Cavity 2, a significant p-value, and a 65,000 dollar tool change

No, the conclusion fails on three independent grounds.

1. Statistical significance is not practical significance. p = 0.03 says the observed difference is unlikely under the null; it says nothing about size. The difference is 0.004 millimetres against a 0.100 millimetre tolerance band, about 4% of the band.
2. Not out of specification, by a wide margin. Both means sit within 0.001 and 0.005 of nominal, and the nearest limit is 0.045 to 0.049 away. With Cpk 1.45, process standard deviation is roughly 0.010 millimetres, so the 0.004 difference is about 0.4 standard deviations, and both cavities are several standard deviations inside specification. No part demonstrated here is at risk of exceeding a limit; the phrase out of specification is simply wrong.
3. The design is confounded. Cavity is perfectly aliased with shift and with resin lot, because cavity 1 ran entirely on first shift before the lot change and cavity 2 on second shift after it. The cavity effect, the shift effect and the material effect are the same variable in this dataset. No t-test can separate them, and no tool decision can be justified from it.

The bimodal histogram reinforces the point: the pooled data look like a mixture of two populations, which is exactly what a shift or lot change produces.

A useful test of the team's own logic: the 95% interval for the difference has an upper bound of 0.0086 millimetres, still under 9% of the tolerance. Even the worst plausible cavity effect from this study does not threaten capability. The decision criterion should be whether any subgroup approaches a specification limit, not whether a mean difference is detectable.

Why more parts does not help

More parts shrink the confidence interval and make the 0.004 difference even more certainly detectable, while leaving the confounding untouched. The study error is structural, not a sample size problem.

Analysis plan

1. Verify the gauge on bore diameter first: a 0.001 millimetre resolution gauge with unknown repeatability cannot resolve a 0.004 effect. A quick crossed Gage R&R, 10 parts, 3 operators, 3 trials, is enough to know whether the effect is even measurable.
2. Stratify. Plot bore diameter as cavity by shift by lot using a multi-vari chart, with time order on the horizontal axis and the grinder change marked. This separates within-part, within-run, between-run and between-cavity variation visually before any test is chosen.
3. Model it properly. With two factors, run a two-way analysis of variance with cavity and shift as factors, including the interaction. If cavity and shift are still collinear, the run must be randomized: alternate cavities across shifts and lots. This is the only way to obtain an interpretable cavity effect.
4. Check assumptions before pooling. The bimodal histogram is a warning against a pooled t-test; each stratum should be checked for normality and equal variances, and the two-sample t is invalid when the pooled distribution is a mixture.
5. Control the known covariate. Record regrind percentage and the grinder change window as a covariate; a mid-week grinder replacement is a plausible common cause of a material shift and is currently uncontrolled.
6. Guard against multiple comparisons. Comparing cavities across shifts, lots and defect modes without adjustment inflates false positives; if several means are compared, use an omnibus test followed by an adjusted pairwise method such as Tukey.

The output should be a variance decomposition and a statement of practical effect size, not another p-value.

Recommendation

Do not authorize the 65,000 dollar tool rework this week. Fund nothing beyond a two-week measurement and stratification study.

Framing, in the language of risk and money

• State the common ground first: the team found a real, repeatable difference and deserves credit for noticing it. The question is whether it is a specification risk or a nuisance effect.
• Show the numbers that carry the decision: 0.004 millimetres against a 0.100 millimetre band, no part near a limit, historical Cpk of 1.45, and the fact that the cavity ran on a different shift and a different resin lot. The tool change cannot be shown to fix anything, because the cavity effect is not yet separable.
• Point out the cost asymmetry: 65,000 dollars plus downtime for a change that could be material- or shift-driven, with a fallback plan of two weeks of data at negligible cost.
• Name the interim risk management: if Quality genuinely fears exceeding limits, run 100% bore inspection on second shift with a defined limit, which costs far less than tooling and protects the customer now.
• Propose a pre-committed decision rule so the next review is not another debate: authorize tool rework only if a properly randomized study shows a cavity effect that moves the capability of any stratum below 1.33, or if any part exceeds a specification limit.
• Ask the team to bring the multi-vari chart and the variance components to the next review, with the gauge study attached. That converts a conflict over a conclusion into a shared plan for evidence.

This preserves the team's finding, protects the capital, and gives the sponsor a date and a criterion rather than an argument.