Rolled throughput yield (RTY) is the probability that a unit passes through every step of a process without a defect and without rework. You calculate it by multiplying the first-pass yield of each step. If a three-step process runs at 95%, 84% and 88%, the RTY is about 70%, even though no single step looks that bad.
This guide explains the definition, the formula, four worked examples, how RTY differs from first-pass yield and final yield, and what to do when the number comes out lower than you hoped.
TL;DR
- RTY is the chance a unit gets through all process steps defect-free the first time, with no rework, repair or adjustment counted as a pass.
- The formula is simple: multiply the first-pass yield (FPY) of every step. RTY = FPY₁ × FPY₂ × … × FPYₙ.
- RTY is always lower than your weakest step, and it falls fast as steps are added. Twenty steps at 99% each give only about 81.8%.
- A high final yield with a low RTY points to a hidden factory of rework that costs time and money.
- Improve RTY by fixing the individual steps with the lowest first-pass yield, using real station-level data.
Table of Contents
- What rolled throughput yield means
- The rolled throughput yield formula
- How to calculate rolled throughput yield, step by step
- Rolled throughput yield examples
- Why more steps mean a lower RTY
- Rolled throughput yield vs. first-pass yield vs. final yield
- What your RTY result tells you
- How RTY connects to DPMO and sigma level
- Common mistakes when calculating RTY
- Perspective: why we teach RTY early
- Build the skill behind the metric
- FAQ
- Sources
What rolled throughput yield means
The international standard for Lean Six Sigma, ISO 13053-1:2011, defines RTY in section 5.4 as the probability that a single unit can pass through a series of process steps free of defects. The standard adds the detail that matters most in practice: the yield at each step does not include rework, repair, additional adjustment, or delay for down time.
That last point is what makes RTY different from the number most plants and offices report. A unit that fails inspection, gets fixed and ships still counts as a good unit in a final yield report. In RTY, that unit counts as a failure at the step where the problem first appeared.
Think of it as a single question asked of the whole process: if I start 100 units, how many arrive at the end having gone right the first time at every step? RTY answers that question as a percentage.
Why it matters in Six Sigma projects
RTY gives a project team one number that reflects the whole chain, not just the best-looking station. It shows up in the Measure phase, where you establish a baseline, and again in Control, where you check that gains hold. If you are new to the vocabulary, our Six Sigma definitions page covers the terms that surround it, including DPMO, sigma level and yield.
The rolled throughput yield formula
Minitab’s documentation explains the calculation as the product of the individual throughput yields at each process step:
RTY = FPY₁ × FPY₂ × FPY₃ × … × FPYₙ
For each step, first-pass yield is:
FPY = units that pass the step the first time ÷ units that entered the step
When you count good units, count only those that make it through without rework or scrap. Express each yield as a decimal (95% becomes 0.95), multiply them, and convert the result back to a percentage.
How to calculate rolled throughput yield, step by step
- Map the process. List every step where a unit can be inspected, tested or judged acceptable or not.
- Collect first-pass data per step. Record how many units entered and how many passed without any rework, repair or adjustment.
- Compute FPY for each step. Divide units passed by units entered.
- Multiply the FPYs. Use decimals, not percentages.
- Sanity check. The result must be lower than your lowest single-step FPY. MFG Calcs offers the same quick check. If your RTY is higher, a step is probably counting reworked units as passes.
In a spreadsheet, put the step yields in a column, say B2:B5, and use =PRODUCT(B2:B5).
Rolled throughput yield examples
Example 1: labels through printing, laminating and cutting
Minitab’s own worked example follows 1,000 labels through three steps:
| Step | Units in | Units passed first time | FPY |
|---|---|---|---|
| Printing | 1,000 | 950 | 95% |
| Laminating | 950 | 800 | 84% |
| Cutting | 800 | 700 | 88% |
RTY = 0.95 × 0.84 × 0.88 = 0.70, so about 700 of 1,000 labels are acceptable. Notice that the weakest step is 84%, and the overall result is 14 points lower.
