EWMA Robust Max-M Control Chart for Synthetic and Real Data

Abstract

Quality monitoring in multivariate industrial processes requires a control chart capable of detecting changes in the process mean and variability simultaneously. This study implements the Exponentially Weighted Moving Average Robust Max-M Control Chart (ERMM-Chart) for individual multivariate observations using synthetic data and real cement clinker quality data. Robust Phase I parameter estimation is performed using the Fast Minimum Covariance Determinant method to obtain resistant estimates of the process center and covariance matrix. The synthetic data consist of four scenarios: no shift, mean shift, variability shift, and simultaneous mean-variability shift. The real data include two clinker quality characteristics, namely free lime (FCaO) and tetracalcium aluminoferrite (C₄AF). Results show that the ERMM-Chart produces no out-of-control signals under the no-shift scenario and detects process changes under shifted conditions. In the clinker data, the chart indicates a difference in joint process behavior between the Phase I and Phase II. Therefore, the ERMM-Chart can serve as a robust simultaneous multivariate monitoring tool for individual observations.