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Burr Weighting Factors
The table below presents the factors used to provide a minimum variance linear unbiased
estimate of the standard deviation from sample ranges (e, f) or sample standard deviations (g, h), based on the
subgroup size.
(Reference: Burr, Irving W. Control Charts for Measurements with Varying Sample
Sizes. Journal of Quality Technology 1.3 (July 1969), pp. 163-167).
The factors e and f are used to stabilize the estimate of
Process Sigma based on the Range Chart; factors g and h
are used to stabilize the estimate of Process Sigma
based on the Sigma Chart.
| Subgroup Size |
e |
f |
g |
h |
| 2 |
1.553 |
1.752 |
2.196 |
1.752 |
| 3 |
2.145 |
3.63 |
4.130 |
3.660 |
| 4 |
2.660 |
5.476 |
6.094 |
5.615 |
| 5 |
3.115 |
7.246 |
8.074 |
7.589 |
| 6 |
3.524 |
8.931 |
10.060 |
9.572 |
| 7 |
3.895 |
10.535 |
12.051 |
11.561 |
| 8 |
4.236 |
12.061 |
14.044 |
13.553 |
| 9 |
4.551 |
13.517 |
16.038 |
15.546 |
| 10 |
4.844 |
14.908 |
18.034 |
17.541 |
| 11 |
|
|
20.031 |
19.537 |
| 12 |
|
|
22.028 |
21.534 |
| 13 |
|
|
24.026 |
23.531 |
| 14 |
|
|
26.024 |
25.529 |
| 15 |
|
|
28.022 |
27.527 |
| 16 |
|
|
30.021 |
29.525 |
| 17 |
|
|
32.019 |
31.523 |
| 18 |
|
|
34.018 |
33.522 |
| 19 |
|
|
36.017 |
35.521 |
| 20 |
|
|
38.016 |
37.520 |
See also:
Fixed or
Varying Subgroup Sizes for X-Bar charts
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