Why multiply instead of average?

A unit must pass every step on its first attempt. Multiplying conditional step yields gives the fraction completing the whole sequence that way.

Can reworked units count as first-pass successes?

No. A unit that needed repair, rerun or repeat acceptance has already left the uninterrupted first-pass cohort.

Why are expected units fractional?

The result applies measured percentages to a planned starting count. It is an expectation, not an assertion that a fraction of a physical unit passed.

What if I have only three steps?

Set the unused fourth step to one hundred percent. Keep the remaining yields conditional on the same first-pass route.

Quality calculator

Rolled Throughput Yield Calculator

Combine four conditional first-pass yields to estimate how many starting units pass the complete sequence without rework.

What this calculator does

Combine four conditional first-pass yields to estimate how many starting units pass the complete sequence without rework.

Formula used

Rolled yield = step 1 × step 2 × step 3 × step 4, as fractions
Expected first-pass units = starting units × rolled yield fraction
Expected first-pass loss = starting units × (1 − rolled yield fraction)
First-pass loss percentage = 100 − rolled yield percentage

Inputs explained

Step 1 First-Pass Yield: Share passing step 1 without rework or repeat inspection.
Step 2 Conditional First-Pass Yield: Share passing among units with no previous step failure.
Step 3 Conditional First-Pass Yield: Share passing among units still free of previous failures.
Step 4 Conditional First-Pass Yield: Share passing among units still on their first-pass route.
Starting Units: Whole units entering this same four-step sequence.

How to use the result

Best suited to lower step 1 yield reduces Completion, higher step 1 yield improves completion.
Expected counts may be fractional; actual observed counts are whole units. Parallel routes and recovered rework output require separate flow accounting.

Current U.S. benchmarks

U.S. manufacturing runs at 75.7% of capacity (Federal Reserve, Aug 2026). New factory orders are up 8.5% year over year (Census).

Common questions

Why multiply instead of average? A unit must pass every step on its first attempt. Multiplying conditional step yields gives the fraction completing the whole sequence that way.
Can reworked units count as first-pass successes? No. A unit that needed repair, rerun or repeat acceptance has already left the uninterrupted first-pass cohort.
Why are expected units fractional? The result applies measured percentages to a planned starting count. It is an expectation, not an assertion that a fraction of a physical unit passed.
What if I have only three steps? Set the unused fourth step to one hundred percent. Keep the remaining yields conditional on the same first-pass route.

Related guides

Deploying Rolled Throughput Yield Across the Whole Line

Last reviewed 2026-10-06.