Example 2: four steps that all look strong
MFG Calcs shows a four-step example with first-pass yields of 96%, 94%, 98% and 97%. Multiply them: 0.96 × 0.94 × 0.98 × 0.97 = 0.858, or 85.8%. Every step is above 94%, yet roughly one unit in seven does not get through cleanly.
Example 3: an electronics assembly line (illustration)
Suppose a board assembly line has four stations. This is a made-up illustration, not client data.
| Station | FPY |
|---|---|
| Solder paste printing | 98% |
| Component placement | 97% |
| Reflow | 96% |
| Functional test | 99% |
RTY = 0.98 × 0.97 × 0.96 × 0.99 = 0.903. Out of 10,000 boards started, about 9,035 pass every station the first time. The other 965 were reworked or scrapped somewhere along the way. If the plant fixes most of them, final yield could still read 99%, which would hide almost 1,000 boards’ worth of repair labor.
Example 4: an invoice approval process (illustration)
RTY is not just for factories. Imagine an accounts payable process, again as an illustration:
| Step | FPY |
|---|---|
| Data entry | 92% |
| Manager approval | 90% |
| Account coding | 95% |
| Payment run | 98% |
RTY = 0.92 × 0.90 × 0.95 × 0.98 = 0.771. Only about 77 of every 100 invoices move from receipt to payment with no correction, query or resubmission. The other 23 each cost someone time. Dummies.com shows a similar purchase order case where a five-step process lands at 51.8%, and notes that a lot of hidden factory activity must be happening to pull the RTY down that far.
Why more steps mean a lower RTY
Because RTY multiplies, every extra step takes a bite. The math is unforgiving even at high yields:
| Steps | FPY per step | RTY |
|---|---|---|
| 1 | 95% | 95.0% |
| 5 | 95% | 77.4% |
| 10 | 95% | 59.9% |
| 20 | 99% | 81.8% |
MFG Calcs confirms the last row: a 20-step process at 99% per step yields about 81.8%. A process that sounds near perfect at each station can still send nearly one unit in five back for work.
This gives you two levers. You can raise the yield of individual steps, or you can remove steps that add no value. A step with a perfect 100% yield contributes nothing to the loss, so effort belongs where the yield is lowest.
Rolled throughput yield vs. first-pass yield vs. final yield
These three metrics are often confused. They answer different questions.
| Metric | What it measures | Counts reworked units as good? |
|---|---|---|
| First-pass yield (FPY) | Share of units that pass one step the first time | No |
| Rolled throughput yield (RTY) | Share of units that pass all steps the first time | No |
| Final yield | Share of units that eventually ship as good | Yes |
SYMESTIC gives a useful illustration in its first pass yield guide: a final yield of 99% can sit alongside an FPY of 85% if 14% of units pass only after rework. The scrap report looks excellent, while a large share of capacity goes into fixing things.
That gap between final yield and RTY is what Six Sigma practitioners call the hidden factory: the unseen work of inspecting, repairing, retesting and expediting that never appears in a standard output report.
Treating rework correctly
The ISO standard is clear that rework is excluded from the yield used in RTY. In practice, three habits keep your data honest:
- Pull first-pass data from station-level test logs or inspection records, not end-of-line counts, as MFG Calcs advises.
- Watch for steps that quietly repair defects and pass the unit along. Their apparent yield hides a lower true FPY.
- Define what counts as a defect before you collect data, and keep the definition fixed so results compare over time.
If each step’s FPY includes rework, the rolled number will read higher than reality.
What your RTY result tells you
A single RTY figure is a starting point. Here is how to read it.
High final yield, low RTY. Heavy rework is in the system. It is waste that adds cost and slows delivery. Start by finding which steps generate the most first-time failures.
RTY close to your lowest FPY. One step dominates the loss. Concentrate the improvement project there.
RTY far below every FPY. The loss is spread across many steps. Look at whether steps can be combined, simplified or eliminated, and at the common causes behind several of them, such as unclear specifications or inconsistent inputs.
Cost of poor quality. Rework.com cites ASQ research estimating that the cost of poor quality typically runs 5% to 30% of annual revenue for manufacturers. Treat that as a broad range, but it explains why a few points of RTY can be worth real money. If you want to put a number on your own project, our ROI of Six Sigma calculator is a good next step.
