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Capability Analysis: How is it made?

Step 2 Calculate the estimated standard deviation

The standard deviation is the statistic which describes the spread of the data. For capability analysis, use the estimated standard deviation of the individual values from the control chart. The estimated standard deviation is a good estimate of the spread because it is based on the average range (Rbar ).

The symbol for the estimated standard deviation is (read "sigma hat").

The formula for the estimated standard deviation is:

Capability3form.gif

was calculated when the control chart was made. for the example is 1.05. The denominator (d2) is a weighting factor whose value is based on the subgroup size from the control chart. The value for d2 in the example, based on a subgroup size of 5, is 2.33.

A short listing of the d2 values for other subgroup sizes is shown below.

n
2
3
4
5
6
7
8
9
10
D2.gif
1.13
1.69
2.06
2.33
2.53
2.70
2.85
2.97
3.08

The estimated standard deviation for the example is:

Capability4form.gif

The estimated standard deviation will be referred to as the standard deviation or sigma hat through the rest of this section.

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