Charts | X-Bar R Theory
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p Chart pn Chart u Chart c Chart X-Bar R X-Bar s I-MR / X-MR Out-of-Control
X-Bar R charts consist of two charts; a chart for X (X-Bar) and a chart for the range (R).
Control Limits
Calculating control limits for continuous charts is a little more difficult than for discrete data such as Poisson or Binomial. Here, we calculate differently for each of the two charts.
X Chart
- Control Line (CL) = X =
ΣXi/n - Upper Control Limit (UCL) =
X + A2R - Lower Control Limit (LCL) =
X - A2R
R Chart
- Control Line (CL) = R =
ΣRi/n - Upper Control Limit (UCL) =
D4R - Lower Control Limit (LCL) =
D3R
Determinine A2, D4 and D3
Calculating the necessary values for A2, D4 and D3 is simply a matter of looking it up in the following table, provided you know the sample size n
| n | A2 | D4 | D3 |
| 2 | 1.880 | 3.267 | 0 |
| 3 | 1.023 | 2.575 | 0 |
| 4 | 0.729 | 2.282 | 0 |
| 5 | 0.577 | 2.115 | 0 |
| 6 | 0.483 | 2.004 | 0 |
| 7 | 0.419 | 1.924 | 0.076 |
| 8 | 0.373 | 1.864 | 0.136 |
| 9 | 0.337 | 1.816 | 0.184 |
| 10 | 0.308 | 1.780 | 0.220 |
| 11 | 0.285 | 1.744 | 0.256 |
| 12 | 0.266 | 1.717 | 0.283 |