Rolled Throughput Yield, First-Pass Yield & the Hidden Factory

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 10 inputs are read from the form on every keystroke: Spinning, Warping, Sizing, Weaving, Dyeing, Finishing & Inspection, Units Started, Share of Failures Recovered by Rework, Rework Cost per Unit and Value of a Good Unit.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Rolled Throughput Yield together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Final Yield After Rework, Hidden Factory, Units That Needed Rework, Units Right First Time, Units Lost Entirely, Cost of the Rework, Value of the Scrap and Weakest Stage Yield — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

Substituting

Every stage here looks acceptable in isolation and the reported yield is 93%. Only 78.5% of units went through without being handled twice, and the 1,461 reworked units consumed capacity that produced nothing extra. Averaging the six stage yields gives 96.1%, which is not a yield at all - it is the arithmetic mistake that hides this entire effect.

How to use it

1. Work through the input groups in order — Stage First-Pass Yields and Rework & Value. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Rolled Throughput Yield in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Final Yield After Rework, Hidden Factory, Units That Needed Rework, Units Right First Time, Units Lost Entirely, Cost of the Rework, Value of the Scrap and Weakest Stage Yield) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Rolled Throughput Yield before a trial is booked, so machine time and material in Quality Systems, Traceability, Utilities & Factory Decisions are committed against a calculated figure rather than an estimate.
• Costing and quotation — Rolled Throughput Yield is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Spinning) shows how much of the gap in Rolled Throughput Yield each variable explains.
• Teaching and study — the accepted ranges bracket normal Quality Systems, Traceability, Utilities & Factory Decisions practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• Stage yields are treated as independent, which overstates the rolled figure when a single root cause degrades several stages at once - a bad fibre lot shows up in spinning, weaving and dyeing together, and the true joint yield is then better than the product of the marginals. Rework recovery is applied as one rate to every stage; in practice it varies widely by stage and by fault type, and a stage with unrecoverable faults should be entered with a lower recovery. The model counts units, so it assumes a unit is the same thing at every stage - for a route that changes unit of measure between kilograms of yarn, metres of fabric and finished garments, run it per segment rather than end to end. Rework cost is direct cost only and excludes the capacity opportunity cost, which is normally the larger figure.
• Every input is bounded to the range normal practice occupies (Spinning 50 to 100 %, Warping 50 to 100 % and Sizing 50 to 100 %, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Standards and further reading

• ISO 9001 clause 8.7 and 9.1 - control of nonconforming outputs and monitoring of process performance.
• ISO 22514-1 - Statistical methods in process management, capability and performance.
• ASQ definition of rolled throughput yield and the hidden factory, as used in Six Sigma practice.

Questions people ask