Graphical Enhancements

Displaying Auxiliary Data with Stars

See SHWSTR1 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 47.16 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 47.14) and the LIMITS= data set PAINTLIM (listed in Figure 47.15). 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.

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 47.14: Listing of the HISTORY= Data Set PAINT

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

Figure 47.15: Listing of the LIMITS= Data Set PAINTLIM

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 apply only with control charts created with high-resolution graphics devices.

NOTE: A star chart is not the same as a multivariate control chart or a T² 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 T²) and control limits determined for a number of processes simultaneously. For an example of a multivariate control chart, see Figure 49.31. Figure 49.32 displays a multivariate control chart in which the principal components of the T² statistic are displayed with stars.

Displaying Auxiliary Data with Stars

Creating a Basic Star Chart

Adding Reference Circles to Stars

Specifying the Style of Stars

Specifying the Method of Standardization