Formula & Calculator
Rolled Throughput Yield
Calculates the overall probability that a unit passes through an entire multi-step process without any defects at any step.
Interpretation
RTY = Y1 × Y2 × Y3 × ... × Yn. The product of yields at each stage. Measures the probability of a unit passing through all steps without defects. Used to assess overall process quality and hidden losses.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| RTY | Rolled throughput yield | |
| Y1, Y2, ... Yn | First-pass yield at each individual process step |
What it means
Rolled Throughput Yield (RTY) is a measure of the overall quality of a multi‑step process. It is calculated by multiplying the individual yields (first‑pass yields) of each step (Y1, Y2, ..., Yn). For example, if a process has three steps with yields 0.95, 0.98, and 0.97, RTY = 0.95×0.98×0.97 = 0.903. This means that only about 90% of units are expected to pass all steps without any defects (including rework). RTY is more meaningful than the final yield because it accounts for scrap and rework at every stage, exposing hidden waste. It is commonly used in Six Sigma and lean manufacturing to quantify the true effectiveness of a process and to identify the step with the lowest yield (the bottleneck). Improving RTY involves focusing on the weakest links. Understanding RTY helps managers and engineers prioritise improvement resources to maximise overall process quality and reduce total cost of production.
Worked example
Rolled Throughput Yield – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Y1 | 0.95 |
| Y2 | 0.98 |
| Y3 | 0.97 |
| Parameter | Value |
|---|---|
| Each yield | 0.98 |
Common mistakes
- Y1, Y2, ..., Yn: The first‑pass yield of each step in the process – all expressed as fractions (not percentages).
- RTY: The probability that a unit will pass all steps without rework.
- Multiplication: RTY = product of all individual yields – if any step has low yield, RTY drops significantly.
- Interpretation: RTY gives a more realistic measure of overall process quality than simple average yield.
- Units: All yields must be in the same form (fractions).
Applications
Rolled Throughput Yield (RTY) is the product of the yields of each process step, providing an overall measure of the probability that a unit will pass through the entire process without defect. It accounts for the cumulative effect of quality at each step. Quality engineers use RTY to assess the performance of complex, multi‑step processes and to identify which steps contribute most to yield loss. Unlike FPY, RTY is always lower than the individual yields due to compounding. RTY is used in Six Sigma to express the overall defect rate and to set improvement goals. By analysing RTY, organisations can prioritise improvement efforts on steps with the lowest yields, thus maximising overall process efficiency and reducing hidden factory costs.
- Complex process quality assessment in manufacturing and service
- Six Sigma project selection and prioritisation
- Identification of yield‑busting process steps
- Performance evaluation of multi‑stage production lines
- Cost of quality analysis and reduction of total defects
Frequently Asked Questions
RTY is the probability that a unit passes through a multi‑step process without any defects at any step. It is calculated as RTY = Y1 × Y2 × Y3 × … × Yn, where Yi is the first‑pass yield of each step (i.e., the fraction of units that pass that step without rework).
Adding individual step yields and dividing by the number of steps (a simple average) instead of multiplying them. This significantly overstates the true overall yield. For example, if four steps each have 95% yield, the simple average is 95%, but the RTY is 0.95^4 = 81.5%, which is much lower.
RTY gives a realistic picture of the overall process capability. It highlights that even with high yields at each step, the cumulative effect can lead to a significant portion of units being defective by the end of the process. It helps identify improvement areas.
RTY typically assumes no rework (first‑pass). If rework is allowed, the calculation becomes more complex. You would need to model the rework loops to estimate the effective throughput yield. Some definitions of RTY include rework as defects, so it remains a first‑pass metric.
RTY can be converted to DPMO. If a process has n opportunities, the yield = (1 – DPMO/1,000,000)^n. So RTY can be used to estimate DPMO and sigma level.
Focus on improving the lowest‑yielding step (the bottleneck). Also, reduce variation in all steps. Use process improvement tools (Six Sigma, Lean) to increase the yields of individual steps.
It means that out of every 100 units that start the process, only 80 will pass all steps without any rework. The other 20 will require some form of correction at some point.
- Assumes independence of steps (yield at one step does not affect others).
- Does not account for the severity of defects.
- Does not capture the cost of rework.
- Only measures first‑pass performance.
For each step, calculate the first‑pass yield (units passed without rework / units started). Multiply all yields together. If you have defect rates, yield = 1 – defect rate per unit (or per opportunity).
Final yield includes rework; it is the percentage of units that eventually meet quality standards after rework. RTY is without rework. Final yield is always higher than RTY, and the difference reflects the cost of rework.