On the Performance of Phase-I Bivariate Dispersion Charts to Non-Normality

A phase‐I study is generally used when population parameters are unknown. The performance of any phase‐II chart depends on the preciseness of the control limits obtained from the phase‐I analysis. The performance of phase‐I bivariate dispersion charts has mainly been investigated for bivariate normal distribution. However, this assumption is seldom fulfilled in reality. The current work develops and studies the performance of phase‐I |S| and |G| charts for monitoring the process dispersion of bivariate non‐normal distributions. The necessary control charting constants are determined for the bivariate non‐normal distributions at nominal false alarm probability (FAP0). The performance of these charts is evaluated and compared in a situation when samples are generated by bivariate logistic, bivariate Laplace, bivariate exponential, or bivariate t5 distribution. The analysis shows that the proper consideration to underlying bivariate distribution in the construction of phase‐I bivariate dispersion charts is very important to give a real picture of in or out of control process status.