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 sigma 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:

Sigma

k is the number of subgroups
Upper control limit:	Lower control limit:

Subgroup Size A3 B3 B4 2 2.659 ----- 3.267 3 1.954 ----- 2.568 4 1.628 ----- 2.266 5 1.427 ----- 2.089 6 1.287 0.030 1.970 7 1.182 0.118 1.882 8 1.099 0.185 1.815 9 1.032 0.239 1.761 10 0.975 0.284 1.716 11 0.927 0.321 1.679 12 0.886 0.354 1.646 13 0.850 0.382 1.618 14 0.817 0.406 1.594 15 0.789 0.428 1.572 16 0.763 0.448 1.552 17 0.739 0.466 1.534 18 0.718 0.482 1.518 19 0.698 0.497 1.503 20 0.680 0.510 1.490 21 0.663 0.523 1.477 22 0.647 0.534 1.466 23 0.638 0.545 1.455 24 0.619 0.555 1.445 25 0.606 0.565 1.435