non-normal capability analysis
**Non-normal capability analysis** is the **set of methods used to estimate capability when process data does not follow a normal distribution** - it provides realistic defect-risk estimates for skewed or heavy-tail manufacturing metrics.
**What Is Non-normal capability analysis?**
- **Definition**: Capability evaluation using transformations, fitted non-normal distributions, or direct percentile methods.
- **When Needed**: Applied when normality assumption fails and deviation materially affects tail prediction.
- **Method Families**: Box-Cox transformation, Johnson transformation, Weibull/lognormal fits, and percentile capability.
- **Primary Output**: Equivalent capability indices and expected nonconformance under true data shape.
**Why Non-normal capability analysis Matters**
- **Tail Accuracy**: Skewed data needs non-normal methods to avoid underestimating out-of-spec risk.
- **Realistic Decisions**: Prevents over-approval of processes that look good only under normal assumptions.
- **Industry Relevance**: Semiconductor defect and leakage metrics are often non-normal by physics.
- **Improvement Focus**: Shape-aware analysis highlights where tail compression efforts should target.
- **Customer Confidence**: Better risk prediction improves trust in capability commitments.
**How It Is Used in Practice**
- **Shape Diagnosis**: Identify skewness and tail behavior using plots and goodness-of-fit statistics.
- **Method Selection**: Choose transformation or direct percentile approach based on interpretability and fit quality.
- **Validation**: Back-check predicted defect rates against observed out-of-spec counts.
Non-normal capability analysis is **the accurate path for skewed process data** - quality decisions should follow the real distribution, not a convenient assumption.