Sample Size Determination

Sample size is where statistical theory meets production economics. Too few measurements and your capability study is meaningless — the confidence interval around Cpk is so wide it could be anywhere from 0.8 to 2.0. Too many measurements and you have wasted production time and inspection resources measuring parts that did not need measuring.

Traditional sample size formulas for capability studies assume normality and yield requirements like n = 30 for stable Cpk estimates, n = 50+ for Ppk with reasonable confidence intervals. For acceptance sampling, sample sizes come from standard tables (Z1.4, Z1.9) based on lot size and AQL. For hypothesis testing, power analysis determines how many measurements are needed to detect a specific effect size.

The tension is real in low-volume manufacturing. Aerospace, medical devices, and prototyping often cannot produce 30 parts just for a capability study. The choice becomes: produce parts you do not need, or submit capability indices that both parties know are statistically unreliable. Neither option is satisfactory.

EntropyStat fundamentally changes the sample size equation. Because the EGDF produces stable distribution estimates with as few as 5–8 measurements, the minimum sample size for a meaningful capability study drops by a factor of 4–6x compared to traditional methods.

This is not a statistical shortcut — it reflects a genuine methodological difference. Traditional Cpk requires estimating two parameters (mean and standard deviation) of a normal distribution, and both estimators converge slowly with small samples. The EGDF uses entropy-based optimization that constructs the distribution directly from data without intermediate parameter estimation. The mathematical framework, developed over 40+ years at the Czech Academy of Sciences, converges faster because it uses all available information in each measurement, not just its contribution to moment estimates.

The practical impact is significant for low-volume manufacturing: PPAP capability studies on prototype runs, incoming inspection with limited sample quantities, and process validation during ramp-up all become statistically feasible with samples that were previously considered too small. Engineers stop choosing between "not enough data" and "too expensive to measure" — they get reliable results from the data they can reasonably collect.