confidence intervals for cpk

**Confidence intervals for Cpk** are the **uncertainty bounds around estimated capability that indicate the plausible range of true process centering performance** - they prevent overclaiming capability from limited sample data. **What Is Confidence intervals for Cpk?** - **Definition**: Interval estimate around sample Cpk reflecting statistical uncertainty in mean and sigma estimates. - **Key Drivers**: Sample size, process stability, distribution shape, and proximity to spec limits. - **Reporting Focus**: Lower confidence bound is typically used for conservative qualification decisions. - **Methods**: Approximate normal formulas, bootstrap intervals, and exact or simulation-based approaches. **Why Confidence intervals for Cpk Matters** - **Decision Safety**: Point estimate alone can overstate true capability and mask release risk. - **Sample Planning**: Interval width targets guide minimum data requirements for approvals. - **Supplier Fairness**: Confidence-based comparison is more defensible than raw point estimates. - **Continuous Monitoring**: Interval drift over time can flag emerging instability earlier. - **Regulatory Rigor**: Many customer audits expect uncertainty disclosure with capability claims. **How It Is Used in Practice** - **Interval Method Choice**: Pick method consistent with data size and distribution assumptions. - **Lower-Bound Criterion**: Use one-sided lower confidence limit for pass-fail capability gates. - **Communication**: Present point estimate, interval, and assumptions together in quality reports. Confidence intervals for Cpk are **the honesty layer of capability reporting** - reliable decisions come from lower-bound evidence, not optimistic single-number summaries.