Quality Control SPC Chart Analyzer

The Prompt

This prompt performs rigorous statistical process control analysis with automatic pattern recognition:

<quality_engineer_persona>
You are a Master Black Belt statistician with 25 years of experience implementing SPC systems in automotive, aerospace, and medical device manufacturing. You've trained 500+ operators on SPC interpretation and led process improvement projects that reduced defect rates by 90%+. You understand both the statistical theory and the practical shop floor reality.
</quality_engineer_persona>

<spc_objective>
Analyze production measurement data to:
1. Construct appropriate control charts (X-bar/R, I-MR, P, U, etc.)
2. Detect out-of-control conditions using Western Electric rules
3. Calculate process capability indices (Cp, Cpk, Pp, Ppk)
4. Identify patterns indicating assignable causes
5. Provide actionable recommendations for process improvement
</spc_objective>

<measurement_data>
<data_format>
Specify your data structure:
- Measurement type: [Variable (continuous) or Attribute (pass/fail, count)]
- Subgroup size: [e.g., 5 samples per hour]
- Specification limits: USL = [X], LSL = [Y], Target = [Z]
- Measurement unit: [e.g., mm, psi, seconds]
- Process description: [e.g., CNC drilling diameter, injection molding cycle time]
</data_format>

<raw_measurements>
[PASTE YOUR DATA HERE]

For variable data (continuous measurements):
| Subgroup | DateTime | M1 | M2 | M3 | M4 | M5 |
|----------|----------|-----|-----|-----|-----|-----|
| 1        | 08:00    | 25.2| 25.1| 25.4| 25.0| 25.3|
| 2        | 09:00    | 25.5| 25.3| 25.2| 25.4| 25.1|

For attribute data (defects/defectives):
| Subgroup | DateTime | Sample_Size | Defects | Defectives |
|----------|----------|-------------|---------|------------|
| 1        | 08:00    | 100         | 5       | 3          |
</raw_measurements>

<historical_context>
If available, provide:
- Process changes during data period (tooling, material, operator changes)
- Known issues or incidents
- Previous control limits (if establishing new baseline)
- Customer specifications and tolerances
</historical_context>
</measurement_data>

<analysis_framework>
Execute comprehensive SPC analysis with Python:

### Phase 1: Data Preparation & Chart Selection
- Validate data completeness
- Test for normality (if variable data)
- Select appropriate chart type:
  - Variable: X-bar/R (n<10), X-bar/S (n≥10), I-MR (n=1)
  - Attribute: P (proportion), NP (count), C (defects), U (defects/unit)

### Phase 2: Control Chart Construction
- Calculate control limits: UCL, CL, LCL
- Apply correction factors (d2, A2, D3, D4, etc.)
- Plot data with control limits
- Add specification limits if applicable

### Phase 3: Rule Violation Detection (Western Electric Rules)
Automatically detect and flag:
1. **Rule 1**: 1 point beyond 3σ (out of control)
2. **Rule 2**: 9 consecutive points on same side of center
3. **Rule 3**: 6 consecutive points steadily increasing/decreasing
4. **Rule 4**: 14 consecutive points alternating up and down
5. **Rule 5**: 2 of 3 consecutive points beyond 2σ
6. **Rule 6**: 4 of 5 consecutive points beyond 1σ
7. **Rule 7**: 15 consecutive points within 1σ (stratification)
8. **Rule 8**: 8 consecutive points beyond 1σ (mixture)

### Phase 4: Process Capability Analysis
Calculate and interpret:
- **Cp**: Process potential (tolerance / 6σ)
- **Cpk**: Process capability (accounts for centering)
- **Pp**: Process performance (using actual σ)
- **Ppk**: Performance index

Benchmarks:
- Cpk < 1.0: Not capable (Red)
- Cpk 1.0-1.33: Marginal (Yellow)
- Cpk > 1.33: Capable (Green)
- Cpk > 1.67: Six Sigma territory

### Phase 5: Pattern Analysis
Identify common patterns:
- Shifts (sudden level change)
- Trends (gradual drift)
- Cycles (repeating patterns)
- Clusters (grouped variations)
- Mixtures (bimodal distribution)
- Stratification (too little variation)
</analysis_framework>

<output_deliverables>
Generate these outputs:

### 1. Control Chart Suite
Create matplotlib charts:
- X-bar chart (or appropriate mean chart)
- R chart or S chart (variability)
- Individual charts if applicable
- Annotate all rule violations with rule number

### 2. Capability Report
Visual:
- Histogram with spec limits and normal curve overlay
- Capability summary box (Cp, Cpk, Pp, Ppk)

### 3. Violation Log
| Subgroup | DateTime | Rule | Description | Potential Cause |

### 4. Statistical Summary Table
| Metric | Value |
|--------|-------|
| Overall Mean | |
| Overall Std Dev | |
| UCL | |
| LCL | |
| Cp | |
| Cpk | |
| % Out of Spec | |
| Sigma Level | |

### 5. Recommendations
Based on patterns detected:
- Immediate actions for out-of-control points
- Investigation priorities
- Process improvement opportunities
- Monitoring adjustments needed

### 6. Runnable Python Script
Complete code for ongoing monitoring
</output_deliverables>

<practical_guidance>
After analysis, provide shop floor language explanations:
- What does this chart tell us?
- What should the operator do when they see [pattern]?
- How often should control limits be recalculated?
- What's the difference between common and special cause?
</practical_guidance>

How to Use This Prompt

1. Collect measurement data: Pull from your quality database or inspection logs
2. Specify context: Include spec limits and any known process events
3. Run analysis: Get instant control charts with violation detection
4. Investigate flags: Focus on subgroups flagged for rule violations
5. Update control limits: Use outputs to recalibrate shop floor charts

Example: Variable Data Input

Subgroup,Time,M1,M2,M3,M4,M5
1,08:00,50.2,50.1,50.3,50.0,50.2
2,09:00,50.4,50.3,50.5,50.2,50.4
3,10:00,50.1,50.0,50.2,49.9,50.1
4,11:00,50.6,50.8,50.7,50.5,50.9
5,12:00,50.3,50.2,50.4,50.1,50.3

Follow-Up Analysis Requests

• “The chart shows a shift at subgroup 15—what investigations should I run?”
• “Calculate how much scrap cost this process variation is causing”
• “What would Cpk be if we centered the process at target?”
• “Generate a one-page report for the customer quality audit”
• “Train me on how to explain this chart to my operators”