percentile-based capability

**Percentile-based capability** is the **distribution-agnostic method that estimates capability using empirical or modeled percentiles instead of sigma assumptions** - it is robust for skewed data and provides intuitive tail-risk alignment. **What Is Percentile-based capability?** - **Definition**: Capability assessment derived from percentile distances to specification limits, often using median-centered formulations. - **Key Principle**: Uses actual tail behavior directly rather than forcing normal-equivalent spread. - **Typical Metrics**: Equivalent non-normal capability indices from lower and upper percentile bounds. - **Applicability**: Useful when transformations are unstable or distribution fit is uncertain. **Why Percentile-based capability Matters** - **Assumption Robustness**: Works even when data shape is skewed, bounded, or heavy-tailed. - **Tail Relevance**: Directly focuses on out-of-spec percentiles that drive customer risk. - **Transparency**: Percentile logic is often easier to explain to cross-functional stakeholders. - **Model Independence**: Reduces reliance on fragile parametric fit assumptions. - **Practical Accuracy**: Frequently aligns better with observed defect rates in non-normal processes. **How It Is Used in Practice** - **Percentile Estimation**: Estimate key quantiles from sufficient data or validated nonparametric methods. - **Limit Comparison**: Compute distance from center percentile to specs using chosen tail percentiles. - **Validation**: Compare predicted fallout with observed defect counts to confirm method fidelity. Percentile-based capability is **a reliable non-normal SPC alternative grounded in actual tail behavior** - it keeps capability decisions aligned with real defect risk.