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 (Type-1 study and Gage R&R), is the process stable (SPC charts), and is it capable (Cp/Cpk vs Pp/Ppk, also for non-normal data). 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.
- Type-1 gauge study (Cg/Cgk): the Bosch Procedure 1 / VDA 5 study of the gauge alone, with the bias t-test, resolution check, confidence intervals for Cg and Cgk, and the tightest tolerance the gauge can still check. Reproduces the Bosch Booklet 10 worked example, intervals included.
- 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".
- Non-normal capability: Pp/Ppk by the ISO 22514-2 percentile method on exact maximum-likelihood fits (normal, lognormal, Weibull, gamma, exponential) ranked by Anderson-Darling, or by Box-Cox, with a natural lower bound option and the normal-theory result shown alongside. Reproduces a published cycle-time study to the printed decimal.
- 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, Excel workbooks and PDF reports with embedded charts for capability, Type-1 and Gage R&R studies, 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.
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 sequence is a Type-1 study of the gauge on a reference part (Cg and Cgk of at least 1.33, common with German customers), a Gage R&R under 10% (10-30% only with customer approval), then an initial process study with Ppk of at least 1.67. Customer-specific requirements take precedence.
The Type-1 page opens on the Bosch Booklet 10 example: Cg = 2.01 and Cgk = 1.64, capable, but with a statistically significant bias (t = -7.82). The tool passes the gauge and suggests correcting the offset at the next calibration. It also reports that the gauge would still pass down to a tolerance of 0.051.
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:
- 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.
- 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.
- 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.
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.
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.txtRun the application:
streamlit run app/ui/streamlit_app.pyThe app opens at http://localhost:8501.
A typical analysis session:
- 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.
- Enter specifications (section 2) — USL and/or LSL, optional nominal, measurement unit, and traceability metadata (characteristic, part, machine, operator).
- Select the SPC chart (sidebar) — X̄–R, X̄–S, or I–MR, subgroup size, rule set (Nelson / Western Electric / both), and within-σ estimator.
- Review stability (section 5) — control charts with CL/UCL/LCL, flagged out-of-control points, and the violations table.
- Review capability (section 6) — Cp/Cpk (within) beside Pp/Ppk (overall), sigma level, DPMO, the Cpk confidence interval, and all reliability warnings.
- Review the interpretation (section 7) — factual statistical conclusions and, separately, engineering recommendations with their triggers.
- 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, Excel and PDF.
The Type-1 gauge (MSA) page takes a single column of readings of one reference part, plus the reference value, the tolerance and, optionally, the resolution. K and L (20% and 6 by default) are in the sidebar.
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.
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.
| study | what matches |
|---|---|
| Bosch Booklet 10, Procedure 1 worked example (n = 50) | Cg 2.01, Cgk 1.64, both 95% intervals (1.61-2.41, 1.30-1.98), %RE 1.67, "bias significant", T_min(Cgk) 0.050696 |
| BPI Consulting, Type 1 Gage Study (n = 50) | t 2.185, p 0.0337, Cg 0.343, Cgk 0.240, %Var(Rep+Bias) 83.22 |
Two published figures were computed from rounded intermediates (Bosch's
T_min(Cg), BPI's %Var(Rep) of 58.2). The tests and
examples/DATASETS.md record both values.
examples/nonnormal_cycle_time.csv is the 207-order cycle-time study from
iSixSigma (upper limit 30 days, lower bound 0). The published Weibull
(233244.81 PPM), bounded-normal (249535.66) and Box-Cox (227113.29) results
are reproduced exactly. The last two use s / c4, which the source software
applies by default; here it is an option. The one figure not matched (the
unbounded-normal total, 10 PPM apart) is recorded in
examples/DATASETS.md.
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.
python -m pytestThe suite currently contains 961 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 (all three reports),
- Type-1 studies against the Bosch Booklet 10 and BPI worked examples,
- non-normal capability against a published study, exact maximum-likelihood conditions, analytic quantiles and a Monte Carlo convergence check,
- 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
AppTestharness.
Code-coverage percentages are not claimed because coverage is not currently measured.
- 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.
- Non-normal Ppk rests on the fitted model's 0.135 % and 99.865 % tails: with fewer than about 100 observations those are mostly extrapolation, and a poor fit (or a mixture of processes) makes them unreliable. The page warns in both cases. Johnson transformations are not implemented.
- The Type-1 limits (Cg, Cgk >= 1.33; resolution <= 5% of T) and its K = 20%, L = 6 defaults are Bosch conventions; customers may set others.
- 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.
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.
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) · ISO
22514-2 · Clements, "Process capability calculations for non-normal
distributions", Quality Progress 22(9), 1989 · AIAG,
Measurement Systems Analysis Reference Manual, 4th ed. (2010) · Robert Bosch
GmbH, Booklet 10: Capability of Measurement and Test Processes · Burdick,
Borror & Montgomery, Design and Analysis of Gauge R&R Studies (ASA-SIAM, 2005).
Per-formula citations: docs/FORMULAS.md.