PROBPLOT Statement: CAPABILITY Procedure

Example 5.20 Displaying a Lognormal Reference Line

See CAPPROB3 in the SAS/QC Sample LibraryThis example is a continuation of Creating Lognormal Probability Plots. Figure 5.36 shows that a lognormal distribution with shape parameter $\sigma =0.5$ is a good fit for the distribution of Diameter in the data set Rods.

The lognormal distribution involves two other parameters: a threshold parameter $\theta$ and a scale parameter $\zeta$ . See Table 5.62 for the equation of the lognormal density function. The following statements illustrate how you can request a diagonal distribution reference line whose slope and intercept are determined by estimates of $\theta$ and $\zeta$ .

ods graphics off;
symbol v=plus height=3.5pct;
title 'Lognormal Probability Plot for Diameters';
proc capability data=Rods noprint;
   probplot Diameter / lognormal(sigma=0.5 theta=est zeta=est)
                       square
                       pctlminor
                       href      = 95
                       hreflabel = '95%'
                       vref      = 5.8 to 6.0 by 0.1
                       chref     = red
                       cvref     = blue;
run;

The plot is shown in Output 5.20.1.

Output 5.20.1: Lognormal Reference Line

The close agreement between the diagonal reference line and the point pattern indicates that the specific lognormal distribution with $\hat{\sigma }=0.5$ , $\hat{\theta }=5.004$ , and $\hat{\zeta }=-1.003$ is a good fit for the diameter measurements.

Specifying HREF=95 adds a reference line indicating the 95th percentile of the lognormal distribution. The HREFLABEL= option specifies a label for this line. The PCTLMINOR option displays minor tick marks on the percentile axis. The VREF= option adds reference lines indicating diameter values of 5.8, 5.9, and 6.0, and the CHREF= and CVREF= options specify colors for the horizontal and vertical reference lines.

Based on the intersection of the diagonal reference line with the HREF= line, the estimated 95th percentile of the diameter distribution is 5.85 mm.

Note that you could also construct a similar plot in which all three parameters are estimated by substituting SIGMA=EST for SIGMA=0.5 in the preceding statements.