The Phase I Dispersion Charts for Bivariate Process Monitoring

Multivariate control charts are usually implemented in statistical process control to monitor several correlated quality characteristics. Process dispersion charts are used to determine the stability of process variation (which is typically done before monitoring the process location/mean). A Phase‐I study is generally used when population parameters are unknown. This article develops Phase‐I |S| and |G| control charts, to monitor the dispersion of a bivariate normal process. The charting constants are determined to achieve the required nominal false alarm probability (FAP0). The performance of the proposed charts is evaluated in terms of (i) the attained false rate and (ii) the probability of signaling for out‐of‐control situations. The analysis shows that the proposed Phase‐I bivariate charts correctly control the FAP (the false alarm probability) and detect a shift occurring in the bivariate dispersion matrix with adequate probability. An example is given to explain the practical implementation of these charts.