Control limits and alerts

You set up an alert system: "if picking errors exceed 8 a day, raise a signal." In the first week the signal arrives every day; by the second week nobody looks at it. That happens when the limit is set by gut feeling. A control limit is calculated from the metric's own usual variation and signals only when something genuinely changes.

How to calculate the limit

Take 20-30 days when work was stable and find two numbers: the mean and the standard deviation (σ). The limits are the mean ± 3σ.

Example: the warehouse of an online shop that picks and ships about 400 orders a day. Picking errors over 20 days: 4, 6, 3, 5, 7, 4, 5, 6, 2, 5, 4, 8, 5, 3, 6, 5, 4, 7, 5, 4. The total is 98, the mean 4.9 and the standard deviation about 1.48.

Upper limit: 4.9 + 3 × 1.48 ≈ 9.35. Lower limit: 4.9 − 4.45 ≈ 0.45, in practice zero. In Excel the AVERAGE and STDEV.S functions are enough. So up to 9 errors a day is ordinary variation, while 10 or more is outside the usual range.

On the chart, show the errors as a line and the mean and both limits as horizontal lines: where today's point sits is visible at a glance. Calculate the limit once rather than every day; otherwise it, too, "drifts" daily and hides the real change.

2σ or 3σ

Why 3σ? With a roughly normal distribution 99.7 percent of days fall inside this limit, so a chance excursion occurs about once in 370 days. With a 2σ limit a signal would arrive on 4.6 percent of days, about once every 22 days, even if nothing changed. That is crying wolf: a false alarm once a month teaches people not to trust it. So make 3σ the signal and 2σ only a "watch" marker.

Two rules

Rule one: a single point beyond 3σ. Say on the second day of observation there were 11 errors, above 9.35. Find the cause: a scanner broke, a new employee worked, or a new item in similar packaging arrived. One point is not yet a new level, but do not ignore it.

Rule two: eight points in a row on one side of the mean. Suppose over the next eight days errors are 6, 7, 6, 7, 6, 8, 7, 6. None exceeded 9.35, but all are above 4.9, and the average is 53 ÷ 8 ≈ 6.6. The process has quietly worsened by about 35 percent. A simple limit of "more than 9 errors" would never have signalled. The chance of eight days in a row on one side is (1/2)^8 ≈ 0.4 percent, close to 3σ, so the rule is sound.

Both rules rely on a stable baseline. If something happened during the first 20 days (a warehouse move, say), the limit comes out wider and fewer signals arrive.

A limit is not a target

A control limit says what the process is doing now; a target says what you want to achieve. The limit may be 9 while the target is no more than 3 errors a day. You cannot lower the limit on paper to the target: the signal would then arrive every day. To reach the target you have to change the process (the picking method, labels, rack layout), and recalculate the limit from new data afterwards.

What to do with a signal

• One owner and one action: after a signal the owner records the cause in a log within a working day.
• Exclude days with known events (a broken scanner, a technical outage) from the limit calculation.
• If the number of orders swings sharply, track errors per 100 orders instead of errors per day.
• Recalculate the limit every quarter and after any change to the process.

Conclusion

A good alert is rare, but when it comes it is taken seriously. Set the limit from data, not by feel, keep the rules few and clear, and give every signal an owner. In its management report and discrepancy analysis, CountLab calculates the usual variation of the metrics and helps set limits for internal control.