First-pass yield is the share of units that pass without rework — tougher and more honest than final yield. For a multi-step process, multiply each step’s yield for the rolled throughput yield.
The example
Steps at 98%, 97%, 99%.
| A | B | |
|---|---|---|
| 1 | Item | Value |
| 2 | Step FPYs | 98/97/99% |
| 3 | Rolled | → ~94.1% |
The formula
The formula:
How it works
How it works:
- Step FPY = units passing without rework ÷ units entering — reworked units don’t count as first-pass.
- It’s stricter than final yield, which counts reworked-then-passed units as good.
- For a multi-step process, rolled throughput yield =
PRODUCT(step_FPYs). - Three 98% steps roll to ~94% — small per-step losses compound across the line.
Rolled yield exposes hidden rework. Each step might report 97–99% “yield,” looking fine — but multiplied across ten steps that’s only ~80% making it through first time. The gap between final yield and rolled FPY is the “hidden factory” of rework. PRODUCT(step_yields) in one cell surfaces it.
Try it: interactive demo
Step yields (comma-separated %).
Variations
Rolled throughput yield
Multiply steps:
vs final yield
The rework gap:
Defects per step
Failed first time:
Pitfalls & errors
First-time only. Reworked-then-passed units are not first-pass.
Multiply, don’t average. Rolled yield is the product of step yields.
Percent as decimal. 98% is 0.98 in PRODUCT.
Practice workbook
Frequently asked questions
How do I calculate first-pass yield in Excel?
How is FPY different from final yield?
Why do step yields roll up so low?
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