Creating a Normal Probability Plot

PROBPLOT Statement

Creating a Normal Probability Plot

See CAPPROB1 in the SAS/QC Sample Library

The diameters of 50 steel rods are measured and saved as values of the variable DISTANCE in the following data set:^*

   data measures;
      input diameter @@;
      label diameter='Diameter in mm';
      datalines;
   5.501  5.251  5.404  5.366  5.445
   5.576  5.607  5.200  5.977  5.177
   5.332  5.399  5.661  5.512  5.252
   5.404  5.739  5.525  5.160  5.410
   5.823  5.376  5.202  5.470  5.410
   5.394  5.146  5.244  5.309  5.480
   5.388  5.399  5.360  5.368  5.394
   5.248  5.409  5.304  6.239  5.781
   5.247  5.907  5.208  5.143  5.304
   5.603  5.164  5.209  5.475  5.223
   ;

The process producing the rods is in statistical control, and as a preliminary step in a capability analysis of the process, you decide to check whether the diameters are normally distributed. The following statements create the normal probability plot shown in Figure 9.1:

   title 'Normal Probability Plot for Diameters';
   proc capability data=measures noprint;
      probplot diameter / cframe = ligr;
   run;

If you specify the LINEPRINTER option in the PROC CAPABILITY statement, the plot is created using a line printer, as shown in Figure 9.2. Note that the PROBPLOT statement creates a normal probability plot for DIAMETER by default.

The nonlinearity of the point pattern indicates a departure from normality. Since the point pattern is curved with slope increasing from left to right, a theoretical distribution that is skewed to the right, such as a lognormal distribution, should provide a better fit than the normal distribution. This possibility is explored in the next example.

Figure 9.1: Normal Probability Plot Created with Graphics Device

Normal Probability Plot for Diameters

       --------------------------------------------------------------------     
  6.4 +                                                                    |    
      |                                                                    |    
      |                                                                  + |    
  6.2 +                                                                    |    
D     |                                                                    |    
i     |                                                                    |    
a 6.0 +                                                            +       |    
m     |                                                         +          |    
e     |                                                                    |    
t 5.8 +                                                     + +            |    
e     |                                                   +                |    
r     |                                                  +                 |    
  5.6 +                                              +++                   |    
i     |                                           +++                      |    
n     |                                        +++                         |    
  5.4 +                               +++++++++                            |    
m     |                          +++++                                     |    
m     |                      +++++                                         |    
  5.2 +              + ++ +++                                              |    
      | +     +  + +                                                       |    
      |                                                                    |    
  5.0 +                                                                    |    
       +---------+----+--------+---------+--------+--------+----+---------+     
       1         5   10       25        50       75       90   95        99     
                                                                                
                               Normal Percentiles                               
                                                                                
Observations:    +   (5 Hidden)

Figure 9.2: Normal Probability Plot Created with Line Printer

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