This section describes how scaling factors are calculated when you use medians to estimate sigma. When you select Use Medians instead of Means, sigma is estimated using a scaled median range or median standard deviation. The table below gives the scaling factors, which were obtained using Monte Carlo simulation.
For subgroups of size n drawn from a normal distribution, the following statements are true:
• For sample sizes up to n = 100, JMP uses control chart constants d2(n) and d3(n) that are defined in Table 2 of Harter (1960). For samples with a sample size greater than 100, JMP uses the control chart constant values for sample size 100 in both the sigma and control limit calculations.
• The theoretical median of the ranges is approximately d2_Median*σ, where d2_Median is the value corresponding to n.
• The theoretical median of the standard deviations is approximately c4_Median*σ, where c4_Median is the value corresponding to n.
|
n |
d2_Median |
c4_Median |
|---|---|---|
|
2 |
0.953 |
0.675 |
|
3 |
1.588 |
0.833 |
|
4 |
1.978 |
0.888 |
|
5 |
2.257 |
0.917 |
|
6 |
2.471 |
0.933 |
|
7 |
2.646 |
0.944 |
|
8 |
2.792 |
0.952 |
|
9 |
2.915 |
0.959 |
|
10 |
3.024 |
0.963 |
|
11 |
3.118 |
0.967 |
|
12 |
3.208 |
0.969 |
|
13 |
3.286 |
0.972 |
|
14 |
3.357 |
0.975 |
|
15 |
3.422 |
0.976 |
|
16 |
3.483 |
0.978 |
|
17 |
3.539 |
0.979 |
|
18 |
3.590 |
0.980 |
|
19 |
3.640 |
0.981 |
|
20 |
3.685 |
0.982 |
|
21 |
3.731 |
0.983 |
|
22 |
3.770 |
0.984 |
|
23 |
3.811 |
0.984 |
|
24 |
3.846 |
0.985 |
|
25 |
3.883 |
0.986 |