Abstract
Assess batch consistency from process behavior as well as individual COA results. This note distinguishes specification limits from control limits and outlines the prerequisites for interpreting capability. Several passing lots do not by themselves establish a stable process.
Check stability before capability
Capability indices compare a process distribution with specification limits and depend on appropriate data and assumptions [1]. A sequence of passing results alone does not establish a stable process or predict the next lot.
Illustrative calculation: assume a stable, approximately normal process with lower limit 8, upper limit 12, mean 10.0 and suitable within-process standard deviation 0.5. Cp = (12 − 8)/(6 × 0.5) = 1.33. Cpk = min[(12 − 10)/(3 × 0.5), (10 − 8)/(3 × 0.5)] = 1.33.
If the mean shifts to 11.0 with the same standard deviation, Cp stays 1.33 but Cpk falls to 0.67. The spread is unchanged; the process has moved closer to one limit. These hypothetical values illustrate position and spread, not recommended acceptance thresholds.
| Signal in the lot series | Question | Action before tightening limits |
|---|---|---|
| Mean drifts | Process change or method drift? | Compare retained control and history |
| Spread increases | Sampling or manufacturing variation? | Separate repeats from independent lots |
| Different laboratories disagree | Comparable measurement methods? | Run a shared reference sample |
| All values pass | Enough stable representative data? | Review time sequence and uncertainty |
Build a useful lot dataset
1. Preserve the sampling structure
Record lot, sampling location, preparation and test replicate separately. Multiple readings of one prepared specimen primarily assess measurement repeatability. They do not count as multiple manufacturing lots and should not inflate the apparent evidence for process capability.
2. Separate process and method changes
Annotate changes in equipment, raw material, heat treatment and analytical procedure. Plot results in time order. If the measurement method changes, establish comparability before combining the series into one standard deviation or capability estimate.
3. Define a response to unusual results
Use an agreed investigation path that includes checking sample identity, preparation and the retained reference. Repeating until a passing result appears obscures the original signal. Retain the first result and explain any scientifically justified exclusion or replacement.
Development decision
Set specifications from the material function and measurement capability, then monitor whether the process consistently meets them. Use capability metrics only after stability and the statistical basis have been assessed.
References
[1] NIST/SEMATECH. e-Handbook of statistical methods [Internet]. 6.1.6. What is process capability? [cited 2026 Sep 28]. Available from: https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm
https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm