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where n is the sample size, with .
The value d3 can be expressed as
where is the standard normal cumulative distribution function and d2 is the expected range. Refer to Tippett (1925).
In other chapters d3 is written as d3(n) to emphasize the dependence on n.
In the SHEWHART procedure, d3 is used to calculate control limits for r charts, and it is used in the estimation of the process standard deviation based on subgroup ranges.
For more information, refer to the ASQC Glossary and Tables for Statistical Quality Control, the ASTM Manual on Presentation of Data and Control Chart Analysis, Montgomery (1996), and Wadsworth and others (1986).
You can use the constant d3 to calculate an unbiased estimate
of the standard deviation of the range of
a sample of n normally distributed observations from the sample
range of n observations:
You can use the D2 function to calculate d2.
data; constant=d3(5); put constant; run;
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