Statistical Process Control for People Who Do Not Like Statistics

Statistical process control rests on a single idea that takes a while to accept: some variation is inherent to the process and reacting to it makes things worse. The entire apparatus of control charts exists to tell you which kind of variation you are looking at.

Common cause versus special cause

Common cause variation is the natural noise of a stable process — it is predictable in range even though each individual value is not. Special cause variation comes from something identifiable: a new operator, a worn tool, a different material lot. Adjusting a process in response to common cause variation is called tampering, and it provably increases variation. This is the most valuable thing SPC teaches, and it is free.

Choose the right chart

Using a p chart for measurement data — for example, converting a fabric GSM reading into pass/fail and charting the pass rate — throws away most of the information you paid to collect. Chart the measurement.

Set limits once, then leave them alone

Control limits come from the process, not from the specification. For an X-bar chart, limits are the grand average plus or minus A2 times the average range, where A2 is a constant that depends on subgroup size (0.577 for n=5). Compute them from at least 20 to 25 subgroups collected while the process was behaving.

Then stop recalculating them. Recalculating limits every month absorbs deterioration into the baseline and the chart slowly stops detecting anything. Recompute only after a deliberate process change, and mark the change point on the chart.

Control limits are not specification limits

This confusion causes more damage than any other. Control limits tell you what the process does. Specification limits tell you what the customer needs. A process can be perfectly in control and produce entirely out-of-specification product. Never draw specification limits on a control chart — it invites exactly the wrong reaction.

The signal rules worth using

There are eight standard Western Electric rules. Using all eight raises the false alarm rate to the point where operators stop believing the chart. Use these four:

1. Any point beyond three sigma.
2. Nine consecutive points on the same side of the centre line.
3. Six consecutive points steadily increasing or decreasing.
4. Two of three consecutive points beyond two sigma on the same side.

Rule 2 is the one that catches a slow drift long before rule 1 does, and it is the reason charts beat simple tolerance checks.

Capability, once you are stable

Capability indices are meaningless on an unstable process, because they describe a distribution that does not exist. Once the chart is in control:

Cp  = (USL - LSL) / (6 * sigma)          -- potential, ignores centring
Cpk = min[ (USL - mu), (mu - LSL) ] / (3 * sigma)   -- actual, includes centring

A Cp of 1.8 with a Cpk of 0.9 is a centring problem, and centring problems are usually cheap to fix. A Cp of 0.9 is a variation problem, and those are expensive. Reporting only Cpk hides which one you have.

Making it stick on the floor

Charts maintained by the quality department in an office are decoration. Charts plotted by the operator at the machine, on paper, with a pen, are a control system. The act of plotting is what creates the attention. Digitise later, after the habit exists.