XRCHART Statement: SHEWHART Procedure

Example 18.38 Applying Tests for Special Causes

Note: See Mean and Range Charts-Tests for Special Causes in the SAS/QC Sample Library.

This example illustrates how you can apply tests for special causes to make $\bar{X}$ and R charts more sensitive to special causes of variation.

The weight of a roll of tape is measured before and after an adhesive is applied. The difference in weight represents the amount of adhesive applied to the tape during the coating process. The following data set contains the average and the range of the adhesive amounts for 21 samples of five rolls:

data Tape;
   input Sample $ WeightX WeightR;
   WeightN=5;
   label WeightX = 'Average Adhesive Amount'
         Sample  = 'Sample Code';
   datalines;
C9  1270  35
C4  1258  25
A7  1248  24
A1  1260  39
A5  1273  29
D3  1260  21
D6  1259  37
D1  1240  37
R4  1260  28
H7  1255  19
H2  1268  36
H6  1253  36
P4  1273  29
P9  1275  22
J7  1257  24
J2  1269  41
J3  1249  36
B2  1264  31
G4  1258  25
G6  1248  36
G3  1248  30
;

The following statements create $\bar{X}$ and R charts, apply several tests to the $\bar{X}$ chart, and tabulate the results:

title 'Tests for Special Causes Applied to Adhesive Tape Data';
ods graphics on;
proc shewhart history=Tape;
   xrchart Weight*Sample / tests    = 1 to 5
                           odstitle = title
                           tabletests
                           zonelabels;
run;

The charts are shown in Output 18.38.1, and the table is shown in Output 18.38.2. The TESTS= option requests Tests 1, 2, 3, 4, and 5, which are described in Tests for Special Causes: SHEWHART Procedure. The TABLETESTS option requests a basic table of subgroup statistics and control limits with a column indicating which subgroups tested positive for special causes.

The ZONELABELS option displays zone lines and zone labels on the $\bar{X}$ chart. The zones are used to define the tests.

Output 18.38.1: Tests for Special Causes Displayed on $\bar{X}$ and R Charts

Tests for Special Causes Displayed on X and  Charts


Output 18.38.1 and Output 18.38.2 indicate that Test 1 is positive at sample D1 and Test 5 is positive at sample P9. Test 1 detects one point beyond Zone A (outside the control limits), and Test 5 detects two out of three points in a row in Zone A or beyond.

Output 18.38.2: Tabular Form of $\bar{X}$ and R Charts

Tests for Special Causes Applied to Adhesive Tape Data

The SHEWHART Procedure

Means and Ranges Chart Summary for Weight
Sample Subgroup
Sample
Size
3 Sigma Limits with n=5 for Mean Special
Tests
Signaled
3 Sigma Limits with n=5 for
Range
Lower
Limit
Subgroup
Mean
Upper
Limit
Lower
Limit
Subgroup
Range
Upper
Limit
C9 5 1241.7065 1270.0000 1276.8650   0 35.000000 64.441879
C4 5 1241.7065 1258.0000 1276.8650   0 25.000000 64.441879
A7 5 1241.7065 1248.0000 1276.8650   0 24.000000 64.441879
A1 5 1241.7065 1260.0000 1276.8650   0 39.000000 64.441879
A5 5 1241.7065 1273.0000 1276.8650   0 29.000000 64.441879
D3 5 1241.7065 1260.0000 1276.8650   0 21.000000 64.441879
D6 5 1241.7065 1259.0000 1276.8650   0 37.000000 64.441879
D1 5 1241.7065 1240.0000 1276.8650 1 0 37.000000 64.441879
R4 5 1241.7065 1260.0000 1276.8650   0 28.000000 64.441879
H7 5 1241.7065 1255.0000 1276.8650   0 19.000000 64.441879
H2 5 1241.7065 1268.0000 1276.8650   0 36.000000 64.441879
H6 5 1241.7065 1253.0000 1276.8650   0 36.000000 64.441879
P4 5 1241.7065 1273.0000 1276.8650   0 29.000000 64.441879
P9 5 1241.7065 1275.0000 1276.8650 5 0 22.000000 64.441879
J7 5 1241.7065 1257.0000 1276.8650   0 24.000000 64.441879
J2 5 1241.7065 1269.0000 1276.8650   0 41.000000 64.441879
J3 5 1241.7065 1249.0000 1276.8650   0 36.000000 64.441879
B2 5 1241.7065 1264.0000 1276.8650   0 31.000000 64.441879
G4 5 1241.7065 1258.0000 1276.8650   0 25.000000 64.441879
G6 5 1241.7065 1248.0000 1276.8650   0 36.000000 64.441879
G3 5 1241.7065 1248.0000 1276.8650   0 30.000000 64.441879