What it means
Every process varies a little. Invoices take slightly different amounts of time to process, and machines produce parts that are not perfectly identical.
The challenge is to know when a change is just noise and when something has gone wrong. A control chart answers this by showing a centre line, which is the average, with an upper control limit and a lower control limit set at three standard deviations above and below it.
A standard deviation measures how spread out the data is around the average. If a process is stable, nearly all points should fall inside the limits.
When a point lands outside the limits, or several points in a row drift in one direction, the process is said to be out of control. That does not necessarily mean the output is bad, only that something has changed.
The team then looks for a cause, such as new staff, a faulty machine or a change in supplier. Finance and operations teams use these charts for more than factory output.
They track the cost of processing an order, the time to close the books, the rate of invoice errors and the accuracy of forecasts. A stable, in-control process is easier to budget for because its results are predictable.
Do not confuse control limits with targets or specification limits. Control limits come from the process's own history and show what it is doing, while targets show what the business wants.
A process can be perfectly stable and still miss its target, in which case the process needs redesigning, not just monitoring. Charts need care in set-up.
The limits should be calculated from a period when the process was behaving normally, and they should be recalculated only after a genuine improvement has been made. Otherwise the chart may either hide problems or raise false alarms.
In practice
Real-world examples.
Example
An accounts payable team plots the weekly cost per invoice. When the cost rises above the upper limit for two weeks, the manager discovers that a new approval step has created delays and extra handling.
Example
A bakery chain charts the weight of its loaves. A run of points near the lower limit shows that an oven is losing moisture, and the maintenance team is called before customers notice.
Example
A finance team charts the number of days taken to close the monthly books. The chart shows that close time is stable at six days, so the director decides to redesign the process if she wants it to be faster. She also notes the date on the chart so everyone can see when the process changed.
Formula
Calculation
Upper control limit = average + 3 x standard deviation
Lower control limit = average - 3 x standard deviation
Suppose the average cost to process an invoice is $8.00, with a standard deviation of $0.50. The upper control limit is 8.00 + (3 x 0.50) = 8.00 + 1.50 = $9.50. The lower control limit is 8.00 - 1.50 = $6.50. If one week's average cost is $10.10, it is above $9.50 and outside the limits, so the team investigates.Case study
Seen in the real world.
Eastwind Components is an illustrative, fictional manufacturer that struggled with returns of faulty parts. The quality manager began plotting the daily defect rate on a control chart, using an average of 2.0% and a standard deviation of 0.4 percentage points.
The upper control limit was 2.0 + (3 x 0.4) = 3.2%. For two weeks, the rate hovered between 2.8% and 3.1%, which was inside the limit, but a run of eight points above the average suggested a shift.
The team investigated and found that a new batch of raw material had slightly different properties. They switched supplier, and the defect rate returned to 2.0%. The illustrative lesson is that the chart flagged a problem before any single point broke the limit. The quality manager also recalculated the limits after the supplier change, since the process had genuinely improved and the old limits no longer described it. The finance team later borrowed the same chart for its monthly payroll error counts.
Watch out
Common mistakes.
- Reacting to every small movement within the limits, which wastes effort chasing normal variation.
- Confusing control limits with targets, when the limits describe what the process does and not what the business wants.
- Calculating limits from too little data, which gives unreliable results.
Questions
People also ask.
What does out of control mean?
It means the process has changed in a way that normal variation does not explain, not necessarily that the output is bad.
Can a chart be used outside manufacturing?
Yes, finance, sales and service teams use them to monitor costs, errors, delays and forecast accuracy.
Why three standard deviations?
In a stable process nearly all points fall within three standard deviations, so a point outside is a strong signal.
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