Charts | X-Bar s 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 s charts consist of two charts; a chart for X (X-Bar) and a chart for the standard deviation (s).
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 + A3s - Lower Control Limit (LCL) =
X - A3s
s Chart
- Control Line (CL) = s =
Σsi/n - Upper Control Limit (UCL) =
B4S - Lower Control Limit (LCL) =
B3S
Determinine A3, B4 and B3
Calculating the necessary values for A3, B4 and B3 is simply a matter of looking it up in the following table, provided you know the sample size n
| n | A3 | B4 | B3 |
| 2 | 2.659 | 0 | 3.267 |
| 3 | 1.954 | 0 | 2.568 |
| 4 | 1.628 | 0 | 2.266 |
| 5 | 1.427 | 0 | 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 |