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 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 scores, and the 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 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 chart.

Figure 13.1: Multivariate Control Chart for Statistics

The 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 chart represents a departure from the variation described by the principal component model that lies within the model hyperplane.