Control Chart Calculator
This control chart calculator builds an individuals and moving range (I-MR) chart from your measurements. Paste readings in time order to get the center line, upper and lower control limits, and a flag on any point outside them.
20 readings read.
Control limits (individuals chart)
- LCL
- 497.809
- Center
- 500.455
- UCL
- 503.101
Average moving range 0.995. Moving range chart upper limit 3.25.
1 point outside the limits: #15 (503.9). Look for a special cause at that time.
Longest run on one side of the center line: 3 points (a run of 8 or more suggests a shift).
Example values are filled in. Replace them with your own; nothing you type leaves your browser.
Worked example
The example values, step by step
- Step 1 · Center line
10,009.1 g ÷ 20 readings
= 500.46 g
- Step 2 · Average moving range
18.9 g ÷ 19 ranges
= 0.99 g
- Step 3 · Upper control limit
500.46 + 2.66 × 0.995
= 503.10 g
- Step 4 · Lower control limit
500.46 − 2.66 × 0.995
= 497.81 g
- Step 5 · Moving range limit
3.267 × 0.995
= 3.25 g
- Step 6 · Out of control
Reading 15 is 503.9 g, above 503.10
= 1 point
Reading the result
The example is 20 fill weights from a filling line, one bottle sampled every 15 minutes. Nineteen readings sit within about a gram of the center, which is the process's normal noise.
Reading 15, at 503.9 g, is above the upper control limit, and the two moving ranges either side of it break the moving range limit. That points to one event, such as a nozzle adjustment or a density change, worth investigating at that time. If the cause is found and removed, recalculate the limits without that point.
| Data | Chart |
|---|---|
| One measurement per sample | Individuals and moving range (I-MR) |
| Small subgroups of measurements (2 to 9) | X-bar and R |
| Larger subgroups of measurements (10 or more) | X-bar and S |
| Share of defective units, varying sample size | p chart |
| Count of defective units, fixed sample size | np chart |
| Count of defects, same area of opportunity | c chart |
| Defects per unit, varying area of opportunity | u chart |
Common data mistakes
- Drawing spec limits on the chart and calling them control limits.
- Recalculating the limits after every new point, so a slow drift never shows up.
- Mixing readings from different machines or shifts into one series, which widens the limits and hides problems.
- Reacting to every point that moves up or down inside the limits. That is common-cause noise, and adjusting for it adds variation.
The methods behind the number
The formula
How it's calculated
- Center line
- Average of the readings (x̄)
- Moving range
- |reading − previous reading|, averaged as MR̄
- Upper control limit
- x̄ + 2.66 × MR̄
- Lower control limit
- x̄ − 2.66 × MR̄
- Moving range limit
- 3.267 × MR̄
Control limits are not spec limits
Control limits come from the process's own variation and show what it does. Spec limits come from the customer and show what it should do. A process can be in control and still make parts out of spec.
Why 2.66
The chart estimates the standard deviation as MR̄ ÷ 1.128 and sets the limits three standard deviations from the center. Three divided by 1.128 is 2.66.
When to use an individuals chart
Use it when each reading stands alone: one batch, one day or one invoice at a time. When you measure several parts per sample, an X-bar and R chart uses the samples better.
Frequently asked questions
How do you calculate control limits?
What does a point outside the control limits mean?
How many data points do I need for a control chart?
What is the difference between an I-MR chart and an X-bar R chart?
Which run rules does this calculator check?
Sources and further reading
- NIST/SEMATECH e-Handbook: Shewhart control charts ↗
- Donald J. Wheeler, Understanding Variation (book)
- Douglas C. Montgomery, Introduction to Statistical Quality Control (book)
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