Track 15 · Applied Statistics for Professionals · Lesson 7 of 12
Statistical process control
Build X̄–R, I-MR, p, c and u control charts, apply the Western Electric rules, and tell a process signal from routine variation.
A workshop turns steel shafts that must measure 25.00 mm ± 0.05 mm. Almost every part is still inside the specification, yet one lathe has quietly drifted upwards. A control chart is the tool that notices the drift weeks before the first scrapped part — and that stops engineers from "fixing" a machine that is only showing normal noise.
Every process varies. Walter Shewhart's insight was to separate two kinds of variation:
- Common-cause variation: the many small, ever-present influences (material, temperature, vibration) that make no two parts identical. It is predictable as a band, not part by part.
- Special-cause (assignable-cause) variation: something that changed — a worn tool, a new operator, a bad batch. It is worth finding and removing.
A control chart plots a statistic over time with a centre line and control limits about 3 standard errors either side. While the points behave like random scatter inside the limits, the process is in statistical control (stable). A point outside, or a non-random pattern, is a signal to look for a special cause.
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It has 9 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Separate common-cause from special-cause variation and explain what a control chart detects
- Compute X̄–R, I-MR and p-chart limits and set them from a stable Phase I baseline
- Apply the Western Electric rules and recognise false alarms and tampering
- Choose between p, c and u charts and explain why control limits are not specification limits