The SHEWHART Procedure

Displaying Auxiliary Data with Stars

Subsections:

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 18.158 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 18.156) and the LIMITS= data set Paintlim (listed in Figure 18.157). 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 18.156: Listing of the HISTORY= Data Set Paint

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 18.157: Listing of the LIMITS= Data Set Paintlim

               

                  

                     
                     

                        
                        
                        

                           
                           

                              
                              


















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 $T^{2}$ 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 $T^{2}$) and control limits determined for a number of processes simultaneously. For an example of a multivariate control chart,
               see Figure 18.223. Figure 18.224 displays a multivariate control chart in which the principal components of the $T^2$ statistic are displayed with stars.