Multivariate control charts: Control charts for calibration curves |
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Authors: | Oto Mestek Ji?í Pavlík Miloslav Suchánek |
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Affiliation: | (1) Department of Analytical Chemistry, Institute of Chemical Technology, Technická 5, 16628 Prague 6, Czech Republic;(2) Department of Mathematics, Institute of Chemical Technology, Technická 5, 16628 Prague 6, Czech Republic |
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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..)T-1.(x-x..), where 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. |
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