Normal Distribution

The normal distribution dominates quality engineering because the Central Limit Theorem guarantees that averages of sufficiently large samples tend toward normality, regardless of the underlying distribution. This mathematical convenience made it the default assumption in an era when computation was expensive.

However, the normality assumption is frequently violated in manufacturing. Surface finish measurements are right-skewed, torque data is often bimodal (due to tool wear), and measurement error from vision systems follows non-Gaussian distributions. When data is not normal, capability indices computed with the standard formula can be off by 30–50%.

The industry is slowly recognizing this. The AIAG SPC manual acknowledges that "appropriate" statistical methods should be used, without mandating normality. But in practice, most software and training still default to the Gaussian assumption.

EntropyStat does not assume, test for, or require normality at any step. The EGDF constructs a continuous distribution function directly from data using entropy-based optimization, fitting whatever shape the data actually exhibits — normal, skewed, bimodal, or otherwise.

This is not the same as applying a normality test and then switching to a non-parametric fallback. Normality tests (Shapiro-Wilk, Anderson-Darling) have well-known power problems: they reject normality too easily with large samples and fail to reject with small ones. EntropyStat sidesteps the entire question by never assuming any parametric form in the first place.

When data happens to be truly normal, the EGDF naturally converges to a shape indistinguishable from a Gaussian CDF — the method does not lose accuracy by being assumption-free. But when data departs from normality, EntropyStat continues to produce accurate distribution estimates while traditional methods silently degrade.