One-sided Adaptive Truncated Exponentially Weighted Moving Average X¯ Schemes for Detecting Process Mean Shifts. Issue 5 (3rd September 2022) - Xie, FuPeng; Castagliola, Philippe; Li, Zhonghua; Sun, JinSheng; Hu, XueLong
ABSTRACT: One-sided type schemes are known to be more appropriate for monitoring a process when the direction of a potential mean shift can be anticipated. The one-sided adaptive truncated exponentially weighted moving average (ATEWMA) X ˉ scheme recommended in this paper is a control chart that combines a Shewhart X ˉ scheme and a new one-sided EWMA X ˉ scheme together in a smooth way for rapidly detecting the upward (or downward) mean shifts. The truncation method used in this paper helps to improve the sensitivity of the recommended scheme for detecting both small and large mean shifts simultaneously. To further improve the detection efficiency of the recommended scheme, we also suggest integrating a variable sampling interval (VSI) feature into the recommended scheme. Markov chain models are established to analyze the run length (RL) properties of the recommended scheme in both the zero-state and the steady-state cases. Comparison results show that the recommended one-sided ATEWMA X ˉ scheme works better than the conventional adaptive EWMA (AEWMA) X ˉ chart and the improved one-sided EWMA X ˉ chart in detecting a wide range of mean shifts. Finally, a numerical example is presented to illustrate the usage of the proposed one-sided ATEWMA X ˉ scheme for detecting process mean shifts.