The 3-Sigma Lower Control Limit (LCL) for an S Chart $\bar { s } - 3 \bar { s } \sqrt { 1 - a _ { n } ^ { 2 } } / a _ { n }$

Short Answer

The 3-sigma lower control limit (LCL) for an S chart is given by LCL = $\bar { s } - 3 \bar { s } \sqrt { 1 - a _ { n } ^ { 2 } } / a _ { n }$ where the values of $a _ { n }$ for n=3, ….., 8 are tabulated in your text. This expression for LCL will be negative if $n \leq$ __________, in which case it is customary to use LCL = __________.