9.7 Measurement System Reanalysis

Why capability improvement degrades the measurement system

Observed variation always contains both the process and the gauge:

$\sigma^2_{observed} = \sigma^2_{process} + \sigma^2_{measurement}$

A successful project reduces $\sigma^2_{process}$ and leaves $\sigma^2_{measurement}$ untouched. The gauge's share of what remains therefore rises, sometimes dramatically.

Worked example. Baseline: $\sigma_{observed} = 0.50$, of which $\sigma_{measurement} = 0.15$.

• $\sigma^2_{process} = 0.50^2 - 0.15^2 = 0.2500 - 0.0225 = 0.2275$, so $\sigma_{process} = 0.477$.
• Measurement share of observed variance $= 0.0225 / 0.2500 = 9.0%$, and %Study Variation $= 0.15/0.50 = 30%$ -- marginal but workable.

The project halves the process standard deviation to $\sigma_{process} = 0.2385$:

• New $\sigma^2_{observed} = 0.2385^2 + 0.15^2 = 0.05688 + 0.0225 = 0.07938$, so $\sigma_{observed} = 0.2818$.
• Measurement share of variance $= 0.0225 / 0.07938 = 28.3%$, and %Study Variation $= 0.15/0.2818 = 53%$ -- now unacceptable.

Nothing about the gauge changed. The project's own success made it inadequate, and every subsequent capability figure computed with it will be understated, because measurement noise is being counted as process variation.

Acceptance criteria

AIAG guidance, applied to %SV or %Tolerance:

ndc should be at least 5, meaning the gauge can distinguish at least five distinct levels of part variation. An ndc below 5 signals inadequate resolving power even when the percentage figures look borderline acceptable.

Note that %Contribution uses variance while %SV uses standard deviation, so the two numbers differ substantially for the same study: 30% study variation corresponds to 9% contribution. Quoting one and comparing it against the other's threshold is a common error.

Which criterion to use when

• Use %Tolerance when the gauge is used to accept or reject product against a specification, because the question is whether the gauge can distinguish good from bad.
• Use %Study Variation when the gauge is used to study and improve the process, because the question is whether the gauge can see the process variation.
• A gauge can pass one and fail the other. A wide tolerance with a tightly controlled process gives a good P/T ratio and a poor %SV, which is precisely the situation a Six Sigma team encounters after a successful project.

Triggers for reanalysis

The first row is the one the Body of Knowledge specifically emphasizes and the one teams most often miss.

What to do when reanalysis fails

Work in order of cost:

1. Improve the procedure. Standardize the fixturing, the clamping force, the location of the measurement, and the operator's technique. Reproducibility problems are often pure method problems and cost nothing to fix.
2. Retrain the appraisers. A large reproducibility component with a small repeatability component points at people, not the instrument.
3. Improve resolution. The gauge discrimination should be no coarser than one tenth of the process variation or of the tolerance, whichever is tighter. A gauge reading to 0.01 mm cannot support a study of a process whose total spread is 0.03 mm.
4. Average repeated readings. Averaging $m$ readings reduces the repeatability standard deviation by $\sqrt{m}$. This is a legitimate short-term measure with an ongoing cost, and it does nothing for reproducibility or bias.
5. Replace the gauge or automate the measurement. The last resort by cost, and sometimes the only real answer.

Recording the reanalysis

The Control phase deliverable is not the number but the decision. Record: the date and reason for the reanalysis, the study design (parts, appraisers, trials), the resulting %SV, %Tolerance, %Contribution, and ndc, the verdict against the criteria, any action taken, and the next scheduled review. Put the review interval into the control plan itself, so the reanalysis happens by schedule rather than by memory.