Specialty › Quality control

SPC control charts (Xbar-R/S, I-MR, EWMA, CUSUM, p/np/c/u)

Statistical process control charts track a process over time — Shewhart variable charts (I-MR, Xbar-R, Xbar-S), attribute charts (p, np, c, u) and the time-weighted EWMA and CUSUM — flagging control-limit and run-rule violations.

What is SPC control charts (Xbar-R/S, I-MR, EWMA, CUSUM, p/np/c/u)?

A control chart separates common-cause variation (inherent noise) from special-cause variation (something changed). Points are plotted in time order against ±3σ control limits computed from the data's own short-term variation — not the spec limits. Xbar-R/S monitor subgroup means with a paired dispersion chart; I-MR handles individual measurements via the moving range.

Shewhart charts react quickly to large shifts but are slow on small sustained ones — that's what EWMA (an exponentially weighted average) and CUSUM (cumulative sums above/below target) are for: they accumulate evidence across points and detect shifts of ~1σ far sooner.

Attribute charts monitor counts: p/np for the proportion/number of defective units per lot, c/u for the number/rate of defects per inspection unit.

When should I use SPC control charts (Xbar-R/S, I-MR, EWMA, CUSUM, p/np/c/u)?

  • Ongoing monitoring of any repeated measurement or count in time order.
  • Establishing whether a process is in statistical control before a capability study.
  • Small sustained shifts (tool wear, slow drift) — use EWMA or CUSUM.

What data does it need?

A measurement/count column in time order + chart type; subgroup size (Xbar charts), a lot-size column (p/np/u), λ (EWMA), or k and h (CUSUM).

What does it report?

The control chart with centre line, ±3σ limits, and flagged violations (beyond-limit points; run-rule points), plus the paired R/S/MR chart where applicable.

What does it assume?

  • Observations in time order, from one process stream.
  • Limits assume approximate normality (variable charts) or binomial/Poisson counts (attribute charts).
  • Control limits should be established from an in-control baseline period.

How do I interpret the result?

A point beyond the limits or a run-rule signal means a special cause — investigate that sample. Never confuse control limits (voice of the process) with spec limits (voice of the customer).

See also

References

  • Shewhart (1931). Economic Control of Quality of Manufactured Product.
  • Montgomery (2020). Introduction to Statistical Quality Control, 8th ed.