A new adaptive EWMA control chart based on Catoni’s function for monitoring process variability

The monitoring of process variability through sample variance has garnered a great deal of attention. Compared to the EWMA control chart, the adaptive EWMA (AEWMA) dispersion chart based on the sample variance demonstrates overall superior detection performance for both small and large shifts. However, the classical AEWMA chart often employs Huber's weight function to adaptively allocate weights. This weight function is efficient under symmetric distributions but becomes inefficient under asymmetric distributions. Note that the sample variance follows a Chi-square distribution, which is asymmetrical and heavy-tailed when the sample size is small. Motivated by this, this paper proposes a new weight function based on Catoni's function for the AEWMA dispersion chart. Extensive simulations indicate that the new AEWMA dispersion chart outperforms the AEWMA dispersion chart based on Huber's weight. Additionally, we introduce a penalized optimization method that is more computationally efficient and accurate than the conventional grid searching approach for determining the optimal design parameters of the proposed control chart.