PROC CAPABILITY and General Statements

Example 5.3 Displaying a Confidence Interval for Cpk

Note: See Displaying a Confidence Interval for Cpm in the SAS/QC Sample Library.

In this example, the capability index $C_{pk}$ is computed for the amplification data in Amps. To examine the accuracy of this estimate, the following statements calculate a 90% confidence interval for $C_{pk}$, then display the interval on a histogram (shown in Output 5.3.1) with the INSET statement:

title 'Boosting Power of Telephone Amplifiers';
proc capability data=Amps noprint alpha=0.10;
   var Decibels;
   spec  target = 5  lsl = 4  usl = 6
        ltarget = 2 llsl = 3 lusl = 4;
   histogram Decibels / odstitle = title;;
   inset cpklcl cpk cpkucl / header = '90% Confidence Interval'
                             format = 6.3;
run;

The ALPHA= option in the PROC CAPABILITY statement controls the level of the confidence interval. In this case, the 90% confidence interval on $C_{pk}$ is wide (from 0.328 to 0.496), indicating that the process may need adjustments in order to improve process variability. Confidence limits for capability indices can be displayed using the INSET statement (as shown in Output 5.3.1) or saved in an output data set by using the OUTPUT statement. For formulas and details about capability indices, see the section Specialized Capability Indices. For more information about the INSET statement, see INSET Statement: CAPABILITY Procedure.

Output 5.3.1: Confidence Interval on $C_{pk}$

Confidence Interval on Cpk


The following statements can be used to produce a table of process capability indices including the index $C_{pk}$:

ods select indices;
proc capability data=Amps alpha=0.10;
   spec  target = 5  lsl = 4  usl = 6
        ltarget = 2 llsl = 3 lusl = 4;
   var Decibels;
run;

Output 5.3.2: Process Capability Indices

Boosting Power of Telephone Amplifiers

The CAPABILITY Procedure
Variable: Decibels (Amplification in Decibels (dB))

Process Capability Indices
Index Value 90% Confidence Limits
Cp 0.508962 0.439538 0.576922
CPL 0.411920 0.326620 0.495136
CPU 0.606004 0.501261 0.708127
Cpk 0.411920 0.327599 0.496241
Cpm 0.488674 0.425292 0.556732