How RTY connects to DPMO and sigma level
RTY is a yield metric. DPMO (defects per million opportunities) and sigma level describe the same quality from a different angle. ISO 13053-1 notes that a sigma score of 6 corresponds to 3.4 DPMO, with calculations based on a 1.5 sigma shift of the mean. A conversion table from Conyso maps 6.0 sigma to a yield of 99.99966%.
A process with ten steps would need extremely high yield at each one to reach a respectable RTY. That is one reason Six Sigma pushes for very low defect rates at every step instead of settling for “good enough” locally. To convert between DPMO and sigma for a single step, try our sigma level calculator. For the distribution theory behind it, see our guide to standard deviation and the normal distribution in Six Sigma.
Common mistakes when calculating RTY
- Counting reworked units as passes. This is the most common error and it inflates the result.
- Using final inspection data only. You need yields by step.
- Mixing definitions of a defect across steps. Agree on criteria before measuring.
- Ignoring steps that feel minor. A small step at 90% costs as much as a major one at 90%.
- Using percentages in the multiplication. Convert to decimals first, or the answer will be wildly off.
- Measuring once. A single snapshot hides variation. Track RTY over weeks and watch the trend.
Perspective: why we teach RTY early
We see the same pattern across the professionals who study with us. They arrive with a dashboard full of green numbers, and a process that still feels slow and expensive. Rolled throughput yield is often the metric that explains the gap, because it makes rework visible.
That is why we treat yield metrics as core knowledge in our Six Sigma programs, not an advanced extra. Once you can calculate RTY and trace it back to the steps that cause the loss, the rest of a DMAIC project becomes far more concrete. You know where to measure, where to analyze and what a win looks like.
Our programs are built so you can learn this at your own pace and from home. Study materials and the certification exam come in one all-inclusive price, so there are no hidden fees. Our own stated guarantee is a 30-day satisfaction promise, and certificates are issued immediately on completion. If you want to move from reading about RTY to applying it on real projects, a structured certification path is the fastest way we know to get there.
David Lovell
Build the skill behind the metric
Knowing the formula is the easy part. The harder skill is running the project: choosing the process, collecting clean first-pass data, finding root causes and holding the gains. That is what Six Sigma training covers from White Belt through Black Belt.
Our Lean Six Sigma Certification is a self-paced online program with study materials and the exam included. If you want a broader path, our Six Sigma certification package bundles several levels in one enrollment.
Managers working in plants may also want to read how Six Sigma works in manufacturing, and those in supply chains can start with Six Sigma in logistics.
FAQ
What does RTY mean?
RTY stands for rolled throughput yield. It is the probability that a unit passes through every step of a process without a defect and without rework. You find it by multiplying the first-pass yield of each step.
Can rolled throughput yield be higher than first-pass yield?
No. RTY is a product of yields that are each at most 100%, so it can never exceed the lowest step’s FPY. If your calculation says otherwise, check whether rework is being counted as a pass at one or more steps.
What is a good rolled throughput yield?
There is no single target, because it depends on how many steps the process has and what defects cost you. A longer process needs a higher yield at every step to reach the same RTY. Compare your RTY against your own baseline and aim to raise it project by project, starting with the lowest-yield steps.
Does scrap count in rolled throughput yield?
Yes. A scrapped unit failed at the step where it was rejected, so it lowers that step’s first-pass yield. Reworked units lower it too. RTY only counts units that pass first time, every time, at every step.
Sources
- ISO 13053-1:2011, Quantitative methods in process improvement, Six Sigma
- Minitab: What are throughput yield and rolled throughput yield
- MFG Calcs: Rolled Throughput Yield Formula and Calculator
- MFG Calcs: Quality Metrics Calculations
- Dummies: How to Measure Yield for Six Sigma
- SYMESTIC: First Pass Yield
- Rework.com: First Pass Yield and Rolled Throughput Yield
- Conyso: Sigma Level to DPMO and Yield Conversion Table