Multivariate process dispersion monitoring without subgrouping.

Area of Science:

• Statistical Process Control
• Quality Management
• Industrial Statistics

Background:

• Memory-type control charts are crucial for detecting subtle process parameter shifts.
• Monitoring changes in the covariance matrix of multivariate processes is essential for quality control.

Purpose of the Study:

• To propose and evaluate novel adaptive control charts for monitoring multivariate process covariance matrices.
• To compare the performance of proposed charts against existing methods.

Main Methods:

• Development of Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM), and adaptive EWMA (AEWMA) control charts.
• Extensive Monte Carlo simulations to compute control chart performance metrics (length characteristics).
• Application of proposed charts to a real-world dataset for implementation demonstration.

Main Results:

• The adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts significantly outperform the CCUSUM and EWMA charts in detecting covariance matrix shifts.
• The AEWMA chart exhibits superior performance compared to the ACCUSUM chart across various shift sizes.
• The study provides practical implementation guidance using a real dataset.

Conclusions:

• Adaptive control charts, particularly AEWMA, offer enhanced efficiency for monitoring multivariate process covariance matrices.
• The proposed AEWMA chart is recommended for its superior ability to detect shifts in process parameters without subgrouping.