Statistical Methods for Quality Improvement, Third Edition

CHAPTER 9

Multivariate Control Charts for Measurement and Attribute Data

We will assume that p variables X₁, X₂,…, X_p are to be simultaneously monitored, and we will further assume (initially) X ∼ N_p(μ, Σ), with X = (X₁, X₂,…, X_p)′. That is, X is assumed to have a multivariate normal distribution. The general idea is to monitor μ, the correlations between the X_i, and the Var(X_i). A change in at least one mean, correlation (or covariance), or variance constitutes an out-of-control process.

The expressions “when the quality of a product is defined by more than one property, all the properties should be studied collectively” (Kourti and MacGregor, 1996) and “the world is multivariate” suggest that multivariate procedures should routinely be used. Although not used as often as univariate control chart procedures, multivariate procedures have nevertheless been used in many different types of applications, and there have been many research papers on multivariate process control methods published since the second edition of this book.

For example, Nijhius, deJong, and Vandeginste (1997) discussed the use of multivariate control charts in chromatography, Colon and GonzalezBarreto (1997) discussed an application to printed circuit (PC) boards that has 128 variables, de Oliveria, Rocha, and Poppi (2009) illustrated the use of multivariate charts for monitoring biodiesel blends, and Waterhouse, Smith, Assareh, and Mengersen (2010) discussed the use of multivariate charts in a clinical setting. ...