Each step's yield is fine. The whole stream is not.
Rolled throughput yield is the metric that exposes a comforting illusion. A shop where every operation runs 95 percent first-pass yield feels like a quality operation. The compound math says otherwise: across ten steps, 95 percent at each yields 60 percent through the whole line. Six in ten parts make it through clean; the other four take a detour through rework, scrap, or sorting. The cost of that detour is rarely visible in any single station's data. RTY is the only metric that surfaces it.
"Each step's yield is what the operator sees. The product of the yields is what the customer pays for."
The calculation is multiplication, not averaging. Each operation's first-pass yield is a probability between 0 and 1, and RTY is the joint probability that a single part passes all of them in succession. If the steps are 0.99, 0.97, 0.95, 0.96, and 0.94, RTY is the product of those five numbers, which is about 82 percent.
The intuition that breaks most shops is the gap between average per-step yield and rolled yield:
A complex assembly with twenty operations cannot survive on 95 percent FPY at each step. The math says it must. The shop's customer-facing quality will be worse than any single station's data suggests. This is why the per-step FPY targets in high-mix or many-step processes need to be much higher than the targets in short ones.
The same compounding also explains why fixing the worst-performing operation has outsized impact. A step at 85 percent FPY in an otherwise-95 percent line drags RTY much more than it looks: lifting that one station from 85 to 95 might add eight or nine points to the whole RTY. Pareto applies to yield improvement the same way it applies to defect modes.
Imagine a 35-person electronics assembly shop building circuit board sub-assemblies through ten operations: paste application, component placement, reflow, inspection, hand assembly, secondary reflow, functional test, conformal coat, final inspection, and packaging. Each operation reports FPY in the mid- to high-90s. Management considers quality strong.
The first RTY calculation is uncomfortable. Multiplying the ten FPYs together produces an RTY of 64 percent. Roughly one in three boards is taking some detour through rework, secondary inspection, or sorting before reaching packaging. The hidden factory is real and substantial: a small rework team handles about thirty boards a day, and lead time on a clean board is roughly two shifts shorter than a board that touched rework.
The improvement project that emerges is targeted. Of the ten operations, two are clearly dragging the product: paste application at 89 percent and hand assembly at 91 percent. Together they account for most of the RTY shortfall. Six months of focused work on stencil maintenance and a hand-assembly fixture redesign lifts those two to 95 and 96 percent. RTY climbs from 64 to 79. The rework team shrinks. Lead time tightens. None of this would have been visible without the compound view.
Rolled throughput yield is the value-stream extension of first-pass yield and the parent of single-process yield measurements. Like quality rate, RTY rolls up multiple sources of loss into a single defendable number. Used carefully alongside defects per million opportunities, it gives a shop a complete view of where the yield losses live and which step to fix next.
The questions we hear most about this term.
Long-form guides that pick up where this definition leaves off, written for manufacturers running Arda today.
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