Example 43.1: Applying Tests for Special Causes

XRCHART Statement

Example 43.1: Applying Tests for Special Causes

See SHWXR2 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';
   symbol v=dot c=salmon;
   proc shewhart history=tape;
      xrchart weight*sample / tests    = 1 to 5
                              tabletests
                              zonelabels
                              ltests   = 20
                              cframe   = bigb
                              cinfill  = ywh
                              ctests   = vig
                              cconnect = salmon;
   run;

The charts are shown in Output 43.1.1, and the table is shown in Output 43.1.2. The TESTS= option requests Tests 1, 2, 3, 4, and 5, which are described in Chapter 48, "Tests for Special Causes." 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. The LTESTS= option specifies the line type used to connect the points in a pattern for a test that is signaled.

Output 43.1.1: Tests for Special Causes Displayed on $\bar{X}$ and R Charts

Output 43.1.2: 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
sample	Subgroup Sample Size	Lower Limit	Subgroup Mean	Upper Limit	Special Tests Signaled	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

Output 43.1.1 and Output 43.1.2 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.

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