Sigma Level

Sigma level is the executive summary of process capability. It compresses complex distributional information into a single number that management, customers, and suppliers all understand. When someone says "we run at 4.5 sigma," it communicates a specific quality level without requiring statistical expertise to interpret.

The 1.5-sigma shift is a source of perpetual confusion. Motorola's original Six Sigma methodology assumes that processes shift by 1.5σ over time, so "Six Sigma" actually means 4.5 sigma in the short term — corresponding to 3.4 DPMO rather than the 2 parts per billion that a true 6σ process would produce. Some organizations use the shift, others do not, creating apples-to-oranges comparisons.

The bigger issue is that sigma level inherits all the accuracy problems of the Cpk calculation it is derived from. If Cpk is computed from a normal assumption on non-normal data, the resulting sigma level is equally misleading. A process reported at 4.5 sigma might actually be 3.8 sigma when the true distribution shape is considered.

EntropyStat computes sigma levels from the actual defect probability estimated by the EGDF, rather than deriving them from Cpk under normality. The approach is: estimate the true fraction nonconforming from the EGDF tail area beyond specification limits, then convert to the equivalent sigma level using the inverse normal CDF.

This "equivalent sigma level" is honest — it tells you what sigma level a normal process would need to achieve the same defect rate that your actual (possibly non-normal) process produces. A right-skewed process might have a traditional Cpk-derived sigma level of 4.2 but an EGDF-derived equivalent of 3.6, reflecting the heavier upper tail that the normal model missed.

By anchoring sigma level to actual defect probability rather than to parametric assumptions, EntropyStat makes sigma level comparisons meaningful across processes with different distributional shapes. A 4.0-sigma process measured with EntropyStat genuinely produces the same DPMO as any other 4.0-sigma process — regardless of whether the underlying data is normal, skewed, or multimodal.