Multivariate control charts: Control charts for calibration curves

Abstract

The proposed multivariate control charts for p-dimensional vectors are an extension of the conventional control charts for one variable. The controlling quantity is the Mahalanobis distance of vector x from the central value vector x..: D=(x-x..)^TĈ^-1.(x-x..), where Ĉ is the covariance matrix estimate. The quantity D has Hotelling's T² distribution. A PC program was set up for the automatic graphical construction of such charts. The program draws the sequential chart of the quantity D as well as the position of the vectors x in the p dimensional control ellipsoid in the axes of the principal components. In this way a control chart was developed for the calibration curve in the photometric determination of Fe³⁺ with sulfosalicylic acid. Vector x was formed by absorbance values for the calibration curve points (p=5). The chart can assist in detection of even small disturbances of the calibration curve.