First Pass and Rolled Throughput Yield Calculator Widget
Show quality teams where the hidden factory lives. Readers enter the units started and, for up to six process steps, how many passed first time and how many were scrapped; the widget returns each step's first pass yield, the rolled throughput yield, the final yield and the scrap rate.
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<iframe src="https://a2z.tools/embed/w/yield-calculator" title="First Pass and Rolled Throughput Yield Calculator by A2Z Tools" width="100%" height="880" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>
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<div data-a2z-widget="yield-calculator" data-height="880"></div> <script async src="https://a2z.tools/embed.js"></script>
Adds a small script (what it does) that sizes the widget to fit its content, loads it lazily and keeps it isolated from your page's CSS.
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How it works
Units started enter step 1. At each step you enter how many passed without any rework and how many were scrapped; the rest were reworked and carried on. First pass yield for a step is passed-first-time divided by units entering it, and the units entering the next step are those entering this one minus its scrap. Rolled throughput yield multiplies the step yields together and estimates the probability that a unit gets through every step with no defect at all. Three steps at 90% each give 0.9 x 0.9 x 0.9 = 72.9%, even though a final inspection might report 100% if every reject was reworked. That gap between final yield and RTY is the hidden factory of rework. Scrap rate is the share of started units that never came out. Add a defect count and the opportunities per unit and the widget also reports DPMO, defects per million opportunities. Counts are checked so a step cannot pass more units than it received.
Calculation method
- FPY(step) = units passing first time / units entering the step
- Units entering step k+1 = units entering step k - units scrapped at step k
- RTY = FPY(1) x FPY(2) x ... x FPY(n)
- Final yield = good units out of the last step / units started; scrap rate = 1 - final yield
- DPMO = defects / (units started x opportunities per unit) x 1,000,000
Worked examples
Three steps at 90%
Inputs: 1,000 started; each step passes 900 first time; no scrap
Result: RTY 72.9%; final yield 100%; scrap 0%
Every reject was reworked, so final inspection hides 27.1% of units that needed fixing.
Three steps with scrap
Inputs: 1,000 started; step 1 950 pass, 10 scrap; step 2 940 pass, 5 scrap; step 3 960 pass, 5 scrap
Result: FPY 95.00%, 94.95%, 97.46%; RTY 87.91%; final yield 98%; scrap rate 2%
980 good units out, but only about 879 in every 1,000 would have made it without any rework.
Limitations
- Uses unit counts per step; the Poisson estimate RTY = e^(-DPU) used in some Six Sigma texts is not applied.
- Assumes reworked units re-enter the same flow; units reworked off-line and returned later are hard to count this way.
- DPMO depends on how opportunities are defined, so it is only comparable between processes that count them the same way.
Where publishers use it
- Six Sigma Yellow and Green Belt study material on DMAIC metrics
- A PCB assembly house explaining yield through solder paste, placement and reflow
- Pharmaceutical or food plants tracking batch release first time right
- Quality-engineering blogs on the cost of rework
- Supplier development pages asking vendors to report RTY
Questions
Why is RTY lower than my final yield?
Final yield counts reworked units as good; rolled throughput yield does not. A line that scraps 2% overall but sends about 4% of units to rework at each of three steps has a final yield of 98% and an RTY near 88% (0.96^3 = 0.885). The difference is labour, machine time and floor space spent fixing things.
What is the difference between FPY and first time yield?
They are used interchangeably for one step: the share of units that pass without rework or scrap. Some companies use throughput yield for the same idea; check that rework is excluded whatever the name.
How do I count opportunities for DPMO?
An opportunity is each place a defect could occur that the customer cares about - for example each solder joint on a board. 25 defects on 1,000 boards with 5 opportunities each is 25 / 5,000 x 1,000,000 = 5,000 DPMO. Six Sigma performance is 3.4 DPMO.
Can scrap exceed the failures at a step?
No - only a unit that failed first time can be scrapped there. The widget refuses scrap above units entering minus units passed, and refuses a pass count above the units that entered.
Does a high RTY mean high quality to the customer?
It means a capable process. Customer quality is measured after final inspection; RTY tells you how much effort it took to get there, which drives cost and lead time.
Sources
- Certified Six Sigma Yellow Belt Body of Knowledge (2022), section I.B.2 Six sigma metrics - American Society for Quality (ASQ) . Lists defects per unit, DPMO and rolled throughput yield as the standard Six Sigma metrics used through DMAIC; the formulas above are the standard textbook forms. Checked 2026-10-01.
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A2Z Tools First Pass and Rolled Throughput Yield Calculator https://a2z.tools/embed/yield-calculator
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