XBarR chart
XBarR chart (X-Bar and Range chart) is a type of control chart used in statistical process control to monitor the mean and variation of a process when data is collected in subgroups of 2 to 25 observations. It consists of two charts: the X-Bar chart tracking subgroup means and the R chart tracking subgroup ranges.
Map the data fields
- Subgroup/Lot: This field represents the subgroup identifier. All observations sharing the same subgroup value are grouped together.
- Process Value: This field contains the individual measurement value for each observation within a subgroup.
- UCL (SPC Variable): Optional field for custom upper control limits for the SPC Variable (X̄) series.
- LCL (SPC Variable): Optional field for custom lower control limits for the SPC Variable (X̄) series.
- Central line (SPC Variable): Optional field for custom center line values for the SPC Variable (X̄) series.
- UCL (SPC Range): Optional field for custom upper control limits for the SPC Range (R) series.
- LCL (SPC Range): Optional field for custom lower control limits for the SPC Range (R) series.
- Central line (SPC Range): Optional field for custom center line values for the SPC Range (R) series.
Calculation Methodology
The XBarR chart requires subgroup sizes between 2 and 25. Calculations are performed as follows:
Subgroup Mean (x̄ᵢ)
x̄ᵢ = Sum of all values in subgroup i / Number of observations in subgroup i
Subgroup Range (Rᵢ)
Rᵢ = Maximum value in subgroup i − Minimum value in subgroup i
Grand Mean (X̿)
X̿ = Sum of all subgroup means / Number of subgroups (k)
Average Range (R̄)
R̄ = Sum of all subgroup ranges / Number of subgroups (k)
Control Limits — X-Bar Chart
Upper Control Limit (UCL):
UCL = X̿ + A2 × R̄
Lower Control Limit (LCL):
LCL = X̿ - A2 × R̄
Center Line (CL):
CL = X̿
A2 Constants Table
| n | A2 | n | A2 |
|---|---|---|---|
| 2 | 1.880 | 14 | 0.235 |
| 3 | 1.023 | 15 | 0.223 |
| 4 | 0.729 | 16 | 0.212 |
| 5 | 0.577 | 17 | 0.203 |
| 6 | 0.483 | 18 | 0.194 |
| 7 | 0.419 | 19 | 0.187 |
| 8 | 0.373 | 20 | 0.180 |
| 9 | 0.337 | 21 | 0.173 |
| 10 | 0.308 | 22 | 0.167 |
| 11 | 0.285 | 23 | 0.162 |
| 12 | 0.266 | 24 | 0.157 |
| 13 | 0.249 | 25 | 0.153 |
Notes:
- If custom limits are provided, they override the calculated values
- Subgroup size (n) must be between 2 and 25
- The plotted value on the X-Bar chart is the subgroup mean, not individual observations
- XBarR is preferred over XBarS when subgroup sizes are small (typically n ≤ 8)