Run Sum Hotelling's T² Chart for Autocorrelated Processes

Autocorrelation has recently gained significant attention as many industrial outcomes are autocorrelated. This work presents a multivariate run sum T² (MRS) chart for monitoring autocorrelated processes by utilizing a first-order vector autoregressive (VAR(1)) model with an s-skip sampling strategy. To evaluate the performance of the proposed chart, the average run length (ARL) measure is used. Comparative analyses reveal that the proposed MRS chart significantly outperforms the basic T² charts for autocorrelated processes. The s-skip sampling strategy is incorporated into the MRS chart for autocorrelated processes to reduce the impact of autocorrelation. An illustrative example is included to demonstrate the practical implementation of the proposed chart, highlighting its advantages in real-world applications and emphasizing its potential to improve process monitoring across various industrial settings.