Rolled Throughput Yield Calculator
Rolled throughput yield — the probability a unit passes every process step without rework — from the first-pass yields of up to eight steps, with the hidden factory it reveals.
Multiply the first-pass yields of the steps: five steps at 95% each pass only 77% of units cleanly, even though every step looks fine on its own.
How the rolled throughput yield calculator works
Multiply the first-pass yields of the steps: five steps at 95% each pass only 77% of units cleanly, even though every step looks fine on its own. That gap is the hidden factory of rework and scrap. The normalised yield is the per-step yield that would give the same result, and defects per unit is −ln(RTY).
Formula: RTY = Y₁ × Y₂ × … × Yₙ; normalised yield = RTY^(1/n); DPU = −ln(RTY)
Worked examples
| Inputs | Rolled throughput yield | Note |
|---|---|---|
| Five steps: 98, 95, 97, 92, 99 | 82.25 % | 82.3% |
| Ten steps at 95% | 66.34 % | eight steps entered: 66.3% |
| Three steps at 99.9% | 99.7 % | 99.7% |
FAQFrequently asked questions
Why is RTY so much lower than any single step?
Because every unit must clear every step; the losses compound. It is the same arithmetic as a parlay bet — five 95% steps are a 77% chance of a clean run, ten are 60%.
What is a good RTY?
It depends on the number of steps; that is what the normalised yield is for. World-class processes run 99.9% or better per step; 95% per step over a dozen steps leaves less than half the units untouched by rework.
What is the hidden factory?
The rework, retesting and scrap that first-pass yield does not show because the final yield looks fine after rework. RTY exposes it, and the units row counts it.
How does this relate to sigma level?
Defects per unit converts to a sigma level: DPU of 0.0027 is about 4.5σ long-term; 3.4 per million opportunities is the 6σ target. The six sigma DPMO calculator does that conversion.
Where these figures come from
- Nakajima (1988) — Introduction to TPM — the origin of Overall Equipment Effectiveness and its six big losses
- Health and Safety Executive — the UK workplace safety regulator
Last checked: September 2026. Definitions follow standard operations-management practice; where plants commonly differ, the page says so.