Multivariate Six Sigma is an extension of the traditional Six Sigma methodologies to deal with processes in which multiple response variables are measured and in which the quality of a product depends on the joint values of those variables or attributes. Rather than concentrating on each response variable separately using univariate methods, multivariate statistical methods are employed to explain the multiple responses as an integrated whole. In complex processes in which the variables exhibit strong correlations, misleading results can be obtained if the multiple responses are not considered together.

STATGRAPHICS Centurion contains a powerful set of procedures for implementing Multivariate Six Sigma. Among the tools provided are:

Multivariate Graphical Displays - includes tools such as radar plots, glyphs, matrix plots, draftsman and casement plots.

Multivariate Capability Analysis - estimates the joint probability that a set of variables will be within established specifications based on a multivariate normal distribution.

Sample Sample       Variable Mean Std. Dev. LSL Nominal USL Small 6.09821 2.51154   5.0 10.0 Large 5.68214 1.94171   5.0 10.0   Observed Estimated Estimated Variable Beyond Spec. Beyond Spec. DPM Small 5.35714% 6.01462% 60146.2 Large 1.78571% 1.30827% 13082.7 Joint 7.14286% 7.18235% 71823.5 The StatAdvisor This procedure determines the percentage of items beyond a set of multivariate specification limits.  In this case, the estimated frequency of non-conformities with respect to at least one of the 2 variables equals 71823.5 per million.

Multivariate Control Charts - plots a T-squared chart, control ellipse, or Multivariate EWMA control chart to detect variation attributable to special causes.

Neural Network Classifier - classifies observations into groups based upon the values of multiple response variables.

Multivariate Calibration - uses Partial Least Squares to analyze data in which there are more variables than observations.

Principal Components Analysis - derives linear combinations of multiple responses that describe the principal variation amongst multiple response variables.

Multiple Response Optimization - provides a procedure for maximizing the desirability of multiple responses after a designed experiment has been performed.