Gavand1969/process-control-spc
GitHub: Gavand1969/process-control-spc
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# Process Control & SPC Toolkit
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[](https://asq.org/cert/six-sigma-green-belt)
[](https://www.aiag.org)
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A pure-Python **Statistical Process Control (SPC) toolkit** built around a simulated tobacco rod weight dataset — modeled on the manufacturing context at **Philip Morris International (PMI)**.
The project demonstrates the full Six Sigma DMAIC measurement and analysis workflow: synthetic factory data generation, X-bar & R control charts with proper AIAG/Montgomery constants, Western Electric out-of-control rules, process capability analysis (Cp/Cpk/Pp/Ppk), Pareto of defect causes, and an auto-generated control-plan report.
## Why This Exists
This toolkit was built to bridge **process quality engineering** and **data science**:
- **PMI Quality Assurance Engineer context**: Tobacco rod fill weight (target 1000 mg ±15 mg) is a critical quality characteristic in cigarette manufacturing. Monitoring it with X-bar & R charts and capability analysis maps directly to the measurement systems and reporting used in PMI's production environment.
- **ASQ Six Sigma Green Belt path**: I'm pursuing CSSGB certification through the **Syracuse University Onward to Opportunity (O2O)** program. Every module here — control chart construction, WECO rules, capability indices, Pareto analysis — aligns with the ASQ CSSGB Body of Knowledge (Section III: Measure, Section V: Control).
- **Recruiter signal**: This is a working, tested codebase — not a notebook. Production-quality structure with unit tests, typed functions, docstrings, and AIAG-aligned math.
## Charts
### X-bar Chart — Line B (Quality Event Visible)
The deliberate out-of-control event on Line B (days 18–22) is clearly visible. Red triangles mark Western Electric rule violations. The process recovers after corrective action on day 23.
### X-bar & R Chart — All Lines Combined
### Histogram with Specification Limits
Normal distribution overlay with USL=1015 mg and LSL=985 mg shaded rejection zones.
### Process Capability Gauge
### Pareto Chart of Defect Causes
## Process Capability Results
Computed from 1,800 observations (30 days × 4 shifts × 3 lines × 5 samples/shift). SPC constants for n=5: **A2=0.577, D3=0, D4=2.114, d2=2.326** (Montgomery, *Introduction to Statistical Quality Control*, 8th ed., Table VI).
**Formulas:**
Cp = (USL − LSL) / (6 × σ_within) where σ_within = R̄ / d2
Cpk = min((USL − mean) / (3 × σ_within), (mean − LSL) / (3 × σ_within))
Pp = (USL − LSL) / (6 × σ_overall) where σ_overall = s (sample std dev)
Ppk = min((USL − mean) / (3 × σ_overall), (mean − LSL) / (3 × σ_overall))
### All Lines Combined
| Index | Value | Interpretation |
|-------|--------|---------------------------------------|
| Cp | 1.4559 | Good potential capability (> 1.33) |
| **Cpk** | **1.4453** | **Process centered and capable** |
| Pp | 1.3338 | Long-term performance acceptable |
| Ppk | 1.3241 | Long-term performance acceptable |
| σ level | 4.34σ | Above 4σ threshold |
### By Machine Line
| Line | Cp | Cpk | Pp | Ppk | Mean (mg) | σ_within |
|---------|--------|--------|--------|--------|-----------|----------|
| Line A | 1.4984 | 1.4951 | 1.4168 | 1.4137 | 999.97 | 3.337 |
| **Line B** | **1.3992** | **1.3477** | **1.2069** | **1.1625** | **1000.55** | **3.573** |
| Line C | 1.4738 | 1.4547 | 1.4268 | 1.4084 | 999.81 | 3.393 |
## Western Electric Rules Implemented
The WECO rules detect non-random patterns in control charts beyond simple 3σ exceedances. All eight rules are implemented in [`src/rules.py`](src/rules.py).
| Rule | Trigger | Purpose |
|------|------------------------------------------------|------------------------------------|
| **1** | 1 point beyond ±3σ (Zone A) | Obvious out-of-control |
| **2** | 2 of 3 consecutive points beyond ±2σ, same side | Sustained shift detection |
| **3** | 4 of 5 consecutive points beyond ±1σ, same side | Gradual drift detection |
| **4** | 8 consecutive points same side of centerline | Persistent centering shift |
| **5** | 6 consecutive points trending up or down | Systematic trend / tool wear |
| 6 | 15 consecutive points within ±1σ | Stratification / subgroup mixing |
| 7 | 14 consecutive points alternating up-down | Over-control / tampering |
| 8 | 8 consecutive points beyond ±1σ, both sides | Mixture — two process distributions|
Rules 1–5 are applied by default in the report. All eight are unit tested.
**35 out-of-control signals** were detected across all lines — concentrated on Line B during the quality event window (subgroups 97–188, corresponding to days 18–23 shifts).
