An Introduction to Multivariate Control Charts


Alloway, James A., Jr.; Raghavachari, M.   (1991, ASQC)   Syracuse University, Syracuse, NY

Annual Quality Congress, Milwaukee WI    Vol. 45    No. 0
QICID: 9740    May 1991    pp. 773-783
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Article Abstract

Using multivariate control charts is more appropriate than using multiple Shewhart charts when the overall quality of a product depends on several interdependent correlated characteristics that must be considered simultaneously. They are based on Hotelling's T2 statistic, and charts are available for both location and spread. This paper considers charts for location only.

Like univariate control charts, multivariate control charts uses the Standard Given and the No Standard given categories. The authors use bivariate control charts to illustrate two equivalent methods of displaying the control charts, using Shewhart control charts for the X and Y components. Control charts for the case of standard given and no standard given are included, using an ellipse display format. Also, analysis based on the Bonferroni inequality is used to identify out of control characteristics. Matrix notation is needed when handling more than two characteristics simultaneously; electronic spreadsheets and some hand-held calculators can perform the complex calculations for matrix notation.

Calculating control limits for multivariate control charts based on Hotelling's T2 statistic assumes that the joint distribution of the characteristics follows a multinormal distribution. The assumption of normality is more difficult to satisfy than in the univariate case; however, studies show that control charts based on Hotelling's T2 statistic are quite robust to departures from normality and errors that occur due to round-off fatigue or poorly calibrated equipment.


Bonferroni method,Hotelling's T2 statistic,Multivariate control charts,Shewhart control chart,Statistics

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