Bivariate Dispersion Control Charts for Monitoring Non-Normal Processes

Multivariate control charts are well known to be more sensitive to the occurrence of variation in processes with two or more correlated quality variables than univariate charts. The use of separate univariate control charts to monitor multivariate process can be misleading as it ignores the correlation between the quality characteristics. The application of multivariate control charts allows for the simultaneous monitoring of the quality characteristics by forming a single chart. The charts operate on the assumption that process observations are normally distributed, but in practice this is not always the case. In this study, we examine and present multivariate dispersion control charts for detecting shifts in the covariance matrix of normal and non-normal bivariate processes. These control charts, referred to as SMAX, QMAX, MDMAX and MADMAX, rely on dispersion estimates, such as the sample standard deviation (S), interquartile range (Q), average absolute deviation from median (MD) and median absolute deviation (MAD), respectively. We compare the performances of these charts to the existing multivariate generalized variance |S| and RMAX charts for bivariate processes using normal and non-normal parent distributions. The average run length (ARL) measure is used for the evaluation and comparison of the charts. A real life and simulated datasets are used to demonstrate the application of the charts.