First pass yield (FPY) is the share of units that come out of one process step right the first time, without rework or scrap. Rolled throughput yield (RTY) multiplies the FPY of every step and shows the share that gets through the whole process untouched — usually much lower than any single step suggests.
92.0% of units get through every step right the first time.
Units per 1,000 that need rework or are scrapped somewhere along the line.
Weakest step: step 4 (96.4%). It dominates the loss — start there.
FPY(step) = units good the first time / units entering the step RTY = FPY₁ × FPY₂ × … × FPYₙ Units lost at step i (per 1,000 entering the line) = units reaching step i × (1 − FPYᵢ) Hidden factory ≈ 1,000 × (1 − RTY) units per 1,000 that needed rework or were scrapped
A four-step electronics line: assembly, soldering, coating and final test. How many boards pass every step first time?
Every step looks fine on its own (all above 96 %), yet only 92 % of boards pass the whole line first time. The weakest step, final test, dominates the loss — improving it by two points would lift RTY more than polishing any other step.
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Act as a quality engineer and help me calculate first pass yield (FPY) and rolled throughput yield (RTY) for my process. Use exactly these formulas: FPY(step) = units good the first time / units entering the step RTY = FPY₁ × FPY₂ × … × FPYₙ (multiply, never average) Units lost at each step per 1,000 units entering the line = units reaching the step × (1 − FPY of that step) Rules: 1. Work step by step and show the running product after every step. 2. Repeat my percentages first and check the decimal separators. 3. If a step's FPY is missing or unclear, ask me — never assume one. 4. Tell me which step loses the most units and how much RTY would rise if it improved by one percentage point. 5. Remind me that rework counts as a failure for FPY. My steps and FPY: Step 1 = Step 2 = Step 3 = (add more as needed)
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Start the free course →FPY describes one step: the share of units that pass it right the first time. RTY describes the whole process: the share that passes every step right the first time. RTY is the product of the step FPYs, so it is always lower than or equal to the lowest step.
Because each step only passes on the good units of the previous one, the losses compound. Ten steps at 99 % each leave about 90 % of units untouched; twenty steps leave about 82 %.
It is all the rework, retesting and repair that happens to make units good in the end. Final yield can look high while a large share of capacity is spent fixing things; 1 − RTY shows how big that hidden factory is.
Both measure defects across a process. RTY is the probability of a unit passing with zero defects; if you know the defects per unit you can estimate it and convert to DPMO. Use the DPMO calculator to express the result as a sigma level.
Last tested: October 2026 · Tested with: automated math tests (3+ cases) · Reviewed by: Quality for Everyone editorial team
