Control Charts

Control charts are the most widely used tool in SPC. Operators, engineers, and managers all rely on them to make real-time decisions: Should we stop the line? Is this shift performing differently from the last? Has the tool change actually improved the process?

The effectiveness of a control chart depends entirely on how its limits are calculated. Limits set too tight produce false alarms (crying wolf), limits set too wide miss real process shifts (silent failures). Traditional X-bar/R charts assume normally distributed subgroup means, which is often justified by the Central Limit Theorem for large subgroups but breaks down for individual measurements (I-MR charts) and small subgroups.

Modern quality teams need control charts that adapt to the actual data distribution — not charts that require engineers to first prove normality before trusting the signals.

EntropyStat generates control limits from the EGDF rather than from parametric assumptions. For any dataset — normal, skewed, heavy-tailed, or multimodal — the entropy-based CDF provides the exact quantiles needed for control limits (e.g., the 0.135% and 99.865% points that correspond to traditional 3-sigma limits).

This approach is especially valuable for I-MR charts (individual and moving range), where the normality assumption is most fragile. Traditional I-MR limits computed from the average moving range assume the underlying data is normal. For skewed processes, this produces asymmetric error rates — too many false alarms on one side, too few on the other. Entropy-based limits are inherently distribution-appropriate.

The ELDF further enhances control charting by detecting when a process is operating in multiple modes (clusters). Instead of a single pair of control limits spanning two populations, EntropyStat can flag modal shifts as a distinct signal type — giving operators actionable information rather than a generic "out of control" alarm.