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The CAPABILITY Procedure

Computing Statistical Intervals

[See CAPINT1 in the SAS/QC Sample Library]The following statements create the data set Cans, which contains measurements (in ounces) of the fluid weights of 100 drink cans. The filling process is assumed to be in statistical control.

data Cans;
   label Weight = "Fluid Weight (ounces)";
   input Weight @@;
datalines;
12.07  12.02  12.00  12.01  11.98  11.96  12.04  12.05  12.01  11.97
12.03  12.03  12.00  12.04  11.96  12.02  12.06  12.00  12.02  11.91
12.05  11.98  11.91  12.01  12.06  12.02  12.05  11.90  12.07  11.98
12.02  12.11  12.00  11.99  11.95  11.98  12.05  12.00  12.10  12.04
12.06  12.04  11.99  12.06  11.99  12.07  11.96  11.97  12.00  11.97
12.09  11.99  11.95  11.99  11.99  11.96  11.94  12.03  12.09  12.03
11.99  12.00  12.05  12.04  12.05  12.01  11.97  11.93  12.00  11.97
12.13  12.07  12.00  11.96  11.99  11.97  12.05  11.94  11.99  12.02
11.95  11.99  11.91  12.06  12.03  12.06  12.05  12.04  12.03  11.98
12.05  12.05  12.11  11.96  12.00  11.96  11.96  12.00  12.01  11.98
;
run;

Note that this data set is introduced in Computing Descriptive Statistics of PROC CAPABILITY and General Statements. The analysis in that section provides evidence that the weight measurements are normally distributed.

By default, the INTERVALS statement computes and prints the six intervals described in the entry for the METHODS= option. The following statements tabulate these intervals for the variable Weight:

title 'Statistical Intervals for Fluid Weight';
proc capability data=Cans noprint;
   intervals Weight;
run;

The intervals are displayed in Figure 5.16.4.

Output 5.16.2 Statistical Intervals for Weight
Statistical Intervals for Fluid Weight

The CAPABILITY Procedure
Two-Sided Statistical Intervals for Weight Assuming Normality

Approximate Prediction Interval
Containing All of k Future Observations
Confidence k Prediction Limits
99.00% 1 11.89 12.13
99.00% 2 11.87 12.14
99.00% 3 11.87 12.15
95.00% 1 11.92 12.10
95.00% 2 11.90 12.12
95.00% 3 11.89 12.12
90.00% 1 11.93 12.09
90.00% 2 11.92 12.10
90.00% 3 11.91 12.11

Prediction Interval Containing
the Mean of k Future Observations
Confidence k Prediction Limits
99.00% 1 11.89 12.13
99.00% 2 11.92 12.10
99.00% 3 11.94 12.08
95.00% 1 11.92 12.10
95.00% 2 11.94 12.08
95.00% 3 11.95 12.06
90.00% 1 11.93 12.09
90.00% 2 11.95 12.06
90.00% 3 11.96 12.05

Approximate Tolerance Interval Containing At Least Proportion p of the Population
Confidence p Tolerance Limits
99.00% 0.900 11.92 12.10
99.00% 0.950 11.90 12.12
99.00% 0.990 11.86 12.15
95.00% 0.900 11.92 12.10
95.00% 0.950 11.90 12.11
95.00% 0.990 11.87 12.15
90.00% 0.900 11.92 12.09
90.00% 0.950 11.91 12.11
90.00% 0.990 11.88 12.14

Confidence Limits Containing
the Mean
Confidence Confidence Limits
99.00% 11.997 12.022
95.00% 12.000 12.019
90.00% 12.002 12.017

Prediction Interval Containing
the Standard Deviation of k Future
Observations
Confidence k Prediction Limits
99.00% 2 0.0003 0.1348
99.00% 3 0.0033 0.1110
95.00% 2 0.0015 0.1069
95.00% 3 0.0075 0.0919
90.00% 2 0.0030 0.0932
90.00% 3 0.0106 0.0825

Confidence Limits Containing
the Standard Deviation
Confidence Confidence Limits
99.00% 0.040 0.057
95.00% 0.041 0.055
90.00% 0.042 0.053

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