Compute X-bar and R control chart limits from subgroup data using the standard A2, D3 and D4 constants.
Result
How to use this tool
Enter one subgroup per line, with its values comma-separated.
Use the same number of values in every subgroup, between 2 and 10.
Read the centre line and the upper and lower X-bar limits.
Read R-bar and the R chart limits to judge variation.
Formula & worked example
Subgroups (10, 12, 11) and (11, 13, 12) give centre 11.5, X-bar limits 9.454 to 13.546, and R limits 0 to 5.148.
Limitations — read this before you rely on it
X-bar/R method for rational subgroups of equal size 2 to 10 only; it assumes approximately normal within-subgroup variation and does not apply Western Electric run rules automatically.
Frequently asked questions
A Shewhart control chart: subgroup means track the process centre and subgroup ranges track its variation.
They are the standard published constants for a given subgroup size n, converting the average range into 3-sigma limits.
It signals special-cause variation worth investigating, not automatic proof that product is defective.
At least two for a calculation, but 20 to 25 subgroups are the usual recommendation for stable trial limits.
For subgroup sizes above about 10, the S chart (using standard deviation) is preferred; this tool covers sizes 2 to 10 with the R chart.