5.1 Introduction

Many data from industrial applications are multivariate data. For example, in automobile assembly operation, the dimensional accuracies of body panels are very important in "fit and finish" for automobiles. Many sensors, such as optical coordinate measurement machines (OCMM), are used to measure dozens of actual dimensional locations, for every automobile, at selected key points (see Fig. 5.1). These measurements are definitely multivariate data and they are correlated with each other. Because the body structure is physically connected, the dimensional variation of one location often affects the dimensional variation of other locations. In many industries, such as chemical industries (Mason and Young, 2002), there are plenty of cases where data are multivariate in nature and are correlated. With the rapid development of computer information technology and sensor technology, we are swamped with this kind of multivariate data.

Figure 5.1: Automobile body panel dimensional measurement process.

However, most of the analysis for this kind of data is still performed by univariate statistical methods which deal with these multivariate variables on a one-variable-at-a-time basis (see Fig. 5.2). In the above automobile assembly example, the common practice is that if there are 50 measurement points, then 50 statistical process control charts will be maintained. These 50 control charts could easily overwhelm process operators.

Figure 5.2: SPC chart for individual point.

Also, each control chart can only tell you how large the variation is at each individual point, and, if the variation is out of control, this kind of information provides...