Rolled Throughput Yield (RTY) Calculator

How it works

RTY = Y₁ × Y₂ × … × Yₙ; normalised yield = RTY^(1/n); DPU ≈ −ln(RTY); units to start = target ÷ RTY; sigma level ≈ Z(normalised yield) + 1.5

First-pass yield at a single step tells you how often that step gets it right without rework. Multiply the yields of every step in sequence and you get rolled throughput yield — the probability a unit sails through the whole process untouched — which is always lower than any single step and often shockingly lower than the final-inspection yield, because rework loops quietly repair defects along the way. That gap is the “hidden factory”: capacity, labour and materials consumed in fixing things. RTY exposes it, shows which step drags the product down most, and gives the honest planning ratio for how much to start to ship a given quantity. Because yields multiply, a long process needs every step near-perfect: ten steps at 97% each roll to just 74%.

Worked example

Five steps at 98.5%, 97%, 99.2%, 95.5% and 99%: RTY = 89.6%, normalised yield 97.8% per step (about 3.5σ). To ship 10,000 good units you must start about 11,160, generating roughly 1,160 rework or scrap events (≈ $13,900 at $12 each); step 4 is the weakest link.

Frequently asked questions