X-bar control limits are based on either range or sigma, depending on which chart it is paired with. When the X-bar chart is paired with a range chart, the most common (and recommended) method of computing control limits based on 3 standard deviations is:

X-bar

n is the number of observations

k is the number of subgroups

Upper control limit:

Lower control limit:

Range

k is the number of subgroups.

Upper control limit:

Lower control limit:

Tabular values for X-bar and range charts Subgroup Size A2 d2 D3 D4 2 1.880 1.128 ----- 3.268 3 1.023 1.693 ----- 2.574 4 0.729 2.059 ----- 2.282 5 0.577 2.326 ----- 2.114 6 0.483 2.534 ----- 2.004 7 0.419 2.704 0.076 1.924 8 0.373 2.847 0.136 1.864 9 0.337 2.970 0.184 1.816 10 0.308 3.078 0.223 1.777 11 0.285 3.173 0.256 1.744 12 0.266 3.258 0.283 1.717 13 0.249 3.336 0.307 1.693 14 0.235 3.407 0.328 1.672 15 0.223 3.472 0.347 1.653 16 0.212 3.532 0.363 1.637 17 0.203 3.588 0.378 1.622 18 0.194 3.640 0.391 1.608 19 0.187 3.689 0.403 1.597 20 0.180 3.735 0.415 1.585 21 0.173 3.778 0.425 1.575 22 0.167 3.819 0.434 1.566 23 0.162 3.858 0.443 1.557 24 0.157 3.895 0.451 1.548 25 0.153 3.931 0.459 1.541

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