Control Charts Cheat Sheet

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Selecting a Control Chart:

Data Type Measurement Type Subgroup Size Control Chart
Variable Individual 1 Individual & MR (Moving Range)
Variable Continuous 2-9 (small) X-bar & R
Variable Continuous 10+ (large) X-bar & S
Attribute Defective Constant p Chart
Attribute Defective Variable np Chart
Attribute Defect Constant c Chart
Attribute Defect Variable u Chart

Control Chart Limits (UCL, LCL and Mean)

Control Chart Center Line Upper Control Limit (UCL) Lower Control Limit (LCL)
X-bar Chart $$\bar{X}$$ $$\bar{X} + A_2 \bar{R}$$ $$\bar{X} - A_2 \bar{R}$$
R Chart $$\bar{R}$$ $$D_4 \bar{R}$$ $$D_3 \bar{R}$$
S Chart $$\bar{S}$$ $$B_4 \bar{S}$$ $$B_3 \bar{S}$$
p Chart $$\bar{p}$$ $$\bar{p} + 3\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$ $$\bar{p} - 3\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$
np Chart $$n\bar{p}$$ $$n\bar{p} + 3\sqrt{n\bar{p}(1-\bar{p})}$$ $$n\bar{p} - 3\sqrt{n\bar{p}(1-\bar{p})}$$
c Chart $$\bar{c}$$ $$\bar{c} + 3\sqrt{\bar{c}}$$ $$\bar{c} - 3\sqrt{\bar{c}}$$
u Chart $$\bar{u}$$ $$\bar{u} + 3\sqrt{\frac{\bar{u}}{n}}$$ $$\bar{u} - 3\sqrt{\frac{\bar{u}}{n}}$$

Table of Control Chart Constants:

Sample Size (n) D3 D4 B3 B4 d2 A2
2 0 3.267 0 2.606 1.128 1.880
3 0 2.574 0 1.880 1.693 1.023
4 0 2.282 0.030 1.604 2.059 0.729
5 0 2.114 0.118 1.427 2.326 0.577
6 0.030 2.004 0.185 1.287 2.534 0.483
7 0.118 1.924 0.235 1.182 2.704 0.419
8 0.185 1.864 0.270 1.099 2.847 0.373
9 0.235 1.816 0.296 1.032 2.970 0.337
10 0.270 1.777 0.315 0.975 3.078 0.308
11 0.296 1.744 0.330 0.927 3.173 0.285
12 0.315 1.717 0.342 0.886 3.258 0.266
13 0.330 1.693 0.352 0.850 3.336 0.249
14 0.342 1.672 0.361 0.817 3.407 0.235
15 0.352 1.653 0.369 0.789 3.472 0.223
25 0.435 1.541 0.447 0.668 4.459 0.153
50 0.576 1.427 0.550 0.560 6.864 0.114
100 0.704 1.341 0.620 0.481 10.577 0.080

Posted on April 27, 2023 by  Quality Gurus

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