Statistics

SPC — statistical process control

In French: MSP — maîtrise statistique des procédés

Statistical process control tracks a process over time by means of control charts, so as to distinguish its normal variability from the events that warrant intervention.

Two causes of variation, two responses

Common causes are inherent in the process: they act permanently, on every part, and produce a regular variation. They are not treated one at a time — reducing them requires changing the process itself.

Special causes are one-off and identifiable: a tool wearing, a different batch of material, a changed setting. They are dealt with case by case, and that is what the control chart serves to detect.

The whole value of the method lies in that distinction. Reacting to a common cause as if it were a special cause — adjusting the machine because one part deviates a little — increases variability instead of reducing it. Ignoring a special cause, conversely, lets the process drift.

What a control chart is

It is a chart of the measurements in time order, with a centre line and two control limits. The limits are calculated from the observed variability of the process itself: they describe what it is capable of, not what is expected of it.

The choice of chart follows the nature of the data. For continuous measurements, the mean-and-range chart tracks a regular sample; the individuals chart suits when each measurement is unique. For counts — defective parts, number of defects — other charts apply, with limits calculated differently.

A point outside the limits is not the only signal. A run of points on the same side of the centre line, a continuous trend, a regular alternation: these patterns signal a special cause well before a point goes out, and they are what gives the tool its finesse.

Control limits and tolerances: nothing to do with each other

This is the most widespread confusion, and it empties the method of its meaning. Tolerances come from the customer or the design office: they say what is acceptable. Control limits come from the process: they say what it is spontaneously capable of.

The two are not compared on the same chart — bringing them together is the role of capability. Setting tolerances as the limits of a control chart produces a tool that no longer detects anything as long as the process is wide, and that panics as soon as it is tight.

The control limits, for individual values

Upper control limit UCL = x̄ + 3σ

Centre line CL = x̄

Lower control limit LCL = x̄ − 3σ

Three standard deviations: beyond that, a stable process produces points only very rarely, so an excursion deserves a look. σ is estimated from the short-term variability of the process — the standard deviation of all the data, for its part, includes the drifts one is precisely trying to detect.

The common mistakes

Recalculating the limits at every new point. The limits describe a reference state: updating them continuously makes them absorb the drift they should signal, and the chart ends up declaring normal everything the process does.

Putting a control chart on a process that cannot be corrected. A chart with no planned reaction is a decorative graph; its reason for being is the action it triggers.

On the shop floor — Plastic injection moulding

An individuals chart showed eight consecutive points above the centre line, all within tolerance. No final inspection would have flagged anything. The cause was a mould beginning to wear: treated at that moment, it avoided the stoppage that would have occurred three weeks later.

The other tools illustrated by this trade: plastics and chemicals.

Frequently asked questions

What is the difference between SPC and capability?

SPC looks at stability over time, capability looks at the ability to hold the tolerances. A process can be perfectly stable and incapable — it always does the same thing, and that thing is out of tolerance. The order counts: measuring a capability on an unstable process gives a meaningless figure, since it changes from one day to the next.

How many points are needed to set the limits?

About twenty points at a minimum, and preferably about thirty, sampled over a period representative of normal operation. Setting limits on ten points taken in the same hour describes that hour and will trigger false alarms from the next day.

What should be done when a point goes outside the limits?

Look for the cause before adjusting anything. The reflex — correcting the machine — treats the symptom and often adds variability. The useful sequence is: check the measurement, look for what has changed, act on the cause, then note the event on the chart so that the next person knows.

Does SPC apply outside production?

Yes, as soon as a quantity is tracked over time: processing time, error rate, number of dropped calls. The difficulty is not the method but the measurement frequency — a chart fed once a month no longer detects anything usable.