PROBPLOT Statement: CAPABILITY Procedure

Creating Lognormal Probability Plots

See CAPPROB3 in the SAS/QC Sample LibraryWhen you request a lognormal probability plot, you must specify the shape parameter $\sigma$ for the lognormal distribution (see Table 5.62 for the equation). The value of $\sigma$ must be positive, and typical values of $\sigma$ range from 0.1 to 1.0. Alternatively, you can specify that $\sigma$ is to be estimated from the data.

The following statements illustrate the first approach by creating a series of three lognormal probability plots for the variable Diameter introduced in the preceding example:

ods graphics on;
proc capability data=Rods noprint;
   probplot Diameter / lognormal(sigma=0.2 0.5 0.8)
                       href = 95
                       square;
run;

The ODS GRAPHICS ON statement specifies that the probability plot be produced by using ODS Graphics. The LOGNORMAL option requests plots based on the lognormal family of distributions, and the SIGMA= option requests plots for $\sigma$ equal to 0.2, 0.5, and 0.8. The SQUARE option displays the probability plot in a square format and the HREF= option requests a reference line at the 95th percentile.

The resulting plots are displayed in Figure 5.35, Figure 5.36, and Figure 5.37, respectively. The value $\sigma =0.5$ in Figure 5.36 produces the most linear pattern.

Figure 5.35: Probability Plot Based on Lognormal Distribution with $\sigma =0.2$

Probability Plot Based on Lognormal Distribution with σ=0.2

Figure 5.36: Probability Plot Based on Lognormal Distribution with $\sigma =0.5$

Probability Plot Based on Lognormal Distribution with σ=0.5

Figure 5.37: Probability Plot Based on Lognormal Distribution with $\sigma =0.8$

Probability Plot Based on Lognormal Distribution with σ=0.8

Based on Figure 5.36, the 95th percentile of the diameter distribution is approximately 5.9 mm, since this is the value corresponding to the intersection of the point pattern with the reference line.

The following statements illustrate how you can create a lognormal probability plot for Diameter using a local maximum likelihood estimate for $\sigma$ .

ods graphics off;
symbol v=plus height=3.5pct;
title 'Lognormal Probability Plot for Diameters';
proc capability data=Rods noprint;
   probplot Diameter / lognormal(sigma=est)
                       href = 95
                       square;
run;

The plot is displayed in Figure 5.38. Note that the maximum likelihood estimate of $\sigma$ (in this case 0.041) does not necessarily produce the most linear point pattern. This example is continued in Example 5.20.

Figure 5.38: Probability Plot Based on Lognormal Distribution with Estimated $\sigma$

Probability Plot Based on Lognormal Distribution with Estimated σ