What is the difference between first pass yield and rolled throughput yield?

First pass yield (FPY) measures one step, units that pass right the first time divided by units entering that step. Rolled throughput yield (RTY) multiplies the FPY of every step to give the probability a single unit clears the entire process without rework anywhere. FPY is per-step; RTY is the whole line.

How do you calculate rolled throughput yield?

Multiply the first pass yield of every step: RTY = FPY₁ × FPY₂ × … × FPYₙ. For example, four steps at 98%, 95%, 97%, and 96% give RTY = 0.98 × 0.95 × 0.97 × 0.96 ≈ 86.6%. Never average the step yields, RTY is the product, which is always lower.

Why is rolled throughput yield lower than final yield?

Because final yield counts reworked units as good and only looks at units in versus good units out, while RTY penalizes every defect at the step where it happened and counts only units that passed untouched. The gap between the two numbers is the hidden factory, all the rework that final yield cannot see.

What is the hidden factory in manufacturing?

The hidden factory is the rework, retesting, and correction that happens inside a process but never appears in final yield numbers. It consumes labor, machine time, and material without showing up on the yield report. Rolled throughput yield exposes it: the spread between final yield and RTY is the hidden factory quantified.

How can 99% steps produce only 82% yield?

Because rolled throughput yield multiplies. Twenty steps each at 99% first pass yield give 0.99^20 ≈ 0.818, or about 82%. Every station looks nearly perfect alone, but the probability of one unit clearing all twenty untouched is the product of the yields, not their average, so small losses compound.

What is a good rolled throughput yield?

There is no audited benchmark, no standards body certifies an RTY target. What matters is the trend on your own line and the gap between RTY and final yield. A rising RTY with a shrinking gap means the hidden factory is getting smaller, which is the goal regardless of the absolute number.

How does first pass yield relate to OEE?

OEE’s quality factor uses the same right-first-time logic as FPY: only units that pass without rework count as good. The difference is scope, OEE quality is usually measured per machine, while RTY spans the whole line. A line can show a healthy per-machine quality factor and still have a low RTY once every station compounds.

Yield vs First Pass Yield vs Rolled Throughput Yield

Three yields answer three different questions, and why a line built from 99% steps can still ship an 82% rolled yield once you count the rework.

Final yield is good units out divided by units in, and it counts anything that eventually passes, including units that were reworked. First pass yield (FPY) counts only units that pass a step right the first time. Rolled throughput yield (RTY) multiplies every step’s FPY, so a line built from 99% steps can still roll up to just 82%. Three yields, three different questions.

Most plants track one yield number and think they understand their quality losses. They usually understand the smallest of them. Final yield tells you what shipped; it says nothing about the retesting, touch-up, and second passes that got it there. FPY and RTY exist to surface exactly that hidden work. This post defines all three, works an example you can check by hand, and shows why the arithmetic of multiplication is what makes a “good” line quietly expensive. If you want the single-step metric on its own first, start with first pass yield.

What is the difference between yield, FPY, and RTY?

The difference is what each one refuses to count. All three are ratios between 0 and 1, but they draw the line between “good” and “not good” in different places:

Final yield (traditional yield) = good units out ÷ units started. A unit that failed, got reworked, and passed on the second try counts as good. This answers: how many units did we ultimately ship?
First pass yield (FPY), also called first time yield = units that pass a step right the first time ÷ units entering that step. Reworked units do not count, even if they later pass. This answers: how often does this step get it right without a redo?
Rolled throughput yield (RTY) = FPY₁ × FPY₂ × … × FPYₙ across every step. It is the probability that a single unit passes the entire process untouched, no rework at any station. This answers: what is the real chance a unit sails through clean?

The trap is that final yield and RTY can be far apart on the same line. Final yield looks at the two ends of the process, units in, good units out, and is blind to everything that happened in between. RTY looks at every station and penalizes each defect where it occurred. The distance between them is the rework you have been paying for without measuring.

The three yields side by side. Final yield answers a shipping question; FPY answers a step question; RTY answers the honest whole-line question, and only RTY exposes the rework in between.

How do you calculate first pass yield for a step?

Count the units that pass the step correctly the first time and divide by the units that entered. The rework subtraction is the part people miss. The formula is:

FPY = (good units out − reworked units) ÷ units in.

Take a CNC cell that starts 200 housings and finishes 195 to spec, but 12 of those 195 needed a second pass to remove burrs before they passed. Final yield looks like 195 ÷ 200 = 97.5%. First pass yield is (195 − 12) ÷ 200 = 183 ÷ 200 = 91.5%. Same station, same shift; the six-point gap is the touch-up nobody was counting. That gap is the signal, it is where the six big losses and the quality factor of OEE actually live.

