Is the Line B Retraining Mandate Supported?
Priya, an operations lead, is comparing two production lines for last month. Line A ran 12,000 units and logged 240 defects (2.0%). Line B ran 3,000 units and logged 90 defects (3.0%); of those 3,000 units, 1,800 were a new product launched in March, and 60 of the 90 defects were on that new product. Line A ran only the established product. Priya's memo says: "Line B's defect rate is 50% higher than Line A's. Retrain every Line B operator before next quarter." A colleague notes two further facts: Line B is the only line that runs the Tuesday night shift, which has thinner supervision, and the new product's spec tolerances are tighter than the established product's.
1. Verify the "50% higher" claim. Then compute Line B's defect rate for the established product alone and compare it with Line A.
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The arithmetic checks out, but it is an average of two different populations.
- Line B: 90 / 3,000 = 3.0%
- Line A: 240 / 12,000 = 2.0%
- Ratio: 3.0 / 2.0 = 1.5, i.e. 50% higher - correct as stated.
Split Line B by product:
- New product: 60 defects / 1,800 units = 3.33%
- Established product: units = 3,000 − 1,800 = 1,200; defects = 90 − 60 = 30; rate = 2.50%
So like-for-like against Line A's 2.0%, Line B's established-product rate is only 25% higher, not 50%. The headline number is inflated by product mix: the new, tighter-tolerance product is 60% of Line B's volume but 0% of Line A's.
2. Which parts of Priya's memo survive the comparison, and which do not? Name the confounds explicitly.
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Survives: the raw defect-rate difference is real and the direction is unfavorable to Line B. Something on Line B deserves attention.
Does not survive: "retrain every Line B operator." Three confounds undercut it:
- Product mix - Line B's average includes a brand-new, tighter-tolerance product that Line A never ran. Part of the gap is the work, not the workers.
- Shift - Line B uniquely runs Tuesday nights under thinner supervision. A defect that clusters on one shift points to supervision or fatigue, not to skill across all operators.
- Sample size and duration - 90 defects over one month is a thin base, and Line A's 12,000 units carry far more statistical weight.
A defensible next step is a targeted look - defect types on the new product, and Tuesday-night rate separately - before spending on retraining the entire crew. Blanket retraining both overspends and risks insulting operators whose output may be at or near Line A's.
3. Name the single additional data point that would most change the recommendation, and state what result would reverse it.
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The highest-value missing fact: Line A's defect rate on the same new product (or, failing that, the defect rate on the new product at any other line or during the pilot run).
What would reverse the conclusion: if Line A or the pilot also ran the new product and landed near 3.33%, then the new product - not Line B's operators - explains essentially the entire gap. In that case the correct memo is about tolerance spec and process capability for the new product, and the retraining line should be deleted outright.
Runner-up fact: a defect-type breakdown. If the new product's 60 defects are concentrated in one failure mode traceable to a fixture or spec, the fix is engineering, not training - and the cost of retraining 100% of operators against the cost of a fixture change becomes the real decision.