Example 4.4: Computing Capability Indices for Nonnormal Distributions

HISTOGRAM Statement

Example 4.4: Computing Capability Indices for Nonnormal Distributions

See CAPIND in the SAS/QC Sample Library

Standard capability indices such as C_pk are generally considered meaningful only if the process output has a normal (or reasonably normal) distribution. In practice, however, many processes have nonnormal distributions. This example, which is a continuation of Example 4.2 and Example 4.3, shows how you can use the HISTOGRAM statement to compute generalized capability indices based on fitted nonnormal distributions.

The following statements produce printed output that is listed in Output 4.4.1 and Output 4.4.2:

   proc capability data=plates;
      specs lsl=0.3 usl=0.8 alpha=0.05;
      histogram gap / lognormal(indices) noplot;
   run;

The PROC CAPABILITY statement computes the standard capability indices that are shown in Output 4.4.1.

Output 4.4.1: Standard Capability Indices for Variable GAP

The CAPABILITY Procedure

Variable: gap (Plate Gap in cm)

Process Capability Indices
Index	Value	95% Confidence Limits
Cp	0.237112	0.190279	0.283853
CPL	0.316422	0.203760	0.426833
CPU	0.157803	0.059572	0.254586
Cpk	0.157803	0.060270	0.255336

Warning: Normality is rejected for alpha = 0.05 using the Shapiro-Wilk test

The ALPHA= option in the SPECS statement requests a Kolmogorov-Smirnov goodness-of-fit test for normality in conjunction with the indices and displays the warning that normality is rejected at the significance level $\alpha=0.05$ .

Example 4.2 concluded that the fitted lognormal distribution summarized in Output 4.2.2 is a good model, so one might consider computing generalized capability indices based on this distribution. These indices are requested with the INDICES option and are shown in Output 4.4.2. Formulas and recommendations for these indices are given in "Indices Using Fitted Curves".

Output 4.4.2: Fitted Lognormal Distribution Information

The CAPABILITY Procedure

Fitted Lognormal Distribution for gap

Capability Indices Based on Lognormal Distribution
Cp	0.210804
CPL	0.595156
CPU	0.124927
Cpk	0.124927

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