Common and special causes
Every process varies. Common-cause variation is the stable, inherent scatter of the process. Special-cause variation comes from something specific that changed — a new tool, a different material batch, a setup error. Control charts exist to tell the two apart so that you react to the second and leave the first alone.
Building an individuals chart
For single measurements, an individuals (I) chart plots each value against a centre line, usually the mean. Control limits are placed at ± 3σ, where σ is estimated from the average moving range between consecutive points (MR̄) divided by the constant 1.128: UCL = mean + 3·MR̄/1.128, LCL = mean − 3·MR̄/1.128. This within-subgroup estimate is the same short-term σ used for Cp and Cpk.
Run rules
A point beyond a control limit is a strong signal, but patterns matter too. Run rules flag, for example, a long run of consecutive points on one side of the centre line (commonly eight or nine, depending on the rule set), or a steady upward or downward trend. These catch gradual drift and small mean shifts before any point leaves the limits.
Drift versus mean shift
Drift is a gradual movement, typical of tool wear or thermal growth. A mean shift is a step change, typical after a tool change or setup. A chart shows both, and correlating the timing with events — tool changes, program changes, material batches — points to the cause.
Do not over-adjust
Adjusting a stable process because the last point was a little high or low adds variation rather than removing it. Corrections should respond to real signals, and automated corrections should use limits and filtering so they do not chase noise.
Standards and further reading
- Montgomery, D. C., Introduction to Statistical Quality Control
- AIAG Statistical Process Control (SPC) Reference Manual
- Western Electric Company, Statistical Quality Control Handbook