Skip to content
Leantensify Learn

Every step hits its target, so why do so many orders go wrong?

Multiply your step yields to find the probability an order gets through the whole process with no rework, and see the gap against the average everyone quotes.

Rolled Throughput Yield · measure · White Belt · free, no account needed

Use this when

  • Each step reports a good yield but customers still see problems
  • You need to size the rework nobody has costed
  • Somebody has averaged the step yields and called it the process yield

Rolled Throughput Yield

sandbox
Process steps with units entering, units passing first time, and the resulting first-time yield.
StepUnits inPassed first timeFTYRemove
96.0%
98.0%
94.0%worst
99.0%
97.0%

Rolled throughput yield

84.9%

Normalised yield

96.78%

DPMO · one opportunity per step

32,000

Process sigma · includes the 1.5σ shift

3.35

The gapAveraging the step yields gives 96.80%. The real answer — the probability a unit gets through every step with no rework — is 84.9%. Of 1,000 units, about 151 need rework somewhere. That capacity exists, is staffed and is paid for, and it appears in no step’s report.

Normalised yield (96.78%) is the per-step yield you would need at every step to end up with this RTY. It is the geometric mean of the step yields, which is why it lands close to the plain average (96.80%) whenever the steps are similar — the two are near-identical here, and neither of them is the RTY. Normalised yield is for comparing processes with different numbers of steps. It is a poor target, because the fix is nearly always at the worst step rather than spread evenly.

DPMO counts defects, not defective units. 160 step failures against 5,000 opportunities — every unit entering a step is one chance to fail there, so the opportunity count comes from the table rather than from a box you type in. Feeding it the 151 defective units instead would count each unit once and then divide by the number of steps a second time, which raises the sigma level without touching the process. The process sigma includes the conventional 1.5 shift; the long-term Z the defect rate actually implies is 1.85.

How this is calculated
  • First time yield per step = units passing first time ÷ units in. “First time” excludes anything reworked, however quickly.
  • Rolled throughput yield = the product of the step yields, not their average. It is the probability a single unit clears every step untouched.
  • Normalised yield = RTY1/steps — the geometric mean per-step yield.
  • DPMO = defects ÷ opportunities × 10⁶, where a defect is a unit failing a step and an opportunity is a unit entering one — so the denominator is the incoming volumes summed across the steps, which is units × steps when the volumes are equal. Defective units in that numerator is the classic error: it counts a unit that failed three steps once, then divides by three opportunities anyway.
  • Process sigma = Φ⁻¹(1 − DPMO/10⁶) + 1.5. The 1.5 is a convention — Motorola’s allowance for long-term drift — not a derivation, and it is worth 1.5 sigma of flattery to whoever quotes the number without it.

Source: Montgomery, D.C., Introduction to Statistical Quality Control 7e, Sec. 1.4 and Ch. 6; George, M. et al. (2005), The Lean Six Sigma Pocket Toolbook, rolled throughput yield and the hidden factory.

How this is calculated

First time yield per step = units passing first time / units in. Rolled throughput yield = the PRODUCT of the step yields, not their average. Normalised yield = RTY^(1/steps), the geometric mean. DPMO = defective units / (units x opportunities) x 1,000,000, and process sigma = the inverse normal of (1 - DPMO/1,000,000) plus the conventional 1.5 shift.

Source: Montgomery, D.C., Introduction to Statistical Quality Control 7e, Sec. 1.4 and Ch. 6; George, M. et al. (2005), The Lean Six Sigma Pocket Toolbook, rolled throughput yield and the hidden factory.

Learn the method