Rolled Throughput Yield Calculator

Understanding the rolled throughput yield calculator — concept and principle

Rolled throughput yield (RTY) is the probability that a unit passes through every step of a process right the first time, with no rework or scrap at any step. It is a core Lean and Six Sigma measure because it exposes rework that final yield conceals. This calculator multiplies the first-pass yields of each step and also reports the equivalent average yield per step.

Every step looks good on its own, yet only 894 of 1,000 units get through all four without rework.

How it is calculated

RTY = Y₁ × Y₂ × … × Yₖ, with each step yield written as a fraction (the calculator starts from 100% and multiplies by each Yᵢ/100).
Normalised yield per step: Y_norm = RTY^(1/k), the geometric mean of the step yields.

Enter step yields as percentages separated by commas. Each value should be the first-pass yield: the share of units that pass that step without any rework.

The principle

If each step works independently, the chance that a unit survives all of them is the product of the individual chances, exactly as with independent events in probability. A chain of steps each with a high yield can still produce a low overall yield, because the losses compound. The normalised yield answers the question, "what single yield, applied at every step, would give the same RTY?", which makes processes with different numbers of steps comparable. If defects per unit (DPU) follow a Poisson model, RTY ≈ e^(−DPU), which links yield to defect counts.

Worked example

Inputs: 98%, 95%, 99%, 97% (k = 4 steps).
After step 1: 0.98. After step 2: 0.98 × 0.95 = 0.931. After step 3: 0.931 × 0.99 = 0.92169. After step 4: 0.92169 × 0.97 = 0.89404.
RTY = 89.4%.
Normalised yield: 0.89404^(1/4) = 0.97239, so 97.24% per step.

Roughly 1 unit in 10 needs rework or is scrapped somewhere along the line, even though no single step loses more than 5%. Using the Poisson link, −ln 0.894 ≈ 0.112 defects per unit.

How to read the result

RTY is always less than or equal to the lowest step yield. The gap between final yield (what ships) and RTY shows how much rework, the "hidden factory", the process carries. Ten steps at 98% each give only about 81.7% RTY, which is why long processes need very high step yields. Improvement usually pays off most at the lowest-yield step.

Common mistakes

Using final yields after rework instead of first-pass yields, which overstates RTY.
Averaging step yields arithmetically instead of multiplying them.
Including a step that only some units pass through without weighting it.

Keep in mind: The product formula assumes each step's yield is independent of the others. If a defect at one step makes failure at a later step more likely, or if inspection misses defects, the true RTY differs, so validate with actual first-pass data.

Frequently asked questions

What is the difference between RTY and first-pass yield?

First-pass yield usually refers to one step or to the whole process measured once at the end; RTY is the product of first-pass yields across all steps.

Can RTY be higher than the final yield?

No. Final yield counts units that eventually pass, including after rework, so it is at least as high as RTY.

Sources: D. C. Montgomery, Introduction to Statistical Quality Control, Wiley · F. W. Breyfogle III, Implementing Six Sigma: Smarter Solutions Using Statistical Methods, Wiley

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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