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The 3-Sigma Lower Control Limit (LCL) for an S Chart sˉ3sˉ1an2/an\bar { s } - 3 \bar { s } \sqrt { 1 - a _ { n } ^ { 2 } } / a _ { n }

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The 3-sigma lower control limit (LCL) for an S chart is given by LCL = sˉ3sˉ1an2/an\bar { s } - 3 \bar { s } \sqrt { 1 - a _ { n } ^ { 2 } } / a _ { n } where the values of ana _ { n } for n=3, ….., 8 are tabulated in your text. This expression for LCL will be negative if nn \leq __________, in which case it is customary to use LCL = __________.

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