Statistical Process Control

Statistical Process Control (manufacturing-quality/as9100/statistical-process-control)

Use when the task is monitoring an aerospace production process with variable control charts: subgroup data feeds X-bar and R chart limits, the average range gives the process sigma, and the capability indices Cp and Cpk score the process against the specification limits.

Domain quick reference

• X-bar chart limits from the subgroup average xbar and the average range rbar: UCL = xbar + A2 * rbar, LCL = xbar - A2 * rbar.
• R chart limits: UCL = D4 * rbar, LCL = D3 * rbar.
• Process standard deviation estimate from the average range: sigma = rbar / d2.
• Capability indices: Cp = (USL - LSL) / (6 * sigma), CPU = (USL - xbar) / (3 * sigma), CPL = (xbar - LSL) / (3 * sigma), Cpk = min(CPU, CPL).
• Constants A2, D3, D4, d2 depend on the subgroup size n; the module table covers n = 2 through 10, the usual aerospace sampling range.
• Out-of-control rules (Western Electric): one point beyond 3 sigma, eight consecutive points on one side of the centerline, two of three points beyond 2 sigma on one side, four of five points beyond 1 sigma on one side.
• AS9100 clause 8.5.1 frames production process control; SPC charts are the common aerospace evidence that a special process stays in statistical control, summarized here without clause text.

Workflow

1. Collect the subgroup averages, the average range, and the subgroup size n (2 through 10).
2. Compute the X-bar and R chart control limits with xbar_r_limits.
3. Estimate the process sigma from the average range with process_sigma.
4. Compute Cp, CPU, CPL, and Cpk with capability_indices against the specification limits USL and LSL.
5. Detect out-of-control conditions on a point sequence with out_of_control_rules.
6. Validate inputs first: a subgroup size outside 2-10, a negative range, or inverted specification limits raise ValueError.

Pitfalls

• Using a subgroup size outside the constants table: sizes 2-10 are supported; an unsupported n raises ValueError instead of returning bogus limits.
• Confusing the R chart limits with the X-bar limits: R chart limits come from D3 and D4, never from A2.
• Computing Cpk without the process sigma estimate: capability indices need the range-derived sigma, not the sample standard deviation of the subgroup means.
• Inverting the specification limits: USL must exceed LSL or the capability indices are meaningless.
• Reading the Western Electric rules as point rules only: the consecutive-point rules need the run context, not single points.
• A zero average range with a subgroup of identical parts: sigma becomes zero and the capability indices divide by zero.

Behavior contract (gate 3)

The SPC logic is exercised by the gate 3 contract test: scripts/test_statistical_process_control.py against scripts/statistical_process_control_logic.py (stdlib unittest, offline). Run: python3 scripts/test_statistical_process_control.py

Compliance

• Standards referenced, not reproduced: AS9100 clause 8.5.1 frames production process control; the chart constants and capability formulas are common SPC methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.