Example 13.1 Combining Data from Peer Processes

In some situations you might want to build a common principal component model by combining data from multiple peer processes that have similar patterns of stable variation. This enables you to borrow strength from the data. A common set of control limits is then computed for each peer process.

This example uses observations from all regions in the continental United States at each time value to construct a common principal component model. It then applies the model to flight data for one region.

The following statements create a principal component model that contains three principal components from the flightDelays data set and apply the model to data for the Midwest region:

proc mvpmodel data=flightDelays ncomp=3 noprint
              out=mvpair outloadings=mvpairloadings;
   var AA CO DL F9 FL NW UA US WN;
run;
proc mvpmonitor history=mvpair loadings=mvpairloadings;
   time flightDate;
   series region;
   spechart / seriesvalue='MW';
   tsquarechart / seriesvalue='MW';
run;

The flightDelays data set contains observations from all continental United States regions, with multiple observations (one for each region) at each time point as defined by the flightDate variable. The OUTLOADINGS= data set that is produced by PROC MVPMODEL contains the model information. The SERIES statement specifies region as the variable that identifies sequences of related observations. The SERIESVALUE= option selects the Midwest region statistics to be plotted.

The resulting SPE chart is shown in Output 13.1.1.

Output 13.1.1: Multivariate Control Chart for SPE Statistics

The control limits for the SPE chart are computed differently from a case with a single observation per time value, such as the chart shown in Figure 13.3. The control limits are based on different reference distributions for the SPE statistics in addition to different approximations to the reference distribution. See the section Computing SPE Control Limits for more information.

The $T^2$ chart is shown in Output 13.1.2.

Output 13.1.2: Multivariate Control Chart for $T^2$ Statistics

Compare the $T^2$ chart in Output 13.1.2 to the one in Figure 13.1. Both charts display $T^2$ statistics for the same flight delays from the Midwest region, but the charts are different because in this example the principal component model was constructed with data from all regions of the continental United States.

You can produce control charts for all the peer processes (regions in this example) by omitting the SERIESVALUE= option. The following statements illustrate this approach:

proc mvpmonitor history=mvpair;
   time flightDate;
   series region;
   spechart;
   tsquarechart / overlay;
run;

By default, a separate control chart is created for each distinct value of the SERIES variable. The separate SPE charts for each region are not shown. The OVERLAY option in the TSQUARECHART statement specifies that the sequences for each region be plotted on a single $T^2$ chart, which is shown in Output 13.1.3.

Output 13.1.3: Overlaid $T^2$ Charts by Region

You can produce univariate control charts of standardized principal component scores by using the SCORECHART statement. The following statements produce control charts for the three principal components in the model and for each region:

proc mvpmonitor history=mvpair loadings=mvpairloadings;
   time flightDate;
   series region;
   scorechart / comp=all overlay=comp;
run;

The COMP=ALL option requests score charts for all the principal components in the model. The OVERLAY=COMP option overlays the scores for each component in a single control chart. A separate chart is produced for each region. Output 13.1.4 and Output 13.1.5 show the score charts for the Midwest and Northeast regions, respectively.

Output 13.1.4: Score Charts for the Midwest Region

Output 13.1.5: Score Charts for the Northeast Region

You can also overlay scores for different SERIES values in a single chart. The following statements produce a score chart for principal component 1 for each region:

proc mvpmonitor history=mvpair loadings=mvpairloadings;
   time flightDate;
   series region;
   scorechart / overlay=series;
run;

The resulting chart is shown in Output 13.1.6.

Output 13.1.6: Score Charts for Principal Component 1 and All Regions

The MVPMONITOR Procedure

Example 13.1 Combining Data from Peer Processes