First-pass yield (FPY) measures whether work meets requirements without correction. Rolled throughput yield (RTY) tracks that performance across a process. In Lean Six Sigma projects, accepting a unit after rework must not erase its first-attempt failure from the yield calculation. Milan Terek’s 2024 research on Six Sigma metrics explains this distinction.
For practitioners following Lean Six Sigma International’s Certification Programs, yield measurement helps identify failures worth investigating. Project selection depends on records that show where units failed and how much work went into correcting them.
First-pass yield: define the boundary before calculating
Here, FPY refers to an individual process step. Its numerator counts units that meet the step’s requirements on their first attempt, without repair or rework. The same first-pass principle applies to an entire process: Terek’s 2024 paper uses FPY and RTY interchangeably at that broader boundary. A Lean Six Sigma dashboard needs to state the boundary alongside the metric.
Step FPY (%) = units passing the step first time ÷ units entering the step × 100.
Before establishing the FPY baseline, the process owner and project team need an agreed definition of a unit and a failed first attempt. That definition belongs alongside the process boundaries in a SIPOC. Repaired units retain their first-attempt failure status in the FPY calculation.
Multiplying step yields reveals cumulative losses
RTY measures passage through the complete process without rework. The US Environmental Protection Agency’s Lean Government Metrics Guide, published in July 2009, calculates it by multiplying the first-pass percentages for successive steps. With each step yield expressed as a decimal fraction, the formula is:
RTY (%) = FPY1 × FPY2 × … × FPYn × 100.
The EPA guide uses three step yields in its instructional example: 30%, 60% and 90%. These teaching figures do not represent results from a named organisation. A Lean Office project can use the same calculation to track complete and accurate work through successive handoffs.
| Process step | First-pass percentage | Decimal multiplier |
|---|---|---|
| Step 1 | 30% | 0.30 |
| Step 2 | 60% | 0.60 |
| Step 3 | 90% | 0.90 |
RTY = 0.30 × 0.60 × 0.90 × 100 = 16.2%. The EPA guide rounds this result to 16%. Reporting only the final step’s 90% yield would leave the earlier first-pass losses out of view.
Step 1 deserves investigation because it has the lowest first-pass percentage. That alone does not establish the investment priority. Before approving a solution, a Lean Six Sigma sponsor needs to see the rework effort and customer consequences associated with each failure category.
Reconcile RTY with the history of individual units
MIT’s 2004 material on critical parameter management identifies independence as an assumption when multiplying individual yield probabilities. Where failures are related across steps, the product of standalone FPYs does not necessarily equal the observed proportion of units completing every step first time.
Unit-level records give a Lean Six Sigma team a direct check on RTY: divide the count of units completing the defined route without any first-pass failure by the original cohort. Multiplication remains valid when each successive yield is conditional on having passed every preceding step first time. The denominator for each conditional yield includes only units with that first-pass history, so it differs from the denominator for ordinary station-level FPY.
The worked example in Terek’s 2024 paper shows why the count must distinguish defects from affected units. It assumes 20 defects distributed across 17 of 235 units, with those 17 units repaired or scrapped. The RTY calculation is:
RTY = (235, 17) ÷ 235 × 100 = 92.77%.
Subtracting the 17 affected units counts each failed unit once. Subtracting 20 defects would count some units repeatedly. The project’s measurement system analysis should establish whether defect records trace back to unique units and their first attempts.
Use FPY losses to select a DMAIC investigation
Within DMAIC, a yield calculation needs to support a testable problem statement. “Improve RTY” gives the team no failure to investigate. Naming the step and failure category sets a boundary for root cause analysis.
Carlyle Johnson Machine Company improved its returned-material process using value-stream mapping and root-cause investigation, according to a NIST case report published in August 2022. Reported FPY rose from 10% to 90%, while total lead time fell from over 40 days to five days. Those reported outcomes apply to Carlyle Johnson’s process; they provide no forecast for another project.
For a comparable Lean Six Sigma investigation, I would mark rework loops on the value stream map and measure rework hours alongside yield. The control plan should retain the original acceptance criteria. Any change to those criteria needs a separate record so the team can distinguish a revised failure definition from a process improvement.
Lean Six Sigma International’s Certification Programs progress from DMAIC problem solving to measurement-system analysis. Statistical inference is also part of that progression. The LSSx.0 pathway supports training selection according to the complexity of the projects you lead.
Sources
- Quality Innovation Prosperity (2024), Estimating Some Metrics in Six Sigma Through Confidence Intervals: https://www.qip-journal.eu/index.php/QIP/article/view/1972. Full paper: https://www.qip-journal.eu/index.php/QIP/article/download/1972/1398/8611.
- US Environmental Protection Agency (2009), Lean Government Metrics Guide: https://www.epa.gov/sites/default/files/2014-04/documents/metrics_guide.pdf.
- Massachusetts Institute of Technology (2004), Critical Parameter Management & Error Budgeting: https://ocw.mit.edu/courses/esd-33-systems-engineering-summer-2004/6111ad8d6ab6cf23dd0a76e5d8c8eb7b_s9_err_bdgtng_v8.pdf.
- NIST (2022), First Pass Yield Improvement Creates Dramatic Reduction in Lead Time: https://www.nist.gov/mep/successstories/2021/first-pass-yield-improvement-creates-dramatic-reduction-lead-time.
- Lean Six Sigma International (undated, accessed 2026), Certification Programs: https://leansixsigma.org/certifications-programs/.