## Project Structure
process-control-spc/
├── src/
│ ├── __init__.py
│ ├── generate_factory_data.py # Seeded synthetic factory data (1800 obs)
│ ├── spc_charts.py # X-bar, R, run charts with UCL/LCL
│ ├── capability.py # Cp, Cpk, Pp, Ppk calculations
│ ├── rules.py # Western Electric rules 1–8
│ └── report.py # End-to-end runner → charts + report
├── tests/
│ ├── test_capability.py # 17 unit tests for Cp/Cpk math
│ └── test_rules.py # 33 unit tests for WECO rules + constants
├── data/
│ └── factory_measurements.csv # Generated CSV (600 obs × 3 lines)
├── reports/
│ ├── control_plan_report.txt # Control-plan-style summary
│ └── charts/ # All chart PNGs
│ ├── xbar_r_overall.png
│ ├── xbar_r_line_a.png
│ ├── xbar_r_line_b.png ← quality event visible here
│ ├── xbar_r_line_c.png
│ ├── histogram_spec_limits.png
│ ├── capability_gauge.png
│ ├── pareto_defect_causes.png
│ └── run_chart.png
├── requirements.txt
├── .gitignore
├── LICENSE
└── README.md
## How to Run
### 1. Clone and install
git clone https://github.com/Gavand1969/process-control-spc.git
cd process-control-spc
pip install -r requirements.txt
### 2. Generate data
python src/generate_factory_data.py
Creates `data/factory_measurements.csv` with 1,800 rows.
### 3. Run the full report
python src/report.py
Produces all charts in `reports/charts/` and a text control plan summary in `reports/control_plan_report.txt`.
Force-regenerate data:
python src/report.py --regen
### 4. Run unit tests
python -m pytest tests/ -v
All 50 tests pass. Tests verify:
- SPC constants A2=0.577, D3=0, D4=2.114, d2=2.326 for n=5
- Cpk formula correctness against hand-calculated values
- Each Western Electric rule triggers and does not trigger on synthetic edge cases
## Plug In Your Own Data
The toolkit accepts any CSV with measurement data. Match this column schema (or adapt `build_control_chart()` in `spc_charts.py`):
| Column | Type | Description |
|----------------|---------|--------------------------------------------------|
| `sample_id` | int | Unique observation ID |
| `day` | int | Production day |
| `shift` | int | Shift number within day (1–4) |
| `machine_line` | str | Machine/line identifier |
| `weight_mg` | float | Measured characteristic (or rename in call) |
| `out_of_spec` | bool | Pre-computed or set to `None` (report computes) |
import pandas as pd
from src.capability import compute_capability
from src.spc_charts import build_control_chart, plot_xbar_r
df = pd.read_csv("your_data.csv")
df["subgroup_id"] = df["day"].astype(str) + "-" + df["shift"].astype(str)
chart = build_control_chart(df, value_col="weight_mg", group_col="subgroup_id", n=5)
fig = plot_xbar_r(chart, title_prefix="My Process", usl=1015, lsl=985)
cap = compute_capability(df["weight_mg"].values, usl=1015, lsl=985, subgroup_size=5)
print(f"Cpk = {cap.cpk:.4f}")
## What This Demonstrates
| Competency | Implementation |
|---|---|
| **SPC chart construction** | X-bar & R with AIAG-correct A2/D3/D4/d2 constants |
| **Out-of-control detection** | All 8 Western Electric rules, unit tested |
| **Process capability** | Cp, Cpk (short-term), Pp, Ppk (long-term) with proper σ_within vs σ_overall |
| **Root cause analysis** | Pareto chart of defect causes with 80% line |
| **Quality event storytelling** | Line B drift Days 18–22, corrective action Day 23 |
| **Control plan thinking** | Auto-generated control plan summary with recommendations |
| **Software engineering** | Pure Python, typed functions, docstrings, 50 unit tests, zero-error CI |
| **Standards alignment** | AIAG SPC Manual 2nd ed., Montgomery SQC 8th ed., ASQ CSSGB BoK |
## ASQ Six Sigma Green Belt
I am actively pursuing the **ASQ Certified Six Sigma Green Belt (CSSGB)** through the **Syracuse University Onward to Opportunity (O2O)** program. This project directly maps to the ASQ CSSGB Body of Knowledge:
- **Section III (Measure):** Process capability (Cp, Cpk), measurement systems, data collection
- **Section IV (Analyze):** Control charts, process variation, root cause analysis (Pareto, fishbone)
- **Section V (Control):** Control plans, SPC implementation, out-of-control response
The SPC constants used here (A2, D3, D4, d2) are sourced from Montgomery's *Introduction to Statistical Quality Control* — the same reference text used in ASQ certification preparation.
## References
- Montgomery, D.C. (2020). *Introduction to Statistical Quality Control*, 8th ed. Wiley.
- AIAG (2005). *Statistical Process Control (SPC) Reference Manual*, 2nd ed.
- Western Electric Company (1956). *Statistical Quality Control Handbook*.
- ASQ. [Certified Six Sigma Green Belt Body of Knowledge](https://asq.org/cert/six-sigma-green-belt).
*Gavin Anderson · M.S. Data Science · ASQ CSSGB Candidate (Syracuse O2O)*