Syntax

C4

where is the sample size, with .

Description

The C4 function returns the expected value of the standard deviation of independent, normally distributed random variables with the same mean and with standard deviation of 1. This expected value is referred to as the control chart constant .

The value is calculated as

where is the gamma function. As grows, is asymptotically equal to .

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).

In other chapters, is written as to emphasize the dependence on .

You can use the constant to calculate an unbiased estimate of the standard deviation of a normal distribution from the sample standard deviation of observations:

where the sample standard deviation is calculated using in the denominator. 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 standard deviations.

Examples

The following statements result in a value of 0.939985603:

data;
   constant=c4(5);
   put constant;
run;