BIZOMAT MAKEOS · Money
Learning Curve Unit Time and Cost
How long will the nth unit take, and what will the batch cost, as the team learns?
Unit time, cumulative time and average time per unit on a Wright learning curve from the first-unit time and learning rate, with labour cost for the batch.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Time for the first unit | h | Time for the first unit, from a trial build or estimate. |
| Learning rate | % | Time for a doubled quantity as a percentage of the earlier time (assembly often 80–90%, machining 90–95%). |
| Number of units | units | Number of units in the batch. |
| Labour rate | AUD/h | Labour cost per hour. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Time for the first unit
- What it is
- The hours taken to make the very first unit, from a trial build, a time study or an estimate.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h to 1000000 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every unit time, the cumulative time and the batch cost rise in proportion.
- Get it right
- Enter hours, not minutes: 30 minutes is 0.5 hours.
What this means: Learning rate
- What it is
- The time for each doubled quantity as a percentage of the earlier time; for example the second unit compared with the first.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 85% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower learning rate makes later units faster and lowers cumulative time.
- Get it right
- Type the percentage. A lower percentage means faster learning; take it from your own history for similar work.
What this means: Number of units
- What it is
- The number of units in the batch, counting from the first unit ever built.
- Units and format
- Enter a number in units: a count of units. The form accepts 1 units to 100000 units. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The curve counts cumulative units; a repeat order continues from where the earlier batch ended.
What this means: Labour rate
- What it is
- The labour cost per hour used to turn the cumulative time into a batch labour cost.
- Units and format
- Enter a number in AUD/h: Australian dollars per hour. The form accepts 0 AUD/h to 100000 AUD/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 AUD/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Batch cost rises in direct proportion.
- Get it right
- Use the loaded rate from your finance team if overhead should be included.
Method and formulas
- Unit time Tₙ = T₁ n^b, with b = log₂(learning rate).
- Cumulative time = Σ Tᵢ for i = 1…n; average = cumulative ÷ n.
- Batch cost = cumulative time × labour rate.
- Example: at 85%, unit 50 takes 3.9962 h and the batch averages 5.1026 h per unit.
Limitations
- Learning flattens out; production standards eventually limit times.
- Breaks in production cause forgetting and higher times.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Quote new products with falling labour time
- Plan staffing for a ramp-up
- Check whether production times are improving as expected
Who it is for
- Estimators
- Production planners
- Industrial engineers
What you get
- Time for the nth unit
- Cumulative and average time
- Labour cost of the batch
Interpreting the result
- Use average time for quoting a batch and unit time for planning the end of the run.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 146. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Experience curves, supplier track records and the operating team
In First-of-a-Kind Technology by the Numbers
What it covers: A builder's 41st line against a first unit on a 90% curve, the novel package on an 85% curve from A$9.33m, who pays for learning, and a sorter scored on borrowed experience.
Method explained here · BIZOMAT original book
Learning curves: unit and cumulative-average models
In Modular Projects by the Numbers
What it covers: Compare the unit and cumulative-average learning curves for twelve cells (13,191 h against 10,722 h), fit an 84.0% curve from six builds and forecast 870 h for cell 12.
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