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FPY and RTY: the hidden factory

Enter each step’s first pass yield and cost per defect to get rolled throughput yield, parts reworked and scrapped per year and the cost of the hidden factory.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Preliminary estimate
Process steps (FPY 0 = no step)
More than 6 steps? Paste the list from Excel

One row per step: name (optional), FPY in % and cost per defect.

See what was read

Cost per defect: rework, re-inspection and material lost at that step. Parts scrapped later cost more because they have absorbed more work.

Volume and fate of defects
Economic analysis
—Rolled throughput yield (RTY)
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FPY of each step and cumulative RTY

Bars: FPY of each step. Line: chance of a part reaching that point with no defect.

Tap the chart to see the values.

Pareto of hidden factory cost

Annual defect cost by step, largest first, with cumulative percentage.

Tap the chart to see the values.

Project payback

Cash flow of the improvement: investment in year 0 and annual savings escalated at the rate entered, discounted at the MARR.

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The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

RTY = Π FPYᵢ
Defects at step i = units entering × (1 − FPYᵢ); reworked = defects × r; scrapped = defects × (1 − r)
Units moving on to step i + 1 = units entering − scrapped
Annual cost = Σ defectsᵢ × cost per defectᵢ

Assumptions and limits

  • Rework succeeds on the first attempt and the same recovered share applies at every step.
  • FPY independent between steps; defects that escape detection show up as external failures (cost of poor quality calculator).

Standards and technical documents

  • ISO 22400-2:2014: KPIs (quality ratio, scrap ratio, rework ratio)
  • Harry, M.; Schroeder, R. Six Sigma. Currency, 2000 (rolled throughput yield)
  • ISO 9001:2015, seção 9.1.3: análise e avaliação de dados
  • ASQ. The Certified Six Sigma Black Belt Handbook, 3rd ed., 2016

U.S. regulations

  • Uniform Commercial Code §2-314: implied warranty of merchantability
  • Magnuson-Moss Warranty Act (15 U.S.C. 2301 and following): consumer product warranties

Frequently asked questions

How do you calculate RTY?

Multiply the first pass yields of all steps. Five steps at 95% each give an RTY of 0.95⁵ = 77.4%: nearly one part in four goes through some rework or scrap.

What is the difference between FPY and final yield?

Final yield counts good parts at the end, including reworked ones. FPY counts only those that passed the first time. The gap between them is the hidden factory.

Where should improvement start?

At the step with the highest cost on the Pareto, not necessarily the lowest FPY: a late defect costs more because the part has absorbed more work and material.