FPY / RTY Yield Calculator

What are FPY and RTY and why are they important?

First Pass Yield (FPY) measures the percentage of units that pass through a process step correctly the first time, without any rework, repair, or scrap. It is a more honest quality metric than final yield because final yield hides the cost of rework.

Rolled Throughput Yield (RTY) is the product of all individual FPY values across a multi-step process. It reveals the true probability that a unit will flow through the entire process without any defect at any step. RTY is always less than or equal to the lowest individual FPY.

For example, five process steps each with 95% FPY give an RTY of 0.95^5 = 77.4%. This means nearly 1 in 4 units requires rework or generates scrap somewhere in the process — a hidden factory that consumes resources without adding value.

Formula: FPY = Good Units / Total Units (per step) RTY = FPY₁ × FPY₂ × ... × FPYₙ Average FPY = (FPY₁ + FPY₂ + ... + FPYₙ) / n

Example Calculation

A 3-step process: Step 1 produces 95 good out of 100 (FPY=95%), Step 2 produces 90 good out of 95 (FPY=94.7%), Step 3 produces 88 good out of 90 (FPY=97.8%). RTY = 0.95 × 0.947 × 0.978 = 88.0%. Expected output from 100 inputs: 88 units.

When to Use This Calculator

• During process design to predict the expected end-to-end output from a multi-step production process
• When comparing the true cost of quality — RTY exposes hidden rework loops that final yield alone does not reveal
• During Six Sigma projects in the Measure phase to establish the baseline process performance across all process steps
• When evaluating the impact of adding a new process step — even a 98% FPY step reduces overall RTY noticeably in a long process chain
• For production planning — knowing RTY lets you calculate how many units to start to guarantee a required number of good finished units

Common Mistakes to Avoid

• Using final yield instead of RTY — a process with 98% final yield may have RTY of 75% because reworked units are counted as good at the end, hiding the hidden factory
• Forgetting to include rework loops as failed first-pass units — if 10 out of 100 units are reworked and pass on second attempt, FPY is 90%, not 100%
• Assuming all process steps contribute equally — focus improvement efforts on the step with the lowest FPY first, as it has the most leverage on RTY
• Not tracking FPY by step over time — a declining FPY trend at one step warns of equipment wear, material changes, or training gaps before it becomes a crisis

How to Interpret Results

• RTY above 95% indicates a well-controlled process with minimal hidden factory — maintain through SPC and preventive controls
• RTY 85-95% is typical for good manufacturing — focus on the 1-2 lowest FPY steps for maximum improvement impact
• RTY 70-85% suggests significant rework and scrap costs — a structured improvement program (Six Sigma, Lean) can deliver substantial savings
• RTY below 70% indicates a process with major quality issues — every unit has roughly a 1-in-3 chance of needing intervention at some step; prioritize immediate action
• A large gap between average FPY and RTY means you have many steps, each contributing small losses that compound — simplifying the process (fewer steps) can improve RTY dramatically

Related Standards & References

• ISO 13053-1/-2 — Six Sigma DMAIC quantitative methods, in which FPY and RTY are core Measure-phase process performance metrics
• ASQ Six Sigma Body of Knowledge — Defines first pass yield, rolled throughput yield, and the hidden factory concept used in Green/Black Belt certification
• ISO 22400-2 — Manufacturing operations management KPIs, including quality ratio and scrap ratio measures that complement step-level yield tracking
• Montgomery, Introduction to Statistical Quality Control — Standard textbook treatment of yield metrics and their relationship to defect rates and process capability

Frequently Asked Questions

Why is RTY better than final yield for measuring quality?

Final yield only counts units that ultimately pass, regardless of how many were reworked. A process could show 98% final yield while RTY is only 75%, meaning 25% of units needed rework. RTY exposes the 'hidden factory' — the rework loops, retests, and repairs that consume time and money without adding customer value.

How do I improve RTY?

Focus on the step with the lowest FPY first, as it has the greatest impact on RTY. Use root cause analysis (5 Why, fishbone diagram) to identify why defects occur at that step. Common improvements include mistake-proofing (poka-yoke), better incoming material control, operator training, and tighter process parameter control.