Tolerance Intervals

Tolerance intervals answer a question that engineers constantly ask but rarely formulate precisely: "What range of values will 99% of our parts fall within?" This is different from the specification limits (which define what the customer wants) — tolerance intervals describe what the process actually produces.

The gap between tolerance intervals and specification limits directly predicts the defect rate. If the 99% tolerance interval fits comfortably within spec limits, the process is highly capable. If it extends beyond spec, rework or scrap is inevitable.

Traditional tolerance intervals (like the k-factor method) assume normality and require sample size corrections that produce very wide intervals for small samples. A 99%/95% tolerance interval from 10 normally-distributed observations spans roughly ±4.3σ — so wide that it is often useless for engineering decisions.

EntropyStat computes tolerance intervals directly from the EGDF, which produces tighter intervals than parametric methods — particularly for non-normal data and small samples. Because the EGDF captures the actual distribution shape, the tolerance interval reflects the real process spread rather than a normal approximation that may overestimate tail probabilities.

Traditional tolerance intervals based on the normal distribution are inherently conservative: they must account for both sampling uncertainty and the assumption that the distribution is normal. EntropyStat's entropy-based intervals only need to account for sampling uncertainty, because the distribution shape is learned directly from the data. This typically produces intervals 10–30% tighter than the normal-based equivalents, especially for skewed distributions.

For quality engineering, tighter tolerance intervals mean more confident decisions about process capability. A tolerance interval that fits within specification limits with entropy-based methods — but not with normal-based methods — may eliminate unnecessary process improvement projects that were triggered by artificially inflated statistical intervals.

Try our free Cpk calculator → to compute traditional capability indices from your specification limits — then upload your data to see how entropy-based tolerance intervals compare.