A control chart plots a measurement over time against limits calculated from the process itself, so you can tell normal variation from a real change. Pick the chart by the kind of data and the sample size: individuals charts for single readings, X-bar and R for small samples, and p, np, c or u charts for counts of defects. Control limits are not specification limits. A point outside them, or a pattern such as eight in a row on one side of the center, is a signal to find out what changed.
What a control chart is for
Every process varies a little. The question at the machine is whether this part is different because of normal variation or because something changed. A control chart answers that. Walk up to a chart with a point near the limit and you can see whether to leave it alone or go looking for the cause. Done well, it tells you about a problem while the parts are still good.
Control limits are not specification limits
This is the most common confusion. Specification limits come from the print and say what the customer will accept. Control limits come from the process data and say what the process normally does. A process can be in control and still make bad parts if its normal spread is wider than the tolerance. It can also be out of control and still make good parts, for now. You need both pictures. The Cpk vs Ppk guide covers the capability side.
Which chart to use
Start with the data. Measurements, such as a diameter or a weight, are variable data. Counts, such as the number of defective parts or defects per unit, are attribute data.
| Data | Sample | Chart |
|---|---|---|
| Variable | One reading at a time (slow or costly to measure) | Individuals and moving range (I-MR) |
| Variable | Small subgroups, about 2 to 9 | X-bar and R |
| Variable | Larger subgroups, about 10 or more | X-bar and S |
| Attribute, defective parts | Sample size varies | p chart (proportion defective) |
| Attribute, defective parts | Sample size constant | np chart (number defective) |
| Attribute, defects per area or unit | Constant area or unit | c chart (count of defects) |
| Attribute, defects per area or unit | Varying area or unit | u chart (defects per unit) |
A worked example: the bore diameter
This is the same 25-subgroup bore study used in the Cpk guide: five parts every hour, 125 readings. For subgroups of five, the standard constants are A2 = 0.577, D3 = 0 and D4 = 2.114.
| Line | Calculation | Value (mm) |
|---|---|---|
| Average of the subgroup averages (center line) | Add the 25 subgroup averages, divide by 25 | 25.0011 |
| Average range | Add the 25 ranges, divide by 25 | 0.02304 |
| X-bar chart upper limit | Center line plus A2 times the average range | 25.0144 |
| X-bar chart lower limit | Center line minus A2 times the average range | 24.9878 |
| R chart upper limit | D4 times the average range | 0.0487 |
| R chart lower limit | D3 times the average range | 0 |
Plot the 25 subgroup averages against those limits. Subgroup 7 falls just below the lower limit. Subgroup 25 is above the upper limit. The last eight averages all sit above the center line. The range chart stays inside its limits the whole run, so the spread is steady. What changed is the average, which is walking upward. It is the same drift that pulled Ppk below Cpk in the capability study.
Here the chart does what the capability study could only hint at. It points to when the drift began and gives you a time to investigate. Look at tool wear, temperature or an offset someone keeps nudging.
What counts as a signal
- One point beyond a control limit. The strongest signal. Something changed.
- A run on one side of the center line. Eight points in a row is a common rule. Some use seven or nine.
- A steady trend. Six points in a row going up or down is a common rule.
- Patterns. Points hugging the center line too closely, or a sawtooth up and down, also mean something is odd, such as mixed sources or over-adjusting.
Rule sets vary. Your customer or your charting software may use slightly different run lengths. Pick one set, write it down and apply it the same way every time.
How to start a chart
Choose the characteristic
Start with one that matters: a special characteristic or one with a history of trouble. Do not chart everything.
Check the gauge first
A noisy gauge will fill the chart with false signals. Run a Gage R&R.
Pick the chart and the subgroup
Use the table above. For X-bar and R, take subgroups of consecutive parts, so variation inside a subgroup is short-term.
Collect about 20 to 25 subgroups
Over a stretch of normal running, before you calculate limits.
Calculate the limits
Use the formulas above or a workbook. Mark them on the chart.
Plot new points as they come
In real time, at the machine, by the person who made the parts.
Write down the reaction
What the operator does when a signal appears: stop, check, call, contain. Put it in the control plan.
Mistakes beginners make
- Putting the spec limits on the chart. It looks tidy and it hides the signals that matter.
- Reacting to every wiggle. Adjusting the process after each point makes the variation worse. React to signals, not to points that stay inside the limits.
- Recalculating the limits to make the problem go away. Only recalculate after a real, confirmed, permanent change to the process, and note why.
- Charting with no reaction plan. A chart no one acts on is wallpaper.
- Plotting from the office. Charts work when they are at the machine and used by the person who can respond.
The SPC Control Chart workbook builds the charts and applies the signal rules, and the SPC & Process Capability Bundle adds the capability study.
Questions people ask
What is the difference between control limits and specification limits?
Control limits describe what the process does. Specification limits describe what the customer will accept. They are calculated differently and answer different questions.
How many points do I need before I calculate limits?
About 20 to 25 subgroups from normal running is a common starting point.
What is an out-of-control process?
One where the chart shows a signal, such as a point outside the limits or a run on one side of the center, meaning something other than normal variation is at work.
Should I adjust the process when a point is near the limit?
Not for a point that is still inside it. Adjusting for ordinary variation adds more variation. Act on real signals.
Do I need SPC for every characteristic?
No. Use it where it pays: special characteristics, processes that drift and anything your customer requires.