Creating a Multivariate Control Chart in a Phase I Situation

In a Phase I analysis you first perform a principal component analysis (PCA) of the data. Then you can use control charts to determine whether the data that you use to build the principal component model indicate a stable multivariate process. The MVPMONITOR procedure creates multivariate control charts from $T^2$ and SPE statistics computed from a principal component model that the MVPMODEL procedure produced. This example uses the model built in the section Building a Principal Component Model in Chapter 12: The MVPMODEL Procedure.

The following statements fit the model:

proc mvpmodel data=MWflightDelays ncomp=3 noprint
              out=mvpair outloadings=mvpairloadings;
   var AA CO DL F9 FL NW UA US WN;
run;

The NCOMP= option requests a principal component model that contains three principal components. The OUT= option creates a data set that contains the original data, the principal component scores, and the $T^2$ and SPE statistics. The OUTLOADINGS= data set contains the variances and loadings for the principal components.

The following statements produce the multivariate control charts:

ods graphics on;
proc mvpmonitor history=mvpair loadings=mvpairloadings;
   time flightDate;
   tsquarechart / contributions;
   spechart / contributions;
run;

The HISTORY= option specifies the input data set. The LOADINGS= option specifies the data set that contains the principal component model information. The TSQUARECHART statement requests a $T^2$ chart, and the SPECHART statement requests an SPE chart. The CONTRIBUTIONS options that are specified in the TSQUARECHART and SPECHART statements request contribution plots for all out-of-control points in the charts. The TIME statement specifies that the variable flightDate provide the chronological ordering of the observations.

Figure 13.1 shows the $T^2$ chart.

Figure 13.1: Multivariate Control Chart for $T^2$ Statistics

The $T^2$ chart shows an out-of-control point on February 13, 2007. On this day, a strong winter storm battered the midwestern United States. To see which variables contributed to this statistic, you can use the contribution plot shown in Figure 13.2.

Figure 13.2: Contribution Plot

The contribution plot shows that the variables WN, AA, NW, and DL are the major contributors to the out-of-control point.

Figure 13.3 shows the SPE chart.

Figure 13.3: Multivariate Control Chart for SPE Statistics

There are no out-of-control points in the SPE chart. This indicates that the unusual point displayed in the $T^2$ chart represents a departure from the variation described by the principal component model that lies within the model hyperplane.

The MVPMONITOR Procedure

Creating a Multivariate Control Chart in a Phase I Situation