The eight out of control tests on a Shewhart chart

Updated: August 4, 2026 · ISKRIT

A point outside a control limit is only the first of eight signals. The other seven detect patterns that stay inside the limits, and they are what make a control chart more sensitive than a simple tolerance check.

Zones

The band between the centre line and each control limit is split into three equal zones, each one sigma wide. Zone C is nearest the centre line, zone B is the middle, zone A is the outermost, up against the limit. The tests are written in terms of these zones on both sides of the chart.

The eight tests

The two counter-intuitive ones

Tests 7 and 8 flag data that looks too good and data that avoids the middle. Fifteen consecutive points hugging the centre line is not a well behaved process, it usually means the limits were calculated from a period that contained extra variation, or that subgroups were formed across sources that cancel each other. Test 8 is its mirror: points sit away from the centre on both sides, which is the signature of two processes plotted on one chart, two shifts, two instruments, two operators.

The cost of running all eight

Each test has its own false alarm probability, and they add up. Test 1 alone gives roughly one false signal in 370 points. Enabling all eight brings the combined rate to something closer to one in 90. That is a deliberate trade: more sensitivity to real shifts, more investigations that find nothing. A laboratory running daily control samples should decide which tests it applies and write that decision into its procedure, rather than switching them on and off after the fact.

Questions

Do the tests apply to range charts too? Test 1 always does; the run tests are normally applied to the averages chart, since the range distribution is skewed and the zone logic assumes symmetry.

What comes after a signal? Find the special cause. Recomputing limits to make the signal disappear is the one response that guarantees the chart stops working.

All eight are checked automatically, with the indices of the points involved, in the control chart tool.