Confidence Intervals

Point estimates without confidence intervals are dangerously incomplete. A Cpk of 1.35 from 20 measurements might have a 95% confidence interval of [0.95, 1.75] — meaning the true capability could be below the 1.33 threshold. Reporting Cpk = 1.35 without this context gives false confidence.

In practice, confidence intervals drive decision-making about sample size and process qualification. If a customer requires Cpk ≥ 1.33 with 95% confidence, you need the lower confidence bound to exceed 1.33, not just the point estimate. This typically requires larger sample sizes than most engineers expect — often 50–100 measurements for narrow confidence intervals on capability indices.

The width of a confidence interval tells you how much you can trust your estimate. Wide intervals say "collect more data before deciding." Narrow intervals say "the estimate is stable enough to act on." Understanding this distinction prevents premature conclusions based on small samples and unreliable point estimates.

EntropyStat produces tighter effective confidence bounds on capability indices because the EGDF extracts more distributional information per measurement than parametric estimators. When traditional methods estimate mean and sigma from 15 measurements, the resulting Cpk confidence interval is wide because the estimators have not yet converged. The EGDF's entropy-based approach produces more stable distribution estimates from the same data, resulting in practically narrower uncertainty ranges.

This is because the EGDF uses the full information content of each observation — its position relative to all other observations — rather than reducing each measurement to its contribution to the sample mean and variance. In information-theoretic terms, the EGDF makes more efficient use of the available data, which translates to more precise distributional estimates for a given sample size.

The practical result: engineers can reach actionable confidence levels with fewer measurements. A 15-part sample analyzed with EntropyStat provides distributional certainty comparable to what traditional methods achieve with 30–50 measurements. This does not mean EntropyStat claims artificial precision — it means the underlying estimation method is genuinely more data-efficient.