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MULTI-STAGE QUALITY / FIRST-PASS SURVIVAL

Rolled Throughput Yield Calculator

Combine four sequential stage first-pass yields to estimate the share passing every stage without a correction loop.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Sequential process stages

Preparing the calculator...

METHOD / WORKED EXAMPLE

Trace first-pass survival across four process stages

Rolled throughput yield exposes cumulative no-correction survival that can be hidden when each stage percentage is viewed alone. Every supplied stage yield remains visible for review.

WORKED DEFAULT

Check the calculation with the default inputs

Stage yields of 95%, 98%, 97%, and 99% multiply to approximately 89.4039% rolled throughput yield; averaging them would answer a different question.

  1. Convert percentages0.95, 0.98, 0.97, 0.99
  2. Multiply stage survival0.95 x 0.98 x 0.97 x 0.99
  3. Convert to percent89.4039% RTY

READ THE RESULT

Interpret the output in context

The product is meaningful only when stage yields represent sequential first-pass survival for an aligned flow and period.

ASSUMPTIONS AND LIMITS

Know where the model stops

  • Every stage yield uses a compatible first-pass definition.
  • The four stages represent one sequential path without unmodeled bypass branches.

Stage populations, routing, rework treatment, and measurement windows must align; the simple product does not model bypasses or branching flows.

ASQ research: rolled throughput yield

COMMON QUESTIONS

Rolled Throughput Yield Calculator FAQs

Why multiply instead of average stage yields?

Multiplication tracks the share expected to survive every sequential stage on the first attempt. An arithmetic average summarizes the typical stage percentage but does not represent joint survival across all stages. Use decimal factors from the same route, period, unit definition, and rework policy; otherwise even the product does not describe one coherent production flow.

Is rolled throughput yield the same as final yield?

No. Final yield may count units that eventually pass after repair, retest, rerun, or other correction. Rolled throughput yield combines first-pass stage results and therefore exposes cumulative hidden correction loops. Review stage-level counts and routing as well as the combined percentage, because one low-yield stage can dominate the product and branching paths need a richer model.

Can this calculator certify process capability?

No. It multiplies four supplied first-pass yields; it does not establish statistical control, specification suitability, sampling validity, independence, process capability, or product acceptance. Retain source counts, reconcile stage populations, investigate rework and scrap, and use qualified quality review before relying on the number for release, contracts, incentives, or process-change approval.

Use boundary

Calculation path

Convert each stage percentage to a decimal and multiply all four first-pass yields; do not average the stage percentages.

Calculation path

RTY = stage 1 yield x stage 2 yield x stage 3 yield x stage 4 yield.