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First Pass Yield and Rolled Throughput Yield Calculator
Enter units entering, units passing first time and units scrapped at each process step. Get first-pass yield per step, rolled throughput yield across the process, normalized yield, final yield, and how many units went through rework.
First pass yield and RTY calculator
Add one row per process step, in order. Units entering = passed first time + reworked + scrapped.
| Step | First-pass yield | Final yield | Reworked |
|---|---|---|---|
| Machining | 95 % | 99 % | 40 |
| Deburr & wash | 90.91 % | 97.98 % | 70 |
| Final inspection | 98.97 % | 99.48 % | 5 |
| Step | Formula | Value |
|---|---|---|
| First-pass yield | Machining: FPY = 950 / 1000 | 95 % |
| First-pass yield | Deburr & wash: FPY = 900 / 990 | 90.909 % |
| First-pass yield | Final inspection: FPY = 960 / 970 | 98.969 % |
| Rolled throughput yield | RTY = 0.95 × 0.90909 × 0.98969 | 85.473 % |
| Normalized yield | Ynorm = RTY^(1/3) | 94.902 % |
| Final yield | Final yield = Π (entering − scrapped) / entering | 96.5 % |
| Total units reworked | Σ (entering − first pass − scrapped) | 115 |
Formulas used
- First-pass yield (per step)
- FPY = units passing first time / units entering
- Rolled throughput yield
- RTY = FPY₁ × FPY₂ × … × FPYₙ
- Normalized yield
- Ynorm = RTY^(1/n)
- Final yield (per step)
- (units entering − scrapped) / units entering
- Reworked units (per step)
- entering − first pass − scrapped
Assumptions and limits
- A unit passes first time only if it needs no rework, repair or retest at that step.
- Every unit entering a step either passes first time, is reworked, or is scrapped.
- Reworked units that then pass count toward final yield but not first-pass yield.
- RTY multiplies step yields, so it assumes defects at one step are independent of the others.
- Final yield is the product of step yields, which matches units out ÷ units in when each step feeds the next.
Worked example
Example: 1,000 parts start machining; 950 pass first time and 10 are scrapped. 990 go to deburr and wash; 900 pass first time and 20 are scrapped. 970 reach final inspection; 960 pass first time and 5 are scrapped.
| Step | Formula | Value |
|---|---|---|
| First-pass yield | Machining: FPY = 950 / 1000 | 95 % |
| First-pass yield | Deburr & wash: FPY = 900 / 990 | 90.909 % |
| First-pass yield | Final inspection: FPY = 960 / 970 | 98.969 % |
| Rolled throughput yield | RTY = 0.95 × 0.90909 × 0.98969 | 85.473 % |
| Normalized yield | Ynorm = RTY^(1/3) | 94.902 % |
| Final yield | Final yield = Π (entering − scrapped) / entering | 96.5 % |
| Total units reworked | Σ (entering − first pass − scrapped) | 115 |
Result: Rolled throughput yield is 85.47% while final yield is 96.5%; 115 units went through rework.
How to use first-pass yield and RTY
Why final yield hides problems
Final yield counts reworked parts as good, so in the example below the process ships 96.5% of what it starts while only 85.5% of parts get through without being touched twice. The gap between final yield and RTY is the hidden factory: the people, time and floor space spent on rework.
Find the step that costs the most
The step with the lowest first-pass yield takes the largest bite out of RTY. Start improvement there, then recalculate. Because RTY is a product, raising a weak step from 90% to 98% moves RTY more than polishing a step already at 99%.
Compare processes of different lengths
Long processes have lower RTY simply because they have more steps. Normalized yield, the n-th root of RTY, is the average yield per step and lets you compare a 3-step process with a 12-step one.
Count rework honestly
FPY is only as good as the rework records. If operators fix parts in station without logging it, FPY looks better than it is. Make the rework log part of the work instruction.
Common mistakes
- Counting reworked parts as first-pass good. That turns FPY into final yield and hides the rework.
- Averaging step yields instead of multiplying. Average yield overstates how many parts get through every step cleanly.
- Mixing time periods across steps. Use the same production window for every step so the counts line up.
- Leaving out inspection and test steps. Retests are rework. Include those steps or RTY will be too high.
- Comparing RTY of processes with different step counts. Use normalized yield for that comparison.
Frequently asked questions
How do you calculate first pass yield?
Divide the units that pass a step without rework or scrap by the units that entered it. 950 good first time out of 1,000 is 95% FPY.
What is rolled throughput yield?
The probability that a unit passes every step first time. Multiply the first-pass yields of all steps: 95% × 90.9% × 99.0% ≈ 85.5%.
What is the difference between FPY and final yield?
FPY counts only units that pass without rework. Final yield also counts reworked units that eventually pass, so it is always equal to or higher than FPY.
How does RTY relate to DPU and DPMO?
If defects follow a Poisson distribution, RTY ≈ e^(−DPU), where DPU is total defects per unit. The DPMO calculator converts defect counts to DPMO and a sigma level.
What is normalized yield?
The n-th root of RTY for an n-step process, the average first-pass yield per step. It lets you compare processes with different numbers of steps.
Sources
- ASQ Quality Glossary — first-pass yield and rolled throughput yield.
- Breyfogle, F. W., Implementing Six Sigma, Wiley — rolled throughput yield, normalized yield and the RTY–DPU relationship.
- Feigenbaum, A. V., Total Quality Control, McGraw-Hill — the hidden plant of rework and re-inspection.
Results are computed in your browser from the published formulas named above. They are an engineering aid, not a substitute for the governing standard, your drawing, or your customer's requirements.