Composite multivariate quality control using a system of univariate, bivariate, and multivariate quality control rules.

We propose a composite multivariate quality control (CMQC) system to control simultaneously measured variables. This system is designed to detect unacceptable trends and systematic error in one or more variables, unacceptable random error in one or more variables, and unacceptable changes in the correlation structure in any pair of variables. It is also designed to be tolerant of missing data, to be capable of rejecting as few as one or as many as all variables in a run, and to provide the analyst with control statistics and graphics that logically relate to sources of analytical error. Quality control rules for univariate, multivariate, and correlation conditions are incorporated in the system, as are plots displaying CMQC statistic values and control limits for univariate, multivariate, and correlation parameters. We also discuss advantages of the CMQC over the T2 and principal component multivariate quality control methods. We demonstrate the CMQC procedure using data from a laboratory process in which 40 variables were measured during 40 characterization runs and 23 runs analyzing unknowns.