Control limits are the lines that tell you how far a plotted point can wander before you should suspect something has changed. They are calculated from the data itself, using R̄ as the measure of natural spread. The formulas use factors that depend on the subgroup size. These factors come from a standard reference table; you look them up once for your subgroup size and reuse them. For subgroups of 5 the factors are A2 = 0.577, D3 = 0 and D4 = 2.114.
The X̄ chart limits are X̄̄ plus and minus A2 × R̄. The R chart limits are D4 × R̄ for the upper and D3 × R̄ for the lower. Because D3 is zero for subgroups of 5, the R chart has no lower limit at that size; a very small range is simply good news.
Specification limits are a different thing entirely. They come from the customer or the drawing and describe what is acceptable for one carton. Control limits come from the process and describe how subgroup averages behave when nothing has changed. Never draw specification limits on an X̄ chart; averages vary far less than individual pieces, so the comparison misleads.
Standard Procedure
- 1Look up A2, D3 and D4 for your subgroup size from the reference table.
- 2Multiply A2 by R̄, then add to and subtract from X̄̄ for the X̄ limits.
- 3Multiply D4 by R̄ for the upper R limit; multiply D3 by R̄ for the lower R limit.
- 4Draw the limits as dashed lines; keep specification limits off the chart.
Lesson Summary
- ✓X̄ limits: X̄̄ ± A2 × R̄. R limits: D4 × R̄ and D3 × R̄, with factors from a reference table.
- ✓Specification limits judge individual pieces; control limits judge process stability. Do not mix them.