normality testing

**Normality testing** is the **assessment of whether process data sufficiently follows a normal distribution for standard capability formulas to remain valid** - it is a critical assumption check before using Gaussian-based Cp and Cpk interpretations. **What Is Normality testing?** - **Definition**: Statistical and graphical evaluation of distribution shape versus normal model assumptions. - **Common Tests**: Anderson-Darling, Shapiro-Wilk, and probability-plot diagnostics. - **Typical Violations**: Skewness, heavy tails, multimodality, and mixed-population effects. - **Decision Output**: Proceed with normal capability, transform data, or switch to non-normal methods. **Why Normality testing Matters** - **Model Validity**: Using normal formulas on highly skewed data can misstate defect risk dramatically. - **Method Selection**: Normality result determines whether transformation or percentile methods are needed. - **Risk Transparency**: Assumption checks prevent false confidence in capability dashboards. - **Root-Cause Insight**: Non-normality often signals mixed process states or hidden special causes. - **Audit Compliance**: Quality systems expect documented distribution assessment before index reporting. **How It Is Used in Practice** - **Visual Screening**: Inspect histogram and normal probability plot before formal tests. - **Statistical Testing**: Run normality tests with awareness that large N can detect tiny, irrelevant deviations. - **Action Path**: Apply transformation or non-normal capability method when assumption violation is material. Normality testing is **the prerequisite check for meaningful Gaussian capability analysis** - validate the foundation before trusting the index.