How to use the control chart limits calculator
- Choose the chart: average and range, individuals and moving range, proportion defective (p) or count of defects (c).
- Paste the data in time order. For the average chart also give the subgroup size from 2 to 10.
- For a p chart enter the number defective and the sample size on each line.
- Read the center line and limits, then the table that marks each point inside or outside.
Formula
average chart: grand mean +/- A2 x R-bar; range chart: D3 x R-bar and D4 x R-bar
individuals chart: mean +/- 2.660 x average moving range
p chart: p-bar +/- 3 sqrt(p-bar (1 - p-bar) / n)
c chart: c-bar +/- 3 sqrt(c-bar)
A2, D3 and D4 are tabulated constants for the subgroup size, for example A2 = 0.577, D3 = 0 and D4 = 2.114 for subgroups of 5. A lower limit below zero is shown as zero.
Five subgroups of five readings
The 25 example readings give subgroup means near 10.0 and an average range R-bar of 0.0740, with a grand mean of 10.0068. The average chart limits are 10.0068 plus or minus 0.577 x 0.0740, which is 9.9641 to 10.0495. The range chart limits are 0 and 2.114 x 0.0740 = 0.1564.
As a cross check, R-bar / d2 estimates sigma as 0.03182, and 3 x 0.03182 / sqrt(5) gives the same 0.0427 half width. Treated as 25 single readings, the individuals chart gives limits of 9.9048 to 10.1088.
Choosing a chart
Use the average and range chart when you take small groups of readings of one quantity, the individuals chart when you have one reading at a time, the p chart for the share of items that fail an inspection and the c chart for the number of defects found in equal sized units.
For a p chart with changing sample sizes, each point has its own limits. They get narrower as the sample grows.
What a signal means
A point beyond the limits is unlikely to be chance alone if the process is stable, so it is a reason to look for a cause. It is not proof, since a stable process still gives a point beyond 3 sigma about 27 times in 10,000.
The page checks only for points outside the limits. Other rules, such as runs on one side of the center line, are not applied. Once the process is stable, the Process Capability Calculator compares it with specification limits.
Assumptions and limits
- Limits are 3 sigma from the center line and are built from the data you paste.
- The average chart uses the published constants for subgroup sizes 2 to 10.
- Subgroups are consecutive values of equal size. A leftover partial subgroup is ignored.
- Control limits are not specification limits and say nothing about what customers need.
- Up to 2,000 values are read.
Frequently asked questions
Where do the constants come from?
A2, D3 and D4 are standard tabulated values for control charts, built from the expected range of normal readings. The page also shows a cross check using R-bar divided by d2 so you can see the two methods agree.
Why is my lower limit zero?
A proportion, a count or a range cannot be negative. When the formula gives a number below zero, the limit is shown as zero.
How many subgroups do I need?
The page needs at least five subgroups. In practice, 20 to 25 subgroups give much steadier limits, and the limits should be recalculated when the process changes.
What is the 2.660 on the individuals chart?
It is 3 divided by 1.128, where 1.128 is the average range of two normal readings. It turns the average moving range into an estimate of three standard deviations.