Calculate rolled throughput yield by multiplying first pass yields across process steps. Measure total process quality for multi-step manufacturing.
Rolled throughput yield (RTY) is the probability that a unit will pass through every step of a multi-step process without rework or rejection on any step. It is calculated by multiplying the first pass yield (FPY) of each sequential process step. RTY provides a far more accurate picture of overall process quality than final yield because it captures the cumulative impact of defects generated at every stage.
Consider a three-step process where each step has 95% FPY. The final yield might be 99% because rework salvages most defects, but the RTY is 0.95 × 0.95 × 0.95 = 85.7%. This means only 85.7% of units flow through the entire process without requiring any intervention — a much more honest assessment of process capability.
This calculator lets you enter FPY values for up to ten process steps and instantly computes the RTY, revealing the true end-to-end quality of your production line.
RTY reveals how much hidden rework exists in your total process. While final yield can mask quality problems, RTY shows the true probability of producing a defect-free unit end-to-end. It is essential for lean manufacturing and Six Sigma improvement projects. Regular monitoring of this value helps teams detect deviations quickly and maintain the operational discipline needed for sustained manufacturing excellence and competitiveness.
RTY = FPY₁ × FPY₂ × FPY₃ × ... × FPYₙ Where each FPY is expressed as a decimal (e.g., 95% = 0.95). Overall DPU = −ln(RTY)
Result: 81.4% RTY
RTY = 0.95 × 0.90 × 0.98 × 0.97 = 0.8124, or 81.24%. This means only about 81% of units pass through all four steps without any rework at any stage.
RTY's strength comes from its honesty. A manufacturing line with 20 steps, each at 99% FPY, has an RTY of only 81.8%. That means nearly 1 in 5 units needs rework somewhere in the process. Without RTY, this hidden factory remains invisible.
Rank process steps by their FPY from lowest to highest. The step with the lowest FPY offers the greatest leverage for improving RTY. Even a 2% FPY gain at the worst step often improves RTY more than a 5% gain at an already-strong step.
Lean practitioners use RTY to quantify hidden waste (muda), specifically the waste of rework and over-processing. Six Sigma teams use RTY to calculate process sigma levels and set improvement targets during DMAIC projects.
Final yield only measures units that ultimately ship successfully; it includes reworked units. RTY multiplies first-pass yields and reveals the true defect-free probability. RTY is always less than or equal to final yield.
RTY can include any number of sequential steps. The more steps, the more RTY typically drops, since each step's imperfections multiply. This calculator supports up to 10 steps.
Because yields are multiplied, not averaged. Five steps at 95% each give RTY = 0.95^5 = 77.4%, not 95%. This compounding effect is exactly why RTY is so revealing.
A good RTY depends on process complexity. For 3–5 step processes, 90%+ is a strong target. For 10+ step processes, 85%+ is excellent. Six Sigma organizations aim for RTY above 95% even in complex processes.
RTY is designed for sequential steps. For parallel paths that merge, calculate RTY for each path separately and then multiply the merged result at the convergence point.
Overall DPU (defects per unit) across the process equals −ln(RTY). You can then convert DPU to DPMO if you know the number of opportunities per unit, linking RTY to the sigma level of your process.