Control Chart Selector, Shewhart Limits & Detection Power

These are trial limits from a baseline study. ISO 7870-2 expects any subgroup with an assignable cause to be investigated and removed and the limits then recomputed, so the first pass is never the last. The reported standard error of sigma assumes the subgroup ranges are independent; for a subgroup size of 1 the moving ranges overlap by one reading and are correlated, so the true uncertainty is larger than the figure shown, and the individuals chart is the least trustworthy of the three for that reason among others. All the constants assume the individual readings are approximately normal and independent - autocorrelated data such as a continuously monitored dyebath temperature will produce limits that are far too narrow, and count data such as neps or defects per unit needs an attribute chart, not this one. Detection power is calculated for a sustained step change and for the beyond-limits rule alone; run rules change both the detection and the false alarm figures. A negative limit inflation means the overall standard deviation came out smaller than the within-subgroup estimate, which normally signals subgrouping that is not rational or too few subgroups to estimate either quantity reliably. Finally, nothing here is a capability index: control limits describe what the process does, specification limits describe what the customer asked for, and drawing the two on the same chart is the most common and most damaging mistake in factory SPC.