scale parameters, and smoothing constants. To address the limitations of the traditional average run length (ARL) in reflecting the differences in sampling schemes, this study also adopted the average time-to-signal (ATS) as a performance metric. The simulation results demonstrated that the AEWMA VSI chart outperformed both the AEWMA FSI and EWMA charts in terms of sensitivity and stability when detecting small process shifts.