How to Calculate Rolled Throughput Yield

Rolled throughput yield (RTY) is the probability that a single unit passes every step of a multi-step process right the first time, with no scrap and no rework anywhere along the way. You calculate it by multiplying the first pass yield of each step together: RTY = FPY₁ × FPY₂ × … × FPYₙ.

Here is the number that surprises most plant managers: ten steps that each run 98% first-time-good do not give you a 98% process. They give you about 82%. The yields multiply, they don't average, and the compounding is what a single station's yield report can never show you. RTY is the metric that describes what the customer's actual order lives through, every operation, back to back, with one chance each. This post covers the formula, why averaging the steps is the classic mistake, how RTY differs from the first pass yield of any one station, and how to measure it without kidding yourself.

What is rolled throughput yield?

RTY is the yield of the whole chain, not any single link. First pass yield answers "did this one step do it right the first time?" Rolled throughput yield answers the harder question: "did the unit survive the entire sequence untouched?" You get it by multiplying the FPYs, because passing step two only matters for units that already passed step one, and so on down the line.

The multiplication is the whole point. If a unit has to clear seven gates in a row, and each gate has its own small chance of sending it back for rework, the odds of clearing all seven clean are the product of the individual odds, the same math that says flipping seven straight heads is far less likely than any single flip. That is why a line full of "good" stations can still deliver a process yield that looks nothing like any station on it.

How is RTY different from first pass yield?

First pass yield is a property of one step; rolled throughput yield is a property of the whole route. They are built from the same raw counts, units in and units right the first time, but they answer at different scopes. A station can post a proud 97% FPY while the line it lives on delivers 80% RTY, and both numbers are correct. They are simply measuring different things.

The practical distinction is what you do with each. FPY tells you which station to fix; RTY tells you how much the whole process is really costing. A plant that reports only station yields will keep congratulating itself on high nineties while the order that matters, a finished unit, clean, first time, shows up far less often. RTY is the honest roll-up. It is also the number that behaves like the customer's experience, because customers do not buy a station's output; they buy what comes off the end of the line.

One vocabulary note worth getting straight: some references use first time yield (FTY) as the per-step figure and reserve first pass yield for a slightly different count. In practice the terms are used interchangeably on most floors. What matters is the rule underneath: a unit that was reworked, repaired, retested, or scrapped is a first-pass failure at that step, and RTY multiplies whatever per-step number honestly applies that rule.

Why can't you just average the yields?

Because averaging measures the wrong thing. The arithmetic mean of the step yields tells you how good a typical station is; it says nothing about how often a unit survives all of them. Consider the ten 98% steps above. The average step yield is 98%. The RTY is 81.7%. The average is not "close enough", it is off by more than 16 points, and the error grows with every step you add.

Here is a mixed example with hypothetical numbers for a five-step fabricated part, the kind of route where averaging quietly lies:

The average of those five yields is 96.9%. The RTY is 85.4%. If you run the plant off the average, you will budget for 3% loss and staff a rework bench for 15%. The welding step, at 94%, is doing most of the damage, and it is invisible if you only look at the aggregate. RTY plus the per-step FPYs together tell you both the size of the problem and where it lives.

What does RTY reveal that a final yield report hides?

It reveals the hidden factory, the inspect, rework, retest, repair loop that consumes labor and floor space while producing nothing new. Final yield (good units shipped ÷ units started) counts a unit as good even if it failed three times and was fixed three times. RTY refuses that laundering. The gap between a plant's reported final yield and its true RTY is the hidden factory, measured in yield points.

There is a companion figure worth knowing: normalized yield the n-th root of RTY, which converts a whole-process yield back into an equivalent "average step." For the ten-step example, the tenth root of 0.817 is 0.98, it tells you the typical step runs at 98%. Normalized yield is handy for comparing processes with different numbers of steps, but never quote it instead of RTY. RTY is the truth about the finished unit; normalized yield is a convenience for benchmarking.

By the numbers. The compounding is not a rounding footnote. A 20-step process where every step runs an excellent 99% still yields only 0.99²⁰ ≈ 82% RTY. The American Society for Quality puts the total cost of quality at commonly 15–20% of sales revenue and internal-failure costs, scrap, rework, retest, and the downtime they cause, are exactly the losses a falling RTY makes visible. Reference definitions for RTY and first-time yield are maintained in the ASQ Quality Glossary.

Where does rolled throughput yield mislead you?

RTY is honest arithmetic, but it can still point you wrong if the counting underneath it is sloppy. Three traps show up repeatedly on real floors. First, the opportunity trap: RTY counts units passing or failing a step, not the number of ways a unit could fail. A step that inspects fifteen features and one that inspects one feature both contribute a single FPY, so a low-yield step with many opportunities can look identical to a fragile step with one. When you need to compare defect density rather than pass rate, move to defects-per-unit or defects-per-million-opportunities alongside RTY, not instead of it.

Second, the branching trap: RTY assumes one straight route. Lines with parallel paths, model-dependent routings, or optional operations need the yields weighted by the fraction of units that actually take each path, or the roll-up quietly overstates the good product. Third, the rescue trap: if a downstream step "fixes" upstream defects without anyone logging a first-pass failure, both steps report high FPY and the RTY looks clean while the hidden factory hums along. The cure for all three is the same discipline that makes any yield number trustworthy, a written rule for what counts as a first-pass failure, applied at the station, every time.

How do you measure RTY on your line?

Measure each step's FPY honestly, then multiply. The sequence that keeps the number trustworthy:

1. Map every step that can fail. Any operation with an inspection, a test, or the possibility of rework is a step in the chain. Skipping "small" steps because they rarely fail is how RTY drifts upward toward final yield.
2. Write down "good, first time" for each step. Any rework, repair, retest, re-run, or adjustment-after-failure is a first-pass failure, even a ten-second touch-up at the bench. Fuzzy rules are the single biggest source of inflated RTY.
3. Count units in and first-pass-good out at each step, from test logs, inspection records, or station tallies. Rework must be captured where it happens, not reconstructed from memory at month-end.
4. Compute FPY per step, then multiply all of them for the line RTY. Recompute at least weekly, and keep the per-step numbers next to the roll-up so the worst step is obvious.
5. Attach a defect code to every failure. RTY tells you the process bleeds; the codes tell you where and why, feeding a Pareto and your defect tracking.
6. Attack the lowest-FPY step's top defect code with SPC on the driving variable and poka-yoke where the failure is human error. Then re-measure the whole chain, fixing the worst step lifts the entire product, not just one number.

How does RTY connect to OEE and the six big losses?

RTY is the quality story told across stations; the Quality factor inside OEE is the same logic told per machine. Both count first-pass-good units over total units, and both refuse to reward rework. If your OEE Quality term and your station FPYs are built from different rework rules, they will disagree, and reconciling them is a productive audit. The rework that RTY exposes also lands in the six big losses as startup and production rejects, and it steals capacity twice, every reworked unit occupies a machine that could have made a new one, which is why a low RTY quietly caps throughput and shows up in the plant KPI stack as missed schedule.

RTY is only ever as honest as the rework logging beneath it, and paper logs are where honesty goes to die: a bench touch-up takes ten seconds and writing it down takes thirty, so it doesn't get written down. Plants that capture quality checks and rework at the station, the way Harmony turns paper checks into live, searchable records feeding root-cause analysis (see the platform or the CLS field story), usually find their real RTY within a few weeks. It is almost always lower than the reported one, and knowing the true figure is the first honest step toward raising it.