SPC / Process Capability Analyzer

Try it live -> spc-analyzer.streamlit.app — no install. The Gage R&R page opens on the AIAG reference study and reproduces Minitab's published results without any input.

Free, open-source statistics for the three questions a supplier answers before shipping a new part: is the gauge good enough (Gage R&R), is the process stable (SPC charts), and is it capable (Cp/Cpk vs Pp/Ppk). Every method is checked against published results, and every output is a defensible engineering statement, not just a chart:

"Cpk = 1.09 from within-subgroup sigma, but the individuals chart shows an N1 outlier and an N2 run — this Cpk is not trustworthy evidence of future performance until the process is stabilized."

It is intended for quality/manufacturing/process engineers who need SPC charts, Cp/Cpk vs Pp/Ppk analysis, stability assessment, and audit-ready reports from production measurement data.

Key features

• Gage R&R (crossed): ANOVA (random-effects F tests, interaction pooled at p > 0.25 by convention) and the AIAG Average & Range method. Reports EV, AV, interaction, GRR, PV, %Contribution, %Study Var, %Tolerance (k = 6 or 5.15) and ndc. A range chart checks repeat readings before anything is concluded. Verified to the published decimal against Minitab, SAS and BPI analyses of two reference studies.
• Control charts: X̄–R, X̄–S, and I–MR with proper 3σ limits from the published control-chart constants (never plain ±3·stdev of the plotted data).
• Run-rule engine: full Western Electric (4 rules) and Nelson (8 rules) sets, kept distinct (WE4 = 8-in-a-row ≠ Nelson N2 = 9-in-a-row), with structured violations: rule ID, name, affected observations, direction, explanation. Overlapping violations are preserved.
• Capability vs performance, never interchanged: Cp/Cpk from within-subgroup sigma (R̄/d₂, S̄/c₄, pooled, or MR̄/d₂ by regime); Pp/Ppk from overall sigma. One-sided specifications handled correctly (no fake Cp/Pp).
• Stability before capability: SPC rules are evaluated first, and every capability result carries the stability verdict. A high Cpk on an unstable process is explicitly caveated, never silently reported as "capable".
• Sigma level / DPMO (Z-bench from the normal model; the 1.5σ shift is an opt-in, clearly-labeled convention).
• Cpk confidence interval (Bissell 1990 / Montgomery approximation, flagged as approximate, with its assumptions attached).
• Deterministic interpretation engine — rule-based, reproducible, no LLM: statistical conclusions (facts) strictly separated from engineering recommendations (advice), each with a stable trigger code and severity.
• Reliability guards: small-sample, few-subgroups, zero-variation, non-normality (Shapiro–Wilk + Anderson–Darling), and instability warnings — advisory, never suppressing the numbers.
• Reporting: full-precision CSV, 7-sheet Excel workbook, professional PDF report with embedded charts, plus PNG/SVG chart export.
• Streamlit UI with data import (CSV/Excel/manual), cleaning transparency (every excluded row listed with its reason), and configurable thresholds.

PPAP scenario: the gauge first, then the process

A supplier launching a part for an automotive customer must show, for every critical characteristic, that the measurement system is adequate and that the process is capable. The order matters. A capability study run with an unproven gauge measures the gauge as much as the process. The usual bar is a Gage R&R under 10% (10-30% only with customer approval) followed by an initial process study with Ppk of at least 1.67. Customer-specific requirements take precedence.

The AIAG reference study, opened by default on the Gage R&R page, shows what the tool does with a gauge that is not ready:

1. Repeat readings first. The range chart flags appraiser B on part 4 (0.01, 1.03, 0.20 → R = 1.02, above the UCL of 0.88). Every figure below is reported with that caveat until the cell is explained or re-measured.
2. Verdict. GRR is 27.9% of study variation and 22.7% of the tolerance: may be acceptable depending on the application. ndc = 4 (< 5): the gauge cannot reliably tell these parts apart.
3. Where the variation comes from. Repeatability (18.4%) and reproducibility (20.9%) are comparable, so the recommendation is to work on the gauge set-up and the measurement method together. The interaction plot shows where to start on the method: appraiser C reads lowest on all ten parts (average −0.25 against +0.19 for A).

Only once the study passes does the tool recommend proceeding to the capability study on the other page.

