Northline Distribution: rolling yield hides the rework cage
Northline Distribution fills about 4,200 orders a day through four sequential steps: pick, pack, label and manifest, and load. The operations manager reports 96% quality based on a weekly audit of 200 shipped orders that found 8 defects. Finance is challenging a proposed $180,000 automation project because customer complaints about wrong-item and missing-document errors have risen 30% year over year while the audit score has stayed flat. A Green Belt pulled first-pass yield (FPY) for the same month: pick 94.2%, pack 97.8%, label and manifest 96.5%, load 99.1%. Mis-picked orders are corrected in an area known as the cage before loading; the cage captures no data and is staffed by 3.5 full-time equivalents. No project charter exists. The sponsor asks the Belt for the real sigma level and whether the audit is lying.
1. Calculate rolled throughput yield (RTY) and the corresponding sigma level. Explain what the number does and does not tell you.
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Calculation
RTY = 0.942 x 0.978 x 0.965 x 0.991
- 0.942 x 0.978 = 0.9213
- 0.9213 x 0.965 = 0.8891
- 0.8891 x 0.991 = 0.8810, about 88.1%
So roughly 11.9% of orders, about 500 of the 4,200 daily orders, are touched by at least one defect somewhere in the process.
Sigma level
The normal deviate for a 0.8810 yield is about 1.18. Adding the conventional 1.5 shift gives a reported level of roughly 2.7 sigma. The pick step alone costs 5.8 yield points, so the arithmetic also localizes the leverage: pick is the dominant loss, not load.
What it does not tell you
- It is a rolled-yield approximation, valid only if each step is credited with one defect opportunity per unit. If an order can carry two independent defects (wrong item plus missing document), a true DPMO-based sigma will be worse.
- Because the cage corrects mis-picks before load, the 99.1% load yield is inflated; it measures what entered the step, not what the step produced.
- It says nothing about defects that escape to the customer, which is the number Finance is reacting to.
- It cannot substitute for a sigma level computed from counted defect opportunities, so present it as a conservative indicator rather than a certified metric.
2. Why does the final audit stay flat at 96% while customer complaints rise, and what should be measured instead?
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Why the audit is misleading
- Population problem. The audit samples shipped orders, which are the survivors after cage rework. It measures escape quality of a filtered population, not the capability of the process that produced the orders.
- Resolution problem. 8 defects in 200 orders is 4.0%, with a 95% binomial interval of roughly plus or minus 2.7 points. A two-point deterioration is invisible to this sample size, so a flat score is fully consistent with real decline.
- Definition problem. If the audit checks item accuracy but not documentation completeness, the fastest-growing defect mode is simply not in the metric.
What to measure instead
- Cage volume: orders reworked per day, rework minutes, defect mode, finding step, and who found it. This converts an invisible hidden factory into a Pareto.
- FPY per step from the warehouse management system rather than by sampling, with an operational definition of what counts as a first-pass pass.
- Escape rate: defects found by the customer divided by orders shipped, split by mode.
- A detection-point map (found at pick, found in cage, found by customer) to show where errors are currently caught.
First control on the data
Run an attribute agreement study on how auditors classify a defect before trusting any audit trend; three auditors, 50 orders, Cohen's kappa. A metric nobody classifies consistently cannot be defended to Finance.
3. The sponsor wants to fund the automation first. How do you respond using Lean and Six Sigma fundamentals?
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Core objection: automation is a solution in search of a problem definition.
There is no charter, no verified root cause, and no verified baseline beyond a rolled yield of 88.1%. Automating a 2.7-sigma process risks automating the waste and locking the current design in place.
Sequence the argument
- Quantify the hidden factory first. 3.5 FTE in the cage is roughly $250,000 a year fully loaded, before scrap, reships and complaint handling. That number is larger than the proposed capital and it is being spent to protect a metric that does not measure it.
- Lean lens. Walk the value stream from order release to load. The cage is rework, not value; the pick step at 94.2% is the constraint on RTY. A Pareto of pick error modes (look-alike SKUs, slotting, scan bypass, unlabelled bins) is a two-week exercise and determines whether automation addresses the actual driver.
- Six Sigma lens. The proposal is a countermeasure with no verified X. Ask what the automation changes and which Y it moves, and how that will be measured. If the Pareto says look-alike SKUs, slotting plus scan validation is cheaper and testable; if it says volume-driven fatigue, automation may indeed be correct, but now for a verified reason.
Recommendation
Do not reject the capital request; defer it by four weeks against a defined deliverable: charter, cage data capture, MSA on defect classification, pick-mode Pareto, and a validated cost of poor quality. Re-evaluate the automation on the same metric and the same money basis. This satisfies the sponsor's intent while preventing a spend that would be defended by a metric the audit cannot support.