Humidity, Resin Lots and a p-Value of 0.06

Why the current conclusion is unsafe: the correlation comes from six months of aggregated time-series data in which humidity, resin source and machine mix all moved together. Any of the three could produce r = 0.72; time-ordered data also violates the independence assumption behind a simple correlation, so the coefficient is easy to over-read.

Next analysis - a multi-vari / stratification study, not another regression on aggregates:

• Defects by lot: if defects cluster within resin lots regardless of machine, material is the leading suspect.
• Defects by machine within each lot: if they follow the press, equipment leads.
• Defects by time/position within the shift and within the mold: cyclical or within-cavity patterns point to process or tooling, not weather.
• Then a model (or stratified plots) with humidity, resin lot and machine entered together, so the humidity effect is estimated within lots and machines.

What would convince me humidity is causal: the effect persists within every machine and every lot; it shows a dose-response across a range of humidity; and a confirmation run where changing humidity (dehumidification in one bay) changes the defect rate. That is the standard: an association plus a manipulated X that moves the Y.

No - that is a textbook beta-error trap. Failing to reject at alpha = 0.05 is not evidence that the difference is zero; it means the data cannot distinguish the observed difference from chance.

Look at what the data can actually say. About 17,000 units and 33 total defects: the 95% confidence interval on the difference between machine rates is wide, consistent both with "no difference" and with Machine B being close to twice as bad. Both a null result and a practically important difference fit inside it.

Also sanity-check the decision cost. Declaring equivalence now means deferring the overhaul on a press that may be driving a large share of the defects. The cost of a wrong "equivalent" verdict is much larger than the cost of collecting more data.

Options, with their arithmetic:

• Power up. Detecting roughly 0.15% vs 0.23% defect rates at conventional power needs data on the order of 40,000 units per machine - feasible only if the historical data can be reconstructed by machine.
• Reframe the claim. Report "no detectable difference; the interval still allows up to X%," then decide on engineering grounds at the overhaul.
• Improve the test. Use a rate-appropriate method for count data, check the assumption of constant rate (are defects clustered?), and avoid comparing many machines without adjusting for multiple comparisons.

Association is not a verified cause. Before implementation, require:

1. The cause is demonstrated to move the effect, not merely co-vary. A planned change is the cleanest proof: run matched lots on both machines, or swap the suspect resin lot across presses, or run a small DOE on humidity/temperature/material, and watch the defect rate on a control chart.
2. The mechanism is plausible and actionable. The team should be able to explain the physical route (e.g., moisture in resin affecting viscosity) and name the lever they can pull. A cause no one can control is a finding, not a countermeasure.
3. The effect size is worth the fix. Quantify the defect reduction per unit change so it can be compared against the countermeasure's cost.
4. Other candidates have been ruled out, at minimum via FMEA and stratification - no unexplained special causes left on the chart.

Verification run: a documented before/after comparison under normal conditions, with the same measurement system, plus a confirmation that removing the cause returns the process to the earlier level. Until that exists, the team has a suspect, not a root cause.