Architecture

Data input (CSV / Excel / manual)
        ↓
app/data        validation & cleaning (per-row records, nothing silently dropped)
        ↓
app/statistics  descriptive stats · control-chart constants · sigma estimators
        ↓
app/spc         control limits (X̄–R, X̄–S, I–MR) · WE/Nelson rule engine
        ↓
app/capability  Cp/Cpk (within σ) · Pp/Ppk (overall σ) · guards · Cpk CI
app/msa         Gage R&R: ANOVA · Average & Range · range check · ndc
        ↓
app/interpret   deterministic conclusions ⟂ recommendations
        ↓
app/reporting   CSV · Excel · PDF serialization (no statistics recomputed)
        ↓
app/ui          Streamlit presentation (thin; calls app/services only)

Dependencies point downward only. The statistical core (data, statistics, spc, capability, msa, interpret) is pure Python with no UI or I/O dependency and is fully unit-tested. app/services orchestrates the sequence-of-analysis (validate → charts → stability first → sigma → capability → interpretation); app/charts renders validated results without recalculating them; app/reporting serializes without recomputing. Each layer has exactly one source of truth: limits come from app/spc, capability from app/capability, charts from app/charts, interpretation from app/interpret.

The complete statistical methodology — every formula, constant, assumption, convention, and reference — is documented in docs/FORMULAS.md.

Installation

Requires Python 3.10+. On Windows (PowerShell or git-bash):

git clone <repository-url> spc-analyzer
cd spc-analyzer

# Create and activate a virtual environment
python -m venv .venv
source .venv/Scripts/activate        # git-bash
# .venv\Scripts\Activate.ps1         # PowerShell
# source .venv/bin/activate          # Linux/macOS

# Install dependencies
pip install -r requirements.txt

Run the application:

streamlit run app/ui/streamlit_app.py

The app opens at http://localhost:8501.

Usage

A typical analysis session:

1. Upload measurements (section 1) — CSV/Excel file or manual entry; select the measurement column. The cleaning summary shows exactly how many rows are usable and why any were excluded.
2. Enter specifications (section 2) — USL and/or LSL, optional nominal, measurement unit, and traceability metadata (characteristic, part, machine, operator).
3. Select the SPC chart (sidebar) — X̄–R, X̄–S, or I–MR, subgroup size, rule set (Nelson / Western Electric / both), and within-σ estimator.
4. Review stability (section 5) — control charts with CL/UCL/LCL, flagged out-of-control points, and the violations table.
5. Review capability (section 6) — Cp/Cpk (within) beside Pp/Ppk (overall), sigma level, DPMO, the Cpk confidence interval, and all reliability warnings.
6. Review the interpretation (section 7) — factual statistical conclusions and, separately, engineering recommendations with their triggers.
7. Export (section 8) — CSV, Excel, PDF report, or PNG/SVG charts.

For a Gage R&R study, switch to the Gage R&R (MSA) page. Upload a long-format file with one row per reading (part, operator, measurement, optional trial), choose the method, and optionally enter the tolerance. A missing reading is reported by row rather than dropped, because a crossed study must be balanced. Results export to CSV and Excel.

Example

Verification against published results

examples/pistonrings.csv holds 200 real piston-ring diameter measurements (40 samples of 5) from an automotive forging process, taken from the qcc package and originally published as Montgomery's worked X-bar/R example. Because the reference results are published, the dataset doubles as an end-to-end check on this implementation. Analyzed as X-bar/R with subgroup size 5:

quantity	published	this application
x-bar-bar	74.001	74.00118
R-bar	0.023	0.02276
UCL (X-bar)	74.014	74.01431
LCL (X-bar)	73.988	73.98804

Phase I (samples 1-25) is reported stable with no rule violations, Cp 1.70 / Cpk 1.66; including the Phase II samples the drift is caught as N1/N5/N6 and the capability verdict is caveated accordingly. See examples/DATASETS.md.

Gage R&R verification against published results

Two reference studies ship in examples/, each with independently published analyses (examples/DATASETS.md):

study	published analysis	what matches
AIAG MSA 4th ed. example (10 parts × 3 appraisers × 3 trials)	Minitab, Example of Crossed Gage R&R Study	every ANOVA SS/MS/F/p in both models; every variance component, %Contribution, %Study Var and %Tolerance; ndc = 4
same	BPI Consulting (2015), Average & Range	EV 0.202, AV 0.230, GRR 0.306, PV 1.105, TV 1.146, %GRR 26.68
Houf & Burman (1988), thermal impedance	SAS/STAT PROC VARCOMP Example 121.2	all four variance components, GRR, precision-to-tolerance 0.20145

The ANOVA is additionally checked against statsmodels on simulated studies, and a Monte Carlo test checks that the variance-component estimators are unbiased.

