Regression Adjustment for Variables in Multivariate Quality Control

TLDR

Multivariate process control is more challenging than univariate control, with powerful statistics lacking interpretability and separate variable controls being less powerful amid correlation, yet prior work shows that exploiting the likely nature of departures can improve detection. Regression adjustment of each variable against all others yields highly effective charts when only one variable is expected to shift in mean or variance.

Abstract

Multivariate process control problems are inherently more difficult than univariate problems. It is not always clear what type of multivariate statistic should be used, and the most statistically powerful techniques do not indicate the cause(s) of a signal. On the other hand, separate controls on the individual variables are more easily interpretable but may be substantially less powerful, particularly in the face of appreciable correlation between the measures. Previous research has demonstrated the effectiveness of methods that capitalize on the likely nature of a departure from control. If only one variable is likely to undergo a shift in mean or variance then charting of each variable adjusted by regression for all others is particularly effective.