Control Chart Calculator (X̄ and R)
Build X̄ and R control charts from subgroup data: centre lines, control limits and the subgroups that fall outside them.
About the Control Chart Calculator (X̄ and R)
A control chart tracks a process over time. Take samples (subgroups) of n items; the X̄ chart plots their means and the R chart their ranges. The control limits come from the overall mean X̄̄, the average range R̄ and constants that depend on n: UCL = X̄̄ + A₂R̄, LCL = X̄̄ − A₂R̄ for means, and UCL = D₄R̄, LCL = D₃R̄ for ranges.
A point outside the limits suggests an assignable cause rather than ordinary variation. The constants are the standard tabulated values for subgroups of 2 to 10.
The formula
X̄ chart: X̄̄ ± A₂R̄; R chart: D₃R̄ to D₄R̄
- A₂, D₃, D₄
- standard constants for the subgroup size (n = 5: 0.577, 0, 2.114)
Worked example
Example: Process = In control
- Input: Subgroups (one per line, same size): 10 12 11 13 12; 11 10 12 11 13; 12 11 13 12 10; 13 12 11 10 12; 11 13 12 12 11.
- Formula: X̄ chart: X̄̄ ± A₂R̄; R chart: D₃R̄ to D₄R̄
- Result: Process = In control
- X̄̄ (centre line): 11.6
- R̄: 2.8
- X̄ chart: UCL, LCL (A₂ = 0.577): 13.2156, 9.9844
Questions people ask
Why ranges and not standard deviations?
For small subgroups the range is easy to compute and nearly as informative; for larger ones an S chart is used.
Does in control mean good?
It means stable and predictable, not necessarily within the specification.