How to use the rolled throughput yield calculator
- Add a row for each process step and enter its first-pass yield as a percent.
- Enter the number of units that start the process.
- Optionally open the advanced options and enter defects per unit to see the matching yield.
- Read the rolled throughput yield, the expected good units, and where the units are lost.
Formula
rolled throughput yield = yield 1 x yield 2 x ... x yield n
units lost at a step = units arriving x (1 - yield of the step)
defects per unit (Poisson) = -ln(rolled throughput yield), and yield = e^(-defects per unit)
First-pass yield counts only the units that pass a step the first time, without rework. The Poisson link between yield and defects per unit assumes defects fall at random, which real processes often do not.
Three steps in a row
Three steps have first-pass yields of 96%, 98% and 95%. The rolled throughput yield is 0.96 x 0.98 x 0.95 = 0.89376, or 89.38%. Starting with 10,000 units, about 8,937.6 come out good first time and 1,062.4 are lost along the way.
Step by step, the first step loses 400 units (37.7% of the loss), the second loses 192 (18.1%) and the third loses 470.4 (44.3%). The third step has the lowest yield and sees almost as many units as the second, so it loses the most. The tool shows the loss at each step so that effort goes where the most units are lost. A defects per unit of 0.1 matches a yield of e^(-0.1) = 90.48%.
Why not average the yields
Averaging the yields of 96%, 98% and 95% gives 96.3%, which looks better than the real result of 89.38%. A unit must pass every step, so losses multiply. The more steps a process has, the faster the overall yield falls, which is why a line of many good steps can still be a poor line.
To convert defect counts into a sigma level, see the DPMO and Sigma Level Calculator. To balance the line itself, use the Takt Time and Line Balance Calculator.
Reading the loss column
The share of loss shows which step removes the most units from the start quantity. Improving a step that has a high share is worth more than polishing a step with a high yield but a small share. Compare it with what rework costs at that step too.
Assumptions and limits
- Each yield is a first-pass yield, with no credit for rework or repair.
- Steps run in series, and every unit goes through every step.
- Units started is a whole number and the losses are shown as expected averages, so they can have decimals.
- The defects per unit figure assumes defects occur at random and independently.
- Real yields vary from day to day, so treat the result as an average.
Frequently asked questions
What is the difference between first-pass yield and rolled throughput yield?
First-pass yield is for one step. Rolled throughput yield multiplies the first-pass yields of all steps to show the share of units that go right through without any rework.
Can I use units in and units out instead of a percent?
Yes. Divide good units out by units in for each step and enter the result as a percent.
What does the defects per unit figure mean?
It is the average number of defects on each unit that would give your yield if defects were spread at random. It is a model, not a measurement.
What if a step has 0% yield?
The rolled yield is 0%, and the tool says defects per unit is not defined, since no unit gets through.