What is rolled throughput yield and how is it different from final yield?

RTY is the probability a unit passes every process step correctly the first time, calculated by multiplying each step's first-pass yield. Final yield only counts good units at the end and hides rework. In the 4-step example, final yield might look near 96%, but RTY is 0.96 x 0.94 x 0.98 x 0.97 = 85.8%, revealing the rework losses buried between stations.

How do I calculate RTY for a multi-step process?

Get first-pass yield at each step as a decimal, then multiply them all together. For steps at 96%, 94%, 98%, and 97%: RTY = 0.96 x 0.94 x 0.98 x 0.97 = 0.858, or 85.8%. Use FPY (units passing on the first try divided by units entering), not the count after rework, or your RTY will be optimistic and wrong.

What is a good RTY benchmark for a manufacturing line?

It depends on step count, but as a rule of thumb 90% RTY is acceptable for a multi-step line, above 95% is strong, and below 80% signals a hidden factory of rework. Remember RTY compounds: ten steps each at 99% still yields only 90.4%. More steps demand higher per-step FPY to hit the same overall RTY target.

My station yields all look high but RTY is low. What is wrong?

That is the compounding effect, or a station is masking its true FPY by reworking defects before passing parts forward. In the example each step is above 94%, yet RTY is only 85.8%. Check whether any step repairs and re-passes units without logging the first-pass fail. Use true first-pass rates, then attack the lowest-FPY step first, here the 94% station.

Do I use percentages or decimals in the RTY formula?

Convert each yield to a decimal before multiplying: 94% becomes 0.94, 98% becomes 0.98. Multiplying percentages directly gives a meaningless number. The example runs 0.96 x 0.94 x 0.98 x 0.97 = 0.858, then you convert back to 85.8% at the end. Keep enough decimal places through the chain so rounding at each step does not distort the final RTY.

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

First-pass yield (FPY) is a single step's rate: units passing on the first attempt divided by units entering that step, like 0.94 at step two. RTY is the product of every step's FPY across the whole process, so it describes the entire sequence rather than one station. FPY is the input; RTY is the compounded result. You need all the FPY values to compute RTY.

Quality and Inspection

Rolled Throughput Yield Formula

Rolled Throughput Yield (RTY) multiplies the first-pass yield of every step in a process to show the true probability of a unit passing the entire sequence without rework. Use it to reveal cumulative quality losses that individual station yields hide.

Formula

RTY = Step 1 Yield x Step 2 Yield x Step 3 Yield x ... Step N Yield

Variables

Step N Yield: First pass yield at each individual process step (expressed as a decimal, e.g. 0.95 for 95%)

Understanding the Rolled Throughput Yield Formula

RTY measures the probability that a unit passes every step of a process correctly the first time, with no rework or scrap. Individual station yields hide the compounding effect: four steps at 96%, 94%, 98%, and 97% each look healthy, but multiplied together they give 85.8%. That means roughly 1 in 7 units touches a rework loop somewhere. RTY exposes the hidden factory of rescanning, retesting, and retouching that never shows up in a single station's pass rate.

Pull first-pass yield from each step, not final yield. FPY at a step is units passing on the first attempt divided by units entering, before any rework. Get these from station-level test logs or inspection records, not the end-of-line count. Express each as a decimal (0.94, not 94%) and multiply straight through. Watch for steps that quietly repair defects and pass them along, because their apparent yield hides a lower true FPY that RTY needs.

Read RTY as the odds of a clean run. At 85.8% you scrap or rework about 14% of starts across the line. Find your worst step first: the 94% station drags hardest here. Cutting its defects to 98% lifts RTY to about 89.4%. Broadly, 90% RTY is decent for a multi-step line, above 95% is strong, and below 80% signals a hidden factory eating capacity through rework you are not tracking.

Worked Example

A 4-step process has FPY rates of 96%, 94%, 98%, and 97%.

RTY = 0.96 x 0.94 x 0.98 x 0.97
= 0.96 x 0.94 = 0.9024
x 0.98 = 0.8844
x 0.97 = 0.858 = 85.8%

Result: 85.8% RTY despite each step being above 94%

Common Mistake

Using final yield instead of first-pass yield at each step. If a step catches and reworks defects before sending parts forward, its apparent yield looks fine but its FPY is lower. RTY only works correctly when you use true first-pass rates at every step.

Frequently Asked Questions

What is rolled throughput yield and how is it different from final yield?: RTY is the probability a unit passes every process step correctly the first time, calculated by multiplying each step's first-pass yield. Final yield only counts good units at the end and hides rework. In the 4-step example, final yield might look near 96%, but RTY is 0.96 x 0.94 x 0.98 x 0.97 = 85.8%, revealing the rework losses buried between stations.
How do I calculate RTY for a multi-step process?: Get first-pass yield at each step as a decimal, then multiply them all together. For steps at 96%, 94%, 98%, and 97%: RTY = 0.96 x 0.94 x 0.98 x 0.97 = 0.858, or 85.8%. Use FPY (units passing on the first try divided by units entering), not the count after rework, or your RTY will be optimistic and wrong.
What is a good RTY benchmark for a manufacturing line?: It depends on step count, but as a rule of thumb 90% RTY is acceptable for a multi-step line, above 95% is strong, and below 80% signals a hidden factory of rework. Remember RTY compounds: ten steps each at 99% still yields only 90.4%. More steps demand higher per-step FPY to hit the same overall RTY target.
My station yields all look high but RTY is low. What is wrong?: That is the compounding effect, or a station is masking its true FPY by reworking defects before passing parts forward. In the example each step is above 94%, yet RTY is only 85.8%. Check whether any step repairs and re-passes units without logging the first-pass fail. Use true first-pass rates, then attack the lowest-FPY step first, here the 94% station.
Do I use percentages or decimals in the RTY formula?: Convert each yield to a decimal before multiplying: 94% becomes 0.94, 98% becomes 0.98. Multiplying percentages directly gives a meaningless number. The example runs 0.96 x 0.94 x 0.98 x 0.97 = 0.858, then you convert back to 85.8% at the end. Keep enough decimal places through the chain so rounding at each step does not distort the final RTY.
What is the difference between RTY and first-pass yield?: First-pass yield (FPY) is a single step's rate: units passing on the first attempt divided by units entering that step, like 0.94 at step two. RTY is the product of every step's FPY across the whole process, so it describes the entire sequence rather than one station. FPY is the input; RTY is the compounded result. You need all the FPY values to compute RTY.