Note: See Displaying Auxiliary Data with Stars in the SAS/QC Sample Library.
In many control chart applications, it is useful to relate the variation of the process to other variables that are being observed simultaneously with the variable that is charted. You can use the features described here to represent auxiliary multivariate data with stars (polygons) that are superimposed on the control chart. See Figure 17.157 for an illustration.
This display, referred to here as a star chart, enables you to analyze a process with a control chart while visualizing other quantities such as environmental variables, experimental control variables, or other process variables. The control chart itself can be a standard Shewhart chart, a moving average chart (such as an EWMA chart), or a cumulative sum control chart.
The examples in this section use the HISTORY= input data set paint (listed in Figure 17.155) and the LIMITS= data set paintlim (listed in Figure 17.156). The data in paint consist of the subgroup means, ranges, and sample size (pindexx, pindexr, and pindexn) for an index of paint quality that was monitored on an hourly basis, with six auxiliary variables that were measured simultaneously:
thickness, gloss, defects, dust, humidity, and temperature.
Figure 17.155: Listing of the HISTORY= Data Set PAINT
| Control Chart for Diameter Stratified by Machine |
| hour | pindexx | pindexr | pindexn | thick | gloss | defects | dust | humid | temp |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 5.8 | 3.0 | 5 | 0.2550 | 0.6800 | 0.2550 | 0.2125 | 0.1700 | 0.5950 |
| 2 | 6.2 | 2.0 | 5 | 0.2975 | 0.5950 | 0.0850 | 0.1700 | 0.2125 | 0.5525 |
| 3 | 3.7 | 2.5 | 5 | 0.3400 | 0.3400 | 0.4250 | 0.2975 | 0.2550 | 0.2125 |
| 4 | 3.2 | 6.5 | 5 | 0.3400 | 0.4675 | 0.3825 | 0.3485 | 0.2125 | 0.2125 |
| 5 | 4.7 | 0.5 | 5 | 0.5100 | 0.4250 | 0.5950 | 0.4080 | 0.5100 | 0.4675 |
| 6 | 5.2 | 3.0 | 5 | 0.5100 | 0.3400 | 0.6800 | 0.5525 | 0.5525 | 0.5525 |
| 7 | 2.6 | 2.0 | 5 | 0.4250 | 0.0425 | 0.8500 | 0.5355 | 0.5525 | 0.2550 |
| 8 | 2.1 | 1.0 | 5 | 0.3400 | 0.0170 | 0.8075 | 0.5950 | 0.5950 | 0.1700 |
Figure 17.156: Listing of the LIMITS= Data Set PAINTLIM
| Control Chart for Diameter Stratified by Machine |
| Obs | _var_ | _subgrp_ | _type_ | _limitn_ | _sigmas_ | _lclx_ | _mean_ | _uclx_ | _lclr_ | _r_ | _uclr_ | _stddev_ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | pindex | hour | estimate | 5 | 3 | 2.395 | 3.875 | 5.355 | 0 | 2.5625 | 5.4184 | 1.10171 |
The basic variable analyzed with the control chart (in this case, paint index) is referred to as the process. The auxiliary variables (in this case, thickness, gloss, defects, dust, humidity, and temperature) are referred to as vertex variables, because their values are represented by the vertices of the stars. A star chart can reveal relationships between the process and the vertex variables, and it can reveal relationships among the vertex variables.
You can create star charts for any number of vertex variables. However, the resolution of your graphics device and the number of subgroups per page will limit your ability to distinguish the vertices of the stars. A practical upper limit is twelve vertex variables.
You can specify star options in all chart statements of the SHEWHART procedure except the BOXCHART statement. You can use these options to
-
specify the style of the star
-
add reference circles to indicate limits of variation for the stars
-
add a legend identifying the relationship between vertices and vertex variables
-
label the vertices
-
specify colors and line types for individual stars
-
specify the size of the stars
-
specify different methods of standardization for the vertex variables
The star options do not apply if the LINEPRINTER option is specified.
NOTE: A star chart is not the same as a multivariate control chart or a 
chart. A star chart is simply a univariate control chart enhanced with stars that represent auxiliary multivariate data.
A multivariate control chart displays summary statistics (such as ) and control limits determined for a number of processes simultaneously. For an example of a multivariate control chart,
see Figure 17.221. Figure 17.222 displays a multivariate control chart in which the principal components of the 
statistic are displayed with stars.