Synthetic rule-engine example

The repository also ships examples/sample_measurements.csv (58 observations: a stable process seeded with one gross outlier and a sustained shift at the end). Analyzed as I–MR with USL = 11.5, LSL = 8.5 (mm), the application reports:

• Stability: UNSTABLE — rules N1, N2, N4, N5, N6 triggered (the outlier and the tail shift are both caught).
• Capability: Cpk ≈ 1.09 (within), Ppk ≈ 0.88 (overall) — reported but explicitly caveated as unreliable while the process is out of control.
• Headline: "Process is statistically UNSTABLE; capability indices are retained but are not reliable evidence of future performance until the process is brought into control."

The chart image above is the actual output for this dataset.

Testing

python -m pytest

The suite currently contains 890 tests (all passing, on Python 3.10 / 3.11 / 3.12 in CI), covering:

• known-answer verification of every statistic against independently hand-computed values (constants are additionally cross-validated against their exact mathematical definitions),
• every WE/Nelson rule triggered by crafted deterministic sequences,
• the Cp/Cpk-vs-Pp/Ppk separation (including a test proving Pp/Ppk cannot be affected by the within-subgroup sigma),
• edge cases: missing/non-numeric values, duplicates, tiny samples, zero variation, one-sided and invalid specifications,
• chart-model fidelity (rendered values bit-identical to the calculators),
• interpretation scenarios asserting on structured codes, not prose,
• full-pipeline integration tests (CSV → analysis → interpretation → CSV/Excel/ PDF), with PDF content verified by text extraction,
• Gage R&R against two published studies (Minitab, SAS, BPI), an independent ANOVA implementation (statsmodels, stored as fixtures), a hand-computed study and a Monte Carlo unbiasedness check,
• execution of the real Streamlit pages via Streamlit's AppTest harness.

Code-coverage percentages are not claimed because coverage is not currently measured.

Statistical disclaimer

• Stability and capability are different questions. SPC control charts ask "is the process statistically stable/predictable?"; capability indices ask "can the stable process meet the specification?". An unstable process should not be treated as reliably capable regardless of its Cpk.
• Capability indices assume the relevant statistical conditions — approximately normal data, rational subgrouping, and statistical control. The application tests and warns about these assumptions but cannot make an invalid assumption true.
• Capability thresholds (e.g. Cpk ≥ 1.33 "capable") are engineering conventions that vary by industry and customer standard; they are configurable in the app and are not universal statistical laws.
• The Cpk confidence interval is a large-sample approximation and is not exact.
• Gage R&R covers crossed, balanced studies of variable data only. Attribute agreement, nested designs, linearity and bias studies are not implemented. The %GRR bands (10% / 30%) and ndc ≥ 5 are AIAG conventions, configurable in the app, and are applied to %Study Var, not %Contribution.
• This software is an engineering analysis aid. It does not replace professional engineering judgment or customer-specific quality requirements.

License

Apache License 2.0 — see LICENSE and NOTICE.

Apache 2.0 was chosen over MIT deliberately: it carries an explicit patent grant (§3) and a fuller warranty/liability disclaimer (§§7–8), which matter for a tool whose output informs manufacturing quality decisions. Every runtime dependency is permissively licensed (BSD / MIT / PSF / Apache-2.0), so there is no copyleft obligation.

References

Montgomery, D.C., Introduction to Statistical Quality Control, 7th ed. (Wiley, 2013) · AIAG, Statistical Process Control Reference Manual, 2nd ed. (2005) · NIST/SEMATECH e-Handbook of Statistical Methods, §6 · David & Nagaraja, Order Statistics, 3rd ed. (Wiley, 2003) · Bissell, A.F., "How reliable is your capability index?", Applied Statistics 39(3), 1990 · ASTM, Manual on Presentation of Data and Control Chart Analysis (STP-15D) · AIAG, Measurement Systems Analysis Reference Manual, 4th ed. (2010) · Burdick, Borror & Montgomery, Design and Analysis of Gauge R&R Studies (ASA-SIAM, 2005). Per-formula citations: docs/FORMULAS.md.