Deriving Control Chart Constants :: SAS/QC(R) 12.3 User's Guide

Deriving Control Chart Constants

You can use the functions D2, D3, and C4 to calculate standard control chart constants that are derived from , and . For reference, the following equations for some of these constants are provided:

$\displaystyle A_2$	$\displaystyle =$	$\displaystyle k/(d_2 \sqrt {n})$
$\displaystyle A_3$	$\displaystyle =$	$\displaystyle k/(c_4 \sqrt {n})$
$\displaystyle B_3$	$\displaystyle =$	$\displaystyle \max (0,1-(k/c_4) \sqrt {1-c_4^2}\: )$
$\displaystyle B_4$	$\displaystyle =$	$\displaystyle 1+(k/c_4) \sqrt {1-c_4^2}$
$\displaystyle B_5$	$\displaystyle =$	$\displaystyle \max (0,c_4-k\sqrt {1-c_4^2})$
$\displaystyle B_6$	$\displaystyle =$	$\displaystyle c_4+k \sqrt {1-c_4^2}$
$\displaystyle c_5$	$\displaystyle =$	$\displaystyle \sqrt {1-c_4^2}$
$\displaystyle D_1$	$\displaystyle =$	$\displaystyle \max (0,d_2-kd_3)$
$\displaystyle D_2$	$\displaystyle =$	$\displaystyle d_2+kd_3$
$\displaystyle D_3$	$\displaystyle =$	$\displaystyle \max (0,1-kd_3/d_2)$
$\displaystyle D_4$	$\displaystyle =$	$\displaystyle 1+kd_3/d_2$
$\displaystyle E_2$	$\displaystyle =$	$\displaystyle k/d_2$
$\displaystyle E_3$	$\displaystyle =$	$\displaystyle k/c_4$

In the preceding equations, k is the multiple of standard error (k = 3 in the case of 3 $\sigma$ limits), and n is the subgroup sample size. The use of these control chart constants is discussed in the American Society for Quality Control (1983), the American Society for Testing and Materials (1976), Montgomery (1996), and Wadsworth, Stephens, and Godfrey (1986).

Although you do not ordinarily need to calculate control chart constants when using the SHEWHART procedure, you may find the D2, D3, and C4 functions useful for creating LIMITS= data sets that contain control limits to be read by the SHEWHART procedure.