How do you calculate first pass yield?

Divide the units that passed a step the first time, with no rework, repair or scrap, by the units that entered the step, and multiply by 100. For example, 900 units passing first time out of 1,000 entering is an FPY of 90%.

What is rolled throughput yield (RTY)?

Rolled throughput yield is the chance that a unit gets through every step of a process without any rework or scrap. It is the first pass yields of all the steps multiplied together, so four steps at 95%, 90%, 98% and 97% give an RTY of about 81.3%.

What is the difference between first pass yield and final yield?

Final yield counts every unit that eventually ships, including units that were reworked along the way. First pass yield counts only units that were right the first time. The gap between the two is the rework a plant does to fix its own defects, often called the hidden factory.

Why multiply the step yields instead of averaging them?

Because a unit has to get through every step. If step 1 passes 95% first time and step 2 passes 90% of what reaches it, only 95% × 90% = 85.5% get through both untouched. An average of 92.5% would hide the losses compounding from step to step.

Do scrapped units count against first pass yield?

Yes. Units that were scrapped and units that were reworked or repaired both failed the first pass. Count them in the units that entered the step, and leave them out of the units that passed first time.

How does first pass yield relate to the cost of poor quality?

Every unit that misses the first pass costs something to rework or scrap, and those costs are internal failure costs in the cost of poor quality. First pass yield shows where units fail; putting a money value on the failures shows which step to fix first.

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First pass yield (FPY) calculator

First pass yield (FPY) is the share of units that get through a process step right the first time, with no rework, repair or scrap. Rolled throughput yield (RTY) multiplies the FPY of every step together: the chance that a unit gets through the whole process without a single fix.

FPY (each step)equalsUnits passed first time divided by Units in × 100

RTYequalsFPY step 1 × FPY step 2 × … × FPY step n

A unit that fails, is reworked and then passes is not a first-pass unit. Final yield, which counts reworked units as good, hides that rework.

Units at each process step, in order

Step 1
Units in
Passed first time
Step 2
Units in
Passed first time
Step 3
Units in
Passed first time
Step 4
Units in
Passed first time

Pre-filled with the worked example. Passed first time means no rework, repair or scrap at that step; a reworked unit that later passes does not count.

Rolled throughput yield

81.3%

Of every 100 units started, about 81.3 get through all 4 steps with no rework or scrap.

Lowest step

Step 2

90.0% first pass yield

Reworked or scrapped

200 units

Across all steps

First pass yield by step

Step 195.0%

Step 290.0%

Step 398.0%

Step 497.0%

How to calculate it

Count what went right the first time

For each step, count the units in, every unit that entered the step in the period, and the units passed first time, the ones that needed no rework, repair or scrap there. Their ratio is that step's first pass yield.

Multiply the step yields together for the rolled throughput yield. Steps that each look fine on their own can still leave a low RTY, because the losses compound: a unit has to survive every step.

The step with the lowest FPY is usually the place to start, and a root cause analysis there pays off fastest. To put a money value on the rework and scrap, use the cost of poor quality calculator.

Worked example

Illustrative numbers, not a benchmark

A four-step process handles 1,000 units at each step. First time through, 950 pass step 1, 900 pass step 2, 980 pass step 3 and 970 pass step 4.

1FPY step 1 = 950 ÷ 1,000 = 95%. Step 2 = 900 ÷ 1,000 = 90%.
2FPY step 3 = 980 ÷ 1,000 = 98%. Step 4 = 970 ÷ 1,000 = 97%.
3RTY = 0.95 × 0.90 × 0.98 × 0.97 = 0.8128 = 81.3%.

Rolled throughput yield is 81.3%: about 19 of every 100 units need rework or are scrapped somewhere, although no single step is below 90%. Step 2, at 90%, is the one to fix first.

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