Statistical Process Control

Statistical Process Control

Overview

Pure-Python SPC helpers:

• Individuals chart (I-MR) with control limits from the moving range.
• X-bar / R chart with constants from the standard SPC tables.
• Cp and Cpk capability indices.

The chart constants (A2, D3, D4, d2, etc.) are public-domain values widely republished in textbooks; verify against your quality system's standard before regulated reporting.

Prerequisites

1. uv available.

When to Use

• Computing control limits for a new chart.
• Estimating Cp / Cpk for a stable process with bilateral spec limits.
• Sanity-checking a vendor SPC report.

Don't use for

• Autocorrelated process data (time-series-process-data-analysis first).
• Left-censored or interval-censored measurements

(censored-regression).

• Attribute (count / defective) charts (p, np, c, u charts not

implemented).

• Multivariate SPC (Hotelling T², MEWMA — not implemented).

Utility Scripts

• uv run scripts/spc.py individuals --values "12.3,12.5,12.1,12.4,12.6,12.2" --output /tmp/i.json
• uv run scripts/spc.py xbar-r --subgroups "12.3,12.5,12.1|12.4,12.6,12.2|12.2,12.4,12.3" --output /tmp/xr.json
• uv run scripts/spc.py capability --values "12.3,..." --usl 13 --lsl 11 --output /tmp/cap.json

Procedure

1. Confirm the process is stable (no obvious shifts, trends, autocorr).
2. Pick chart type:

• Individuals (I-MR) for one measurement per sample.
• X-bar / R for rational subgroups of 2-10.

1. Compute control limits from a stable baseline window (Phase I); apply

in real time (Phase II).

1. For capability, ensure the process is centred between spec limits;

compute Cp and Cpk.

1. Flag out-of-control signals: points beyond 3-sigma, runs of 7+ on the

same side of the centre line, etc. (Western Electric rules).

Pitfalls

• Computing Cp / Cpk on a process that is not in statistical control

(Phase I diagnostics first).

• Using a one-sigma limit ("99.7% will be in tolerance") when the

underlying distribution is not normal.

• Mixing Phase I (limit estimation) and Phase II (limit application) data.
• Treating Cpk as Cp when only one spec limit applies.
• Ignoring the moving-range constant d2 = 1.128 for n = 2.
• Computing X-bar / R with unequal subgroup sizes (the chart constants

assume equal n).

• Applying control limits to data with strong autocorrelation; the limits

become too tight or too wide.

• Reporting Cp / Cpk with too few data points (< ~30 ideally).

Fallback Strategies

• If autocorrelation is suspected, use time-series-process-data-analysis

to compute ACF; if significant, apply a pre-whitening filter (e.g. ARIMA residuals) before SPC.

• If censoring is suspected, see censored-regression.

Verification

• Run the listed script with representative inputs and an --output file when a deterministic calculation is available.
• Confirm the JSON result contains ok: true, expected units, and no unhandled warnings.
• Check result magnitudes against the stated assumptions, references, and a hand calculation or known operating range before reporting them.

References

• references/control_charts.md — chart constants and formulas.
• Montgomery, Introduction to Statistical Quality Control.

Anti-Patterns

• Reporting "process out of control" from a single point beyond 3-sigma

without checking measurement quality.

• Computing Cpk on visibly bimodal data.
• Using SPC limits to decide on a process change instead of as a

monitoring tool.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: jskherman
• Source: jskherman/engg-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.