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Rolled Throughput Yield Calculator

Each step of a process can look acceptable while the product that comes out of the last step does not. Rolled throughput yield multiplies first pass yield across steps and shows the share of units that make it through everything first time. The gap between RTY and the final yield is your hidden factory.

Your numbers

Step 1 first pass yield

98.5 %

Step 2 first pass yield

97 %

Step 3 first pass yield

99.2 %

Step 4 first pass yield

95.5 %

Step 5 first pass yield

99 %

Enter 100 for any step not used.

Units started

units

Cost of rework or scrap per failed unit

Your results

Rolled throughput yield

89.6%

Units failing at least one step

104

Units passing every step first time

896

Hidden factory cost

$1,455

Rework and scrap cost for units that did not pass first time.

Weakest step yield

95.5%

Normalized yield per step

97.8%

Geometric mean across five steps.

First pass yield must count units that pass without rework. Units that pass after rework are not good first time and should be excluded from FPY.

Save results:

RTY vs step 4 first pass yield

Sweeps Step 4 first pass yield from 85 to 100, holding your other inputs fixed.

See yield by route from your ERP

Optional: we can look at how quality transactions could feed a daily RTY view.

Optional. The tool and every export work without this. No spam.

How to use it

Enter first pass yield for each step. First pass yield is units that pass the step the first time, with no rework or retest, divided by units entering the step. If you have fewer than five steps, enter 100 for the rest. Add units started and the cost of a failed unit to price the hidden factory. The chart sweeps one step so you can see how much RTY improves if the weakest step moves, which is useful for prioritizing Six Sigma projects.

Count rework as a failure for FPY
Use the same time window for every step
Enter 100 for unused steps

The formula

RTY equals the product of FPY across the steps: FPY1 times FPY2 and so on. Four steps at 95 percent give 81.5 percent RTY, not 95. Normalized yield is the geometric mean, RTY to the power of one over the number of steps, a useful comparison between processes with different step counts. Units failing at least one step equal units started times one minus RTY. This is the basis of the Six Sigma view that long processes need very high step yields to ship good product first time.

Reading the result

With the defaults, the five yields look fine individually, between 95.5 and 99.2 percent. Yet RTY is about 87.7 percent, so roughly 123 of 1,000 units fail somewhere and need rework or scrap. At 14 dollars each that is 1,720 dollars per thousand units of hidden factory. The weakest step, number 4, offers the best leverage: moving it from 95.5 to 99 percent raises RTY by about 3.5 points on its own. Use the chart to compare that with fixing step 2.

Common mistakes

Reporting final yield instead of RTY hides all the rework that happens in between, so the factory looks better than it is. Using inconsistent data windows, for example weekly FPY at one step and monthly at another, also distorts the product. Finally, parallel or branching routings are not a simple chain, so multiply only along the path a unit actually takes.

Do not use final yield as a stand-in for RTY
Do not mix reporting periods across steps
Multiply only along the route a unit actually takes

Frequently Asked Questions

What is the difference between FPY and RTY?

FPY is the pass rate at one step with no rework. RTY multiplies FPY across all the steps, giving the share of units that pass the whole process first time with no rework anywhere.

Can RTY be higher than the lowest FPY?

No. The product of numbers at or below 100 percent can never exceed the smallest of them. If it appears to, a step yield was entered above 100 percent or as a fraction instead of a percent.

How is RTY related to sigma level?

A higher RTY corresponds to fewer defects per opportunity. Six Sigma practitioners convert yield to defects per million opportunities using a normal distribution table; this tool only calculates yield.

Does scrap count the same as rework in FPY?

Yes, both mean the unit did not pass first time, so both reduce FPY. Their cost differs, which is why the hidden factory cost field is an average across both.

If step pass and fail counts sit in ERP quality or MES transactions, we can help build a read-only RTY view that updates daily by route and work center.

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