Example 32.7: Constructing Multi-Vari Charts

BOXCHART Statement

Example 32.7: Constructing Multi-Vari Charts

"Multi-vari" charts^* are used in a variety of industries to analyze process data with nested (hierarchical) patterns of variation

within-sample variation (for example, position within wafer)
sample-to-sample variation within batches of samples (for example, wafer within lot)
batch-to-batch variation (for example, across lots)

This example illustrates the construction of a "multi-vari" display. The following statements create a SAS data set named PARM that contains the value of a measured parameter (MEASURE) recorded at each of five positions on wafers produced in lots.

   data parm;   
      length _phase_ $ 5 wafer $ 2 position $ 1;
      input  _phase_ $  &  wafer $ &  position $  measure ;
   datalines;  
      Lot A    01    L    2.424 
      Lot A    01    B    2.441 
      Lot A    01    C    2.421 
      Lot A    01    T    2.449 
      Lot A    01    R    2.500 
      Lot A    02    L    2.681 
      Lot A    02    B    2.571 
      Lot A    02    C    2.546 
      Lot A    02    T    2.659 
      Lot A    02    R    2.692 
      Lot A    03    L    2.180 
      Lot A    03    B    2.135 
      Lot A    03    C    2.443 
      Lot A    03    T    2.290 
      Lot A    03    R    2.259 
      Lot B    01    L    2.465 
      Lot B    01    B    2.448 
      Lot B    01    C    2.523 
      Lot B    01    T    2.744 
      Lot B    01    R    2.883 
      Lot B    02    L    2.372 
      Lot B    02    B    2.145 
      Lot B    02    C    2.531 
      Lot B    02    T    2.474 
      Lot B    02    R    2.562 
        .       .    .     .
        .       .    .     .
        .       .    .     .
      Lot G    03    R    2.843 
   run;

The following statements create an ordinary side-by-side box-and-whisker display for the measurements.

   title 'Box-and-Whisker Display for Measured Parameter';
   proc shewhart data=parm;
      boxchart parm*wafer / 
         stddevs
         nolimits
         cboxfill  = ywh
         cboxes    = dagr
         cframe    = vligb
         cinfill   = ligr
         boxstyle  = schematic
         idsymbol  = square 
         readphase = all
         phaselegend
         nolegend;
   label measure = 'Measurement'
         wafer   = 'Wafer Within Lot';
   run;

The display is shown in Output 32.7.1. Here, the subgroup-variable is WAFER, and the option BOXSTYLE=SCHEMATIC is specified to request schematic box-and-whisker plots for the measurements in each subgroup (wafer) sample. The lot values are provided as the values of the special variable _PHASE_, which is read when the option READPHASE=ALL is specified. The option PHASELEGEND requests the legend for phase (lot) values at the top of the chart, and the NOLEGEND option suppresses the default legend for sample sizes. The NOLIMITS option suppresses the display of control limits, and the STDDEVS option is used to base the estimate of the process standard deviation on subgroup standard deviations rather than subgroup ranges. These two options are recommended whenever you are using the BOXCHART statement to create side-by-side box-and-whisker plots.

Output 32.7.1: Box-and-Whisker Plot Using BOXSTYLE=SCHEMATIC

The box-and-whisker display in Output 32.7.1 is not particularly appropriate for these data since there are only five measurements in each wafer and since the variation within each wafer may depend on the position, which is not indicated. The next statements use the BOXCHART statement to produce a multi-vari chart for the same data.

   symbol v=none;
   title 'Multi-Vari Display for Measured Parameter';
  
   proc shewhart data=parm;
      boxchart measure*wafer / 
         stddevs
         nolimits
         boxstyle          = pointsjoin
         cboxes            = dagr
         cframe            = vligb
         cinfill           = ligr
         idsymbol          = square
         cphaseboxfill     = ywh
         cphasebox         = black
         cphasemeanconnect = bib
         phasemeansymbol   = dot
         readphase         = all
         phaselegend
         nolegend;
   label measure = 'Measurement'
         wafer   = 'Wafer Within Lot';
   run;

The display is shown in Output 32.7.2.

Output 32.7.2: Multi-Vari Chart Using BOXSTYLE=POINTSJOIN

The option BOXSTYLE=POINTSJOIN specifies that the values for each wafer are to be displayed as points joined by a vertical line. The IDSYMBOL= option specifies the symbol marker for the points. The option V=NONE in the SYMBOL statement is specified to suppress the symbol for the wafer averages shown in Output 32.7.1. The option CPHASEBOX=BLACK specifies that the points for each lot are to be enclosed in a black box, and the CPHASEBOXFILL= option specifies the fill color for the box. The option CPHASEMEANCONNECT=BLACK specifies that the means of the lots are to be connected with black lines, and the PHASEMEANSYMBOL= option specifies the symbol marker for the lot means.

The following statements create a slightly different multi-vari chart using the values of the variable POSITION to identify the measurements for each wafer. Note that the option BOXSTYLE=POINTSID is specified and that POSITION is specified as the ID variable. The display is shown in Output 32.7.3.

   proc shewhart data=parm;
      boxchart measure*wafer / 
         nolimits
         stddevs
         cboxes            = dagr
         cframe            = vligb
         cinfill           = ligr         
         cphaseboxfill     = ywh
         cphasemeanconnect = black
         boxstyle          = pointsid
         phasemeansymbol   = dot
         readphase         = all
         phaselegend
         nolegend;
   label measure = 'Measurement'
         wafer   = 'Wafer Within Lot';
   id position;
   run;

Output 32.7.3: Multi-Vari Chart Using BOXSTYLE=POINTSID

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