Control Chart (Attribute)

Attribute Control Charts

Attribute control charts monitor processes with counted (not measured) data — number of defective units, number of defects per unit. They are the counterpart to Shewhart charts (I-MR, X̄-R) for variables data, separating random variation from systematic special causes.

p chart (fraction defective): Proportion of defective units per sample. Sample size may vary. Basis: binomial distribution. Example: daily production 1,000–2,000 pieces, number of rejects per day.

np chart (number defective): Absolute number of defective units with constant sample size n. Easier to interpret than the p chart, but only meaningful when n really is constant.

c chart (defects per unit, constant area): Number of defects per inspection unit when the inspection opportunity (area, length, volume, time) is constant. Basis: Poisson distribution. Example: paint defects per car body.

u chart (defects per unit, variable area): Defects per inspection unit when the opportunity varies (e.g. fabric rolls of different sizes). The chart plots defects/unit; control limits vary with the actual inspection size per point.

Variable control limits: for p and u charts with different sample sizes, UCL and LCL differ per point — the chart shows a stepped limit line. Zones A/B/C are not drawn because σ is not constant.

Approach

• Check the data type: are we counting defective units (p, np) or defect counts (c, u)?
• Check subgroup size: constant (np, c) or variable (p, u)?
• Collect at least 20–25 subgroups of baseline data for stable limits.
• For p/np: ensure n is large enough that n·p̄ ≥ 5 (otherwise limits are asymmetric and unreliable).
• Phase I: compute center line and limits from the baseline.
• Identify and exclude special causes, recompute limits if needed.
• Phase II: ongoing monitoring with fixed limits — new points are checked, not mixed back into the computation.

Rules and Evaluation

Attribute charts use the same principles as Shewhart charts: out-of-limit points, level shifts, and trends indicate special causes. Because of discrete counts and (for p/u) variable σ, the rule set is reduced.

• Rule 1: 1 point outside UCL/LCL — clear special cause.
• Rule 2: 9 consecutive points on the same side of the center line — level shift.
• Rule 3: 6 consecutive increasing or decreasing points — trend.
• Rules 5/6 (constant subgroup size only): zone-based early warnings, like on Shewhart charts.

Rule 4 (14 alternating) is not recommended for attribute charts because count data frequently produces ties. With variable subgroup size, zone-based rules 5–8 are not defined.

Pitfalls

Wrong chart type: p and np charts need fraction data (defective/not defective per unit). c and u charts need defect counts (multiple defects per unit possible). Mixing them yields wrong limits.

Too small n for p/np charts: When n·p̄ < 5 the binomial distribution is poorly approximated by a normal. The 3σ limits become asymmetric and can make the process look more stable than it is.

Constant limits on variable n: For p and u charts with varying sample size, limits must be computed per point. A blanket mean limit underestimates risk for small n and overestimates it for large n.

Ignoring overdispersion: When real variation is larger than binomial/Poisson predicts (heterogeneous samples, mixed sources), standard p/u charts trigger constant false alarms. Laney p'/u' charts help — not yet implemented.

Inconsistent defect definition: Counting "defects per unit" requires a clear definition of what counts. Shifting definitions (or inspectors) create variation that gets falsely attributed to the process.

Specification vs. control limits: On attribute charts too: UCL/LCL come from the data, not from a specification. "Less than 2% reject" is a spec, not a control limit.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Available in the following cycles

• DMAIC: Control
• DMADV: Verify
• 8D: D6 — Implementation