ELDF (Entropic Local Distribution Function)

Global distribution methods (including EGDF and parametric fits) provide a single summary of the data. This is sufficient when the process has one stable operating mode. But many real manufacturing processes exhibit multimodal behavior: two tool inserts with slightly different wear, morning vs. afternoon thermal drift, or mixed material batches.

Local distribution analysis detects these hidden structures. A global fit might show "acceptable" capability with Cpk = 1.4, while a local analysis reveals two clusters — one at Cpk = 1.8 and another at Cpk = 0.9 — with the second cluster producing scrap that the global view masks.

Without local analysis, engineers miss the root cause of intermittent quality issues because the aggregated statistics look acceptable.

The ELDF complements the EGDF by analyzing data at a local scale. Where the EGDF smooths the distribution globally, the ELDF uses entropy-based local density estimation to identify regions of high concentration (clusters) and transitions between modes.

In EntropyStat's standard workflow, the EGDF is fitted first to establish the global distribution. If the ELDF then reveals multiple peaks or clusters, the system flags the data as non-homogeneous — a critical signal that aggregate statistics (mean, Cpk, etc.) may be misleading. Each detected cluster can be analyzed separately with its own EGDF, producing per-cluster capability metrics.

This two-level analysis (EGDF global, ELDF local) is unique to the entropy-based approach. Traditional methods require engineers to manually slice data by suspected factors (time, tool, batch) and test each slice separately. The ELDF discovers these subpopulations automatically, even when the engineer does not know which factor is causing the split.