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Functions |
D3 Function |
computes the standard deviation of the range of independent normal random variables.
D3
where is the sample size, with
.
The D3 function returns the standard deviation of the range of independent, normally distributed random variables with the same mean and with unit standard deviation. The standard deviation returned is referred to as the control chart constant
. The values returned by the D3 function are accurate to ten decimal places.
The value can be expressed as
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where
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where is the standard normal cumulative distribution function and
is the expected range. Refer to Tippett (1925).
In other chapters is written as
to emphasize the dependence on
.
In the SHEWHART procedure, is used to calculate control limits for
charts, and it is used in the estimation of the process standard deviation based on subgroup ranges.
For more information, refer to the American Society for Quality Control (1983), the American Society for Testing and Materials (1976), Montgomery (1996), and Wadsworth, Stephens, and Godfrey (1986).
You can use the constant to calculate an unbiased estimate
of the standard deviation
of the range of a sample of
normally distributed observations from the sample range of
observations:
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You can use the D2 function to calculate .
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