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Glossary · S

Statistical process control (SPC)

Engineering track

In plain words

Watching production measurements with statistics, so that a slow drift is spotted and corrected before it starts producing faulty parts.

Going deeper

A control chart: measurements plotted in order with a mean line and upper and lower control limits, scattering harmlessly at first and then drifting upward across the upper limit. watching for a drift, not a failure upper limit the mean lower limit one measurement after another the drift is visible, and acted on, long before anything is out of specification limits from the process, not the spec the control limits are calculated from how much the process varies when nothing is wrong – they are not the tolerances a point outside them means something has changed and can be found: a new batch, a drifting furnace, a different operator runs and trends inside the limits count too, and catch slower changes reacting to ordinary scatter as if it meant something makes the process worse: that is the mistake the chart exists to prevent, and the one most often made
A control chart separates the scatter a process always has from a change that has a cause. The limits come from the process’s own behaviour, not from the specification, which is what makes a drift visible long before anything is out of tolerance.

Two kinds of variation

Shewhart’s insight in the 1920s was that variation comes in two kinds, and that confusing them makes things worse. Common-cause variation is the scatter a stable process always shows: it has no single cause, and chasing individual points is not only futile but actively harmful, because adjusting a stable process in response to noise increases its variability. Assignable-cause variation comes from something that changed – a new batch of precursor, a drifting furnace, a different operator – and can be found and removed.

A control chart is a tool for telling them apart. Measurements are plotted in the order they were taken, with a centre line and limits calculated from the process’s own short-term variation, conventionally at three standard deviations of the plotted statistic. Inside the limits, leave it alone. Outside, go and look.

Limits are not tolerances

The single most common misunderstanding is to draw the specification limits on the chart and call them control limits. They are unrelated. Control limits describe what the process does; specification limits describe what the customer will accept. A process can be in perfect statistical control and produce nothing but scrap, or be wildly out of control and still be inside specification for now.

Keeping them separate is what gives the chart its value: it detects a change while the output is still acceptable, which is the only time correction is cheap. The signals are not limited to points outside the limits – runs of points on one side of the centre line, steady trends, and unusual patterns all indicate that something has changed, and the standard rule sets trade off sensitivity against false alarms.

Open disagreements, and the research case

It is worth knowing that the field argues with itself. Whether a control chart is best understood as a sequence of hypothesis tests or as Shewhart intended it, how chart performance should be modelled, how the alternatives compare – cumulative-sum and exponentially-weighted charts detect small persistent shifts faster than a Shewhart chart – and how much of the academic literature is relevant to practice, have all been the subject of long and sometimes sharp disputes. A summary that presents SPC as a settled recipe is hiding that.

In a research laboratory the objection is usually that there are too few runs for statistics. That is true for a first experiment and false for a process anyone intends to repeat. Plotting the same measurement – a peak position, a growth’s coverage, a – run after run, with limits from the first stable stretch, costs nothing and catches the slow drift that otherwise gets discovered months later as an unexplained difference between students.

For specialists

Monitoring process parameters statistically to detect drift before it causes defects.

Where this comes from

  1. Economic control of quality of manufactured product Shewhart · Van Nostrand, New York (1931)
  2. Controversies and contradictions in statistical process control Woodall · Journal of Quality Technology 32, 341 (2000) cited by 510