The defect rate is 2.3%.
Which line, which material, which operator?

The Decision

A precision components manufacturer is running at 2.3% defect rate — above the 1.5% contractual threshold on a high-value aerospace account. The operations team has five candidate causes: material batch variation, machine calibration drift, operator technique, ambient temperature, and tooling wear. All five correlate with defect rates in the historical data. All five are expensive to address. The question is which one to address first.

The standard approach — regression of defect rate on all five — produces coefficients for each candidate. It does not answer which intervention on which variable most reduces the defect rate, because it cannot distinguish causes from confounders. Tool wear and machine calibration both correlate with defect rate. But tool wear may cause machine calibration drift, not the other way around. Addressing calibration without addressing tool wear treats the symptom.

The Causal Structure

The causal graph, elicited from the process engineers and quality team, encodes three causal pathways: (1) Material batch variation → dimensional tolerance → defect; (2) Tooling wear → machine calibration drift → surface finish → defect; (3) Ambient temperature → material expansion → dimensional tolerance → defect. Operator technique moderates pathway (2) — it does not cause defects directly, but skilled operators detect and correct calibration drift earlier.

The graph makes two things immediately visible: material batch variation and ambient temperature both feed into dimensional tolerance, making them confounders of each other in regression. And operator technique is a moderator, not a cause — controlling for it in a regression would attenuate the apparent effect of calibration drift without addressing the underlying mechanism.

Three Queries

Rung 2 — optimal intervention: The importance factors rank tooling wear as the highest-VOI intervention target — a 40% reduction in tooling wear produces a 1.1 percentage point reduction in defect rate, sufficient to bring the line below contractual threshold. Material batch tightening produces 0.4pp at three times the cost.

Rung 2 — attribution: Of the current 2.3% defect rate, 58% is attributable to pathway (2), 28% to pathway (1), and 14% to ambient variation. The operator technique moderator accounts for 18% of the pathway (2) contribution — defect rate would be higher on the same equipment with less-experienced operators.

Rung 3 — counterfactual: For the batch of 847 components produced in the period where defect rate was highest, the model estimates that 71% of the defects would not have occurred under the tooling replacement schedule that was delayed by 3 weeks due to supply chain disruption. The delay caused the breach.

The Result

Tooling replacement schedule enforced. Defect rate falls to 1.2% within two production cycles. The contractual threshold is met. The Rung 3 analysis provides the attribution evidence for the supply chain disruption claim — 71% of the breach period defects are causally attributable to the delayed tooling delivery, not to manufacturing process failure.