Why does a line of 99% steps roll up to 82%?

Because RTY multiplies, and multiplying numbers below 1 always drives the product down faster than intuition expects. Each step you add is another chance for a unit to need rework, and the probability of clearing them all is the product, not the average.

Run the arithmetic. A process with twenty steps, each with a first pass yield of 99%, has a rolled throughput yield of 0.99^20 = 0.818, or about 82%. Every station looks nearly perfect on its own report. Nearly one unit in five still needs work somewhere on the line. Stretch it further and the effect is brutal: ten steps at 95% roll to just 60% (0.95^10 ≈ 0.599). This is why averaging step yields lies, the average of those twenty 99% steps is 99%, but the reality a unit experiences is 82%.

Rolled throughput yield as a function of step count when every step runs at 99% FPY. By twenty steps the line clears only 82% of units untouched, even though no single station looks like a problem.

What is the hidden factory, and why does it matter?

The hidden factory is all the rework, retest, and correction that happens inside a process but never shows up in final yield. It is “hidden” because the metric most plants watch, units in, good units out, was designed not to see it. The people, machine time, and material spent fixing units are real costs; they just do not appear on the yield report.

RTY drags the hidden factory into the light because it counts every defect at the station where it happened. When RTY sits ten or fifteen points below final yield, that spread is the hidden factory, quantified. It usually maps directly to overtime you cannot explain, a “rework bench” everyone treats as normal, and cycle-time variation that wrecks throughput. Naming it is the first step to costing it, and first pass yield is the metric that puts a number on it per step.

How do you measure FPY and RTY across a line?

Measure at every step, count rework honestly, then multiply. Here is the procedure that turns a vague quality feeling into an RTY you can defend:

Map the process into real steps. A “step” is any operation with its own pass/fail check, a machining op, an inspection, a test, a fill. If a unit can fail and be sent back there, it is a step.
Count units in at each step. Use the actual count entering, not a plan number. Where possible pull it from the machine or a counter rather than a tally sheet, since the gap between counts is exactly what FPY measures.
Count first-time passes, and rework separately. The discipline is logging the redo. If touch-up and second passes are invisible, FPY collapses into final yield and the hidden factory stays hidden.
Compute FPY per step. (Good out − reworked) ÷ in, for each station. This tells you which step leaks first-time quality, independent of the others.
Multiply for RTY. FPY₁ × FPY₂ × … × FPYₙ. Resist averaging, the product is the truth a unit experiences; the average is a comfort.
Rank steps by their drag on RTY. The lowest FPY step is usually where an hour of improvement buys the most rolled yield. Attack it first, then re-multiply.
Trend RTY over time. One reading is a snapshot; the trend tells you whether the hidden factory is growing or shrinking. Wire the counts to the source so the trend is measured the same way every shift, the way machine monitoring does.

How do these yields relate to OEE and defects per unit?

They connect at the quality factor. OEE’s quality term uses the same right-first-time logic as FPY, only units that pass without rework count as good. But OEE’s quality is usually computed for one machine, while RTY spans the whole line, so a line can show a healthy per-machine quality factor and a punishing RTY once every station compounds. The two metrics are complementary: OEE tells you where a single asset loses quality; RTY tells you what the customer’s unit actually went through.

Defects per unit (DPU) is the bridge for lines where a unit can carry several defects at once. For low defect counts, RTY ≈ e^(−DPU), which is why quality engineers move fluidly between the two. The practical point: pick FPY/RTY when you care about rework and flow, and DPU when you care about defect density, and know they are describing the same reality from two angles.

Which yield should you actually track?

Track all three, but manage to RTY. Final yield keeps finance honest about what shipped, FPY tells the crew which step to fix, and RTY is the number that reflects the true cost of quality across the line. Where they diverge is not noise, it is the map of your hidden factory.

Reference points worth keeping on the table: the U.S. Federal Reserve and standards bodies do not publish yield benchmarks, so there is no audited “good RTY.” The definitions themselves are standardized in the Six Sigma body of knowledge, see ASQ’s Six Sigma resources and OEE’s quality ratio is defined formally in ISO 22400-2:2014. What is not standardized is honest rework counting, and that is where the number lives or dies. Harmony captures counts and quality checks at the station in real time rather than from end-of-shift memory, so FPY and RTY reflect the rework that actually happened, you can see how that looked on a real floor in the CLS case study or explore the module map on the features section of our homepage.