PROC CAPABILITY: Reading Specification Limits

The CAPABILITY Procedure

Example 5.1 Reading Specification Limits

[See CAPSPEC2 in the SAS/QC Sample Library]You can specify specification limits either in the SPEC statement or in a SPEC= data set. In Computing Capability Indices, limits were specified in a SPEC statement. This example illustrates how to create a SPEC= data set to read specification limits with the SPEC= option in the PROC CAPABILITY statement.

Consider the drink can data presented in Computing Descriptive Statistics. Suppose, in addition to the fluid weight of each drink can, the weight of the can itself is stored in a variable named Cweight, and both variables are saved in a data set called Can2. A partial listing of Can2 follows:

data Cans1;
   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
;
data Cans1a;
   label Cweight = "Can Weight (ounces)";
   input Cweight @@;
datalines;
1.07 0.86 1.06 1.08 1.02 0.98 1.04 1.08 1.03 1.03
0.96 1.04 1.00 0.92 0.95 0.93 0.99 1.01 1.00 1.08
1.09 0.98 0.96 0.94 0.90 1.01 0.99 1.12 1.08 1.03
0.97 0.99 1.01 1.12 0.99 0.96 1.00 0.92 0.91 1.04
0.90 1.11 1.01 0.98 0.97 1.10 1.07 1.13 0.96 0.95
1.02 1.15 1.08 1.09 0.90 1.04 1.05 1.00 0.90 1.04
1.00 1.00 1.03 0.88 0.98 1.01 0.97 0.90 1.02 0.95
1.03 1.00 1.08 0.91 0.97 0.98 1.03 0.94 1.07 0.98
1.07 0.98 0.93 0.99 0.91 1.02 0.95 1.05 0.88 1.04
1.04 1.04 1.03 1.08 0.99 0.96 1.05 0.92 1.08 1.07
;
data Can2;
  merge Cans1 Cans1a;
run;

proc print data=Can2(obs=5);
run;

Output 5.1.1 The Data Set Can2

Process Capability Analysis of Fluid Weight

Obs	Weight	Cweight
1	12.07	1.07
2	12.02	0.86
3	12.00	1.06
4	12.01	1.08
5	11.98	1.02

The following DATA step creates a data set named Limits containing specification limits for the fluid weight and the can weight. Limits has 4 variables (_VAR_, _LSL_, _USL_, and _TARGET_) and 2 observations. The first observation contains the specification limit information for the variable Weight, and the second contains the specification limit information for the variable Cweight.

data Limits;
  length _var_ $8;
  _var_    = 'Weight';
  _lsl_    = 11.95;
  _target_ = 12;
  _usl_    = 12.05;
  output;
  _var_    = 'Cweight';
  _lsl_    = 0.90;
  _target_ = 1;
  _usl_    = 1.10;
  output;
run;

The following statements read the specification information from the Limits data set into the CAPABILITY procedure by using the SPEC= option. These statements print summary statistics, capability indices, and specification limit information for Weight and Cweight. Figure 5.1 and Figure 5.2 display the output for Weight. Output 5.1.2 displays the output for Cweight.

title 'Process Capability Analysis of Drink Can Data';
proc capability data=Can2 specs=Limits;
   var Cweight;
run;

Output 5.1.2 Printed Output for Variable Cweight

Process Capability Analysis of Drink Can Data

The CAPABILITY Procedure

Variable: Cweight (Can Weight (ounces))

Moments
N	100	Sum Weights	100
Mean	1.004	Sum Observations	100.4
Std Deviation	0.06330941	Variance	0.00400808
Skewness	-0.074821	Kurtosis	-0.5433858
Uncorrected SS	101.1984	Corrected SS	0.3968
Coeff Variation	6.30571767	Std Error Mean	0.00633094

Basic Statistical Measures
Location		Variability
Mean	1.004000	Std Deviation	0.06331
Median	1.000000	Variance	0.00401
Mode	1.040000	Range	0.29000
		Interquartile Range	0.08500

Note: The mode displayed is the smallest of 2 modes with a count of 8.

Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	158.5862	Pr > \|t\|	<.0001
Sign	M	50	Pr >= \|M\|	<.0001
Signed Rank	S	2525	Pr >= \|S\|	<.0001

Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.987310	Pr < W	0.4588
Kolmogorov-Smirnov	D	0.061410	Pr > D	>0.1500
Cramer-von Mises	W-Sq	0.048175	Pr > W-Sq	>0.2500
Anderson-Darling	A-Sq	0.361939	Pr > A-Sq	>0.2500

Quantiles (Definition 5)
Quantile	Estimate
100% Max	1.150
99%	1.140
95%	1.105
90%	1.080
75% Q3	1.045
50% Median	1.000
25% Q1	0.960
10%	0.910
5%	0.900
1%	0.870
0% Min	0.860

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
0.86	2	1.11	42
0.88	89	1.12	28
0.88	64	1.12	34
0.90	68	1.13	48
0.90	59	1.15	52

Specification Limits
Limit		Percent
Lower (LSL)	0.900000	% < LSL	3.00000
Target	1.000000	% Between	92.00000
Upper (USL)	1.100000	% > USL	5.00000

Process Capability Indices
Index	Value	95% Confidence Limits
Cp	0.526515	0.453237	0.599670
CPL	0.547575	0.446607	0.647299
CPU	0.505454	0.408856	0.600808
Cpk	0.505454	0.409407	0.601501
Cpm	0.525467	0.454973	0.601113

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