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Use Of SPC To Detect Process Manipulation
Control Chart Constants
The table of control chart constants shown below are approximate values used in calculating control limits for the X-bar chart based on rational subgroup size. Subgroups falling outside the control limits should be removed from the calculations to remove their statistical bias. SPC software for only a couple hundred dollars will use 64 bit precision (i.e. significantly more digits than shown here), automatically drop out of control subgroups, recalculate limits for sustained process shifts, and consistently use the correct calculations for various real-world situations, such as batch means and non-normal processes.
Table 1: All you really need to calculate SPC control chart limits.
|
Observations in Subgroup, n |
d3 for Range Limits |
||
|
2 |
0.7979 |
1.128 |
0.853 |
|
3 |
0.8862 |
1.693 |
0.888 |
|
4 |
0.9213 |
2.059 |
0.880 |
|
5 |
0.9400 |
2.326 |
0.864 |
|
6 |
0.9515 |
2.534 |
0.848 |
|
7 |
0.9594 |
2.704 |
0.833 |
|
8 |
0.9650 |
2.847 |
0.820 |
|
9 |
0.9693 |
2.970 |
0.808 |
|
10 |
0.9727 |
3.078 |
0.797 |
|
11 |
0.9754 |
3.173 |
0.787 |
|
12 |
0.9776 |
3.258 |
0.778 |
|
13 |
0.9794 |
3.336 |
0.770 |
|
14 |
0.9810 |
3.407 |
0.763 |
|
15 |
0.9823 |
3.472 |
0.756 |
|
16 |
0.9835 |
3.532 |
0.750 |
|
17 |
0.9845 |
3.588 |
0.744 |
|
18 |
0.9854 |
3.640 |
0.739 |
|
19 |
0.9862 |
3.689 |
0.734 |
|
20 |
0.9869 |
3.735 |
0.729 |
|
21 |
0.9876 |
3.778 |
0.724 |
|
22 |
0.9882 |
3.819 |
0.720 |
|
23 |
0.9887 |
3.858 |
0.716 |
|
24 |
0.9892 |
3.895 |
0.712 |
|
25 |
0.9896 |
3.931 |
0.708 |
Table 2: Used for alternate forms of calculations.
|
Observations in Subgroup, n |
A2 for Xbar Limits based on Range |
A3 for Xbar Limits based on Sigma |
B3 for Sigma chart LCL |
B4 for Sigma chart UCL |
D3 for Range chart LCL |
D4 for Range chart UCL |
|
2 |
1.880 |
2.659 |
0 |
3.267 |
0 |
3.267 |
|
3 |
1.023 |
1.954 |
0 |
2.568 |
0 |
2.574 |
|
4 |
0.729 |
1.628 |
0 |
2.266 |
0 |
2.282 |
|
5 |
0.577 |
1.427 |
0 |
2.089 |
0 |
2.114 |
|
6 |
0.483 |
1.287 |
0.030 |
1.970 |
0 |
2.004 |
|
7 |
0.419 |
1.182 |
0.118 |
1.882 |
0.076 |
1.924 |
|
8 |
0.373 |
1.099 |
0.185 |
1.815 |
0.136 |
1.864 |
|
9 |
0.337 |
1.032 |
0.239 |
1.761 |
0.184 |
1.816 |
|
10 |
0.308 |
0.975 |
0.284 |
1.716 |
0.223 |
1.777 |
|
11 |
0.285 |
0.927 |
0.321 |
1.679 |
0.256 |
1.744 |
|
12 |
0.266 |
0.886 |
0.354 |
1.646 |
0.283 |
1.717 |
|
13 |
0.249 |
0.850 |
0.382 |
1.618 |
0.307 |
1.693 |
|
14 |
0.235 |
0.817 |
0.406 |
1.594 |
0.328 |
1.672 |
|
15 |
0.223 |
0.789 |
0.428 |
1.572 |
0.347 |
1.653 |
|
16 |
0.212 |
0.763 |
0.448 |
1.552 |
0.363 |
1.637 |
|
17 |
0.203 |
0.739 |
0.466 |
1.534 |
0.378 |
1.622 |
|
18 |
0.194 |
0.718 |
0.482 |
1.518 |
0.391 |
1.608 |
|
19 |
0.187 |
0.698 |
0.497 |
1.503 |
0.403 |
1.597 |
|
20 |
0.180 |
0.680 |
0.510 |
1.490 |
0.415 |
1.585 |
|
21 |
0.173 |
0.663 |
0.523 |
1.477 |
0.425 |
1.575 |
|
22 |
0.167 |
0.647 |
0.534 |
1.466 |
0.434 |
1.566 |
|
23 |
0.162 |
0.633 |
0.545 |
1.455 |
0.443 |
1.557 |
|
24 |
0.157 |
0.619 |
0.555 |
1.445 |
0.451 |
1.548 |
|
25 |
0.153 |
0.606 |
0.565 |
1.435 |
0.459 |
1.541 |
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).
