process-capability-calculator
Process capability analysis skill with Cp, Cpk, Pp, Ppk calculations and specification compliance assessment
What this skill does
# Process Capability Calculator
## Overview
The Process Capability Calculator skill provides comprehensive capabilities for analyzing process capability against specification limits. It supports multiple capability indices, normality testing, and defect rate estimation for both short-term and long-term performance assessment.
## Capabilities
- Capability index calculation (Cp, Cpk, Pp, Ppk)
- Specification limit analysis
- Process performance metrics
- Normality testing
- Non-normal data transformation
- Capability histogram generation
- PPM defect rate estimation
## Used By Processes
- SIX-003: Process Capability Analysis
- SIX-002: Statistical Process Control Implementation
- QMS-004: Cost of Quality Analysis
## Tools and Libraries
- Statistical software APIs
- Quality analysis libraries
- Data transformation tools
- Visualization libraries
## Usage
```yaml
skill: process-capability-calculator
inputs:
data: [10.2, 10.1, 10.3, 10.0, 10.2, 10.4, 10.3, 10.2, 10.5, 10.3]
specification_limits:
usl: 10.8
lsl: 9.2
target: 10.0
analysis_type: "short_term" # short_term | long_term
normality_test: true
outputs:
- capability_indices
- ppm_estimates
- sigma_level
- histogram_with_specs
- normality_assessment
- recommendations
```
## Capability Index Formulas
### Short-Term (Potential) Capability
```
Cp = (USL - LSL) / (6 * sigma_within)
Cpk = min[(USL - mean) / (3 * sigma_within), (mean - LSL) / (3 * sigma_within)]
```
### Long-Term (Actual) Performance
```
Pp = (USL - LSL) / (6 * sigma_overall)
Ppk = min[(USL - mean) / (3 * sigma_overall), (mean - LSL) / (3 * sigma_overall)]
```
## Capability Interpretation
| Cp/Cpk Value | Interpretation | Sigma Level |
|--------------|----------------|-------------|
| < 0.67 | Very poor | < 2 sigma |
| 0.67 - 1.00 | Poor | 2 - 3 sigma |
| 1.00 - 1.33 | Marginal | 3 - 4 sigma |
| 1.33 - 1.67 | Good | 4 - 5 sigma |
| 1.67 - 2.00 | Very good | 5 - 6 sigma |
| > 2.00 | Excellent | > 6 sigma |
## PPM Defect Rate Estimation
| Cpk | PPM (one-sided) | % Yield |
|-----|-----------------|---------|
| 1.00 | 1,350 | 99.865% |
| 1.33 | 32 | 99.997% |
| 1.67 | 0.3 | 99.99997% |
| 2.00 | 0.001 | 99.9999999% |
## Integration Points
- Quality Management Systems
- Statistical analysis software
- SPC platforms
- Customer reporting systems
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