Cumulative average time is not the next unit’s time
Under the cumulative-average learning model, each doubling of cumulative output multiplies the average time per unit by the assumed learning factor. Total cumulative time is output multiplied by that average. To budget the next batch, subtract the earlier cumulative total from the later total. Multiplying the next batch by the new cumulative average generally gives a different and incorrect incremental estimate.
Framework checked on 24 October 2026
The method is described in ICMAI Intermediate Paper 12, Management Accounting, section 8.5, Introduction to Learning Curve. The material distinguishes the cumulative-average and incremental-unit models and explains that their same percentage labels do not make them interchangeable. This article uses the cumulative-average model throughout; its examples are original.
Let a be first-unit hours, X cumulative units and r the learning factor. Cumulative average hours Y = a × X raised to b, where b = log(r)/log(2). Total hours T(X) = X × Y. A batch from cumulative quantity m to n needs T(n) − T(m). The illustrations use exact doubling points so the central arithmetic can be checked directly without relying on rounded logarithms.
Define what the unit and learning population mean
A unit might be one product, job or repeat batch, but its definition must remain consistent. Separate material changes in design, crew, process or batch size rather than assuming all repetitions share the same learning history. Record first-unit time and the basis for the learning assumption, including whether downtime and setup are included.
Learning is a model of a process becoming more efficient, not a contractual guarantee. Compare predicted hours with actual completed output and consistent labour records. Do not interpret falling average hours as proof that every cost per unit falls in the same proportion. Materials, outsourced work and fixed capacity can behave differently.
Convert labour hours to cost using an explicit rate
Multiply the relevant incremental hours by the applicable rate only after defining what that rate represents. A labour-hour absorption rate containing fixed overhead is not automatically incremental cash cost. Where wage rates, overtime or staffing change, model the relevant periods separately; an old flat rate can obscure a cost increase despite improved hours.
For a quotation, reconcile cumulative production already completed, the new order quantity and the forecast end point. The order is not generally priced using the historical average for all units. A first-unit estimate copied from a different product or a forgotten starting quantity can distort the quote even when the spreadsheet formula is correct.
Validate the model and its useful horizon
The cumulative-average model requires positive additional production time. ICMAI explains why a learning factor at or below one-half produces an impossible zero or negative incremental-time result at a doubling. A factor of one represents no learning rather than improvement. Validate the input and test the resulting incremental hours before using the budget.
Do not extrapolate indefinitely. Evidence may show a plateau, process reset or loss of learning after a gap. Update future assumptions from supported observations rather than automatically treating the final cumulative average as a future marginal unit time. Keep changes to the learning rate, wage rate and production scope visible as separate explanations of the revised budget.
This is management analysis, not a prescribed statutory labour-cost deduction or employee-performance standard. The examples assume comparable repeat units and an explicitly defined hourly cost, with no tax, financing or employment-law entitlement computed. Operational quality and delivery constraints still need their own assessment.
Worked illustrations
These illustrations use fictional facts and expressly stated assumptions. Amounts are Indian rupees unless a different currency or unit is specified. They are independent examples, not findings about any actual client.
Illustrative example 1: Two units and the second unit
First-unit time is 100 hours and the assumed learning factor 80%. At cumulative output of two, average is 100 × 0.80 = 80 hours, total is 160 hours and incremental second-unit time is 160 − 100 = 60 hours. It is not 80 hours.
Illustrative example 2: Four cumulative units
At four units, the second doubling gives average 100 × 0.80 × 0.80 = 64 hours. Total is 4 × 64 = 256 hours. The additional third and fourth units together need 256 − 160 = 96 hours, averaging 48 hours for that two-unit increment.
Illustrative example 3: Budget units five to eight from total differences
At eight units, cumulative average is 51.2 hours and total is 409.6 hours. Units five to eight require 409.6 − 256 = 153.6 hours. Multiplying those four units by 51.2 instead gives 204.8 hours, overestimating the incremental batch by 51.2 hours.
Illustrative example 4: Turn the incremental batch into an explicit cost
Assume the 153.6-hour batch uses a relevant cost rate of ₹300 per hour. Its budgeted cost is ₹46,080. This does not mean every payroll or overhead item is variable; the example expressly stipulates that the rate is appropriate to the decision.
Illustrative example 5: A weaker learning assumption changes the budget
For an independent scenario with first-unit time 100 hours and a 90% learning factor, four-unit average is 81 hours and total 324 hours. Against the 80% scenario’s 256 hours, the difference is 68 hours. At a stipulated ₹300 per hour, the cost difference is ₹20,400. Validate the assumption rather than choosing the more favourable budget.
Illustrative example 6: Reject a zero-increment input result
With first-unit time 100 hours and an assumed 50% cumulative-average factor, output of two would have average 50 hours and total 100 hours. That implies the second unit takes zero hours. The calculation is a model-validation failure, not evidence of a free additional unit.
Ten-step verification table
| Step | Verification | Evidence to retain |
|---|---|---|
| 1 | Define a comparable production unit | Product, job or batch scope record. |
| 2 | Choose the actual learning-model type | Cumulative-average or incremental-unit methodology. |
| 3 | Validate first-unit time | Observed labour records and inclusion policy. |
| 4 | Support the learning factor | Comparable historical data and technical judgement. |
| 5 | Record cumulative output already completed | Production-history reconciliation. |
| 6 | Calculate cumulative averages and totals | Formula and independent doubling checks. |
| 7 | Subtract totals for the new batch | Incremental-hour budget working. |
| 8 | Validate positive incremental hours and input limits | Exception and model-range checks. |
| 9 | Apply a decision-appropriate hourly rate | Wage/cost-rate and fixed-overhead analysis. |
| 10 | Review actual performance, plateau and changes | Hours, quality, scope and revised-assumption report. |
Sixteen practitioner FAQs
1. What does an eighty-per-cent cumulative-average factor mean?
At each doubling of cumulative output, average time per unit becomes 80% of its previous value.
2. Is that the time of the next individual unit?
No. The cumulative average and incremental unit time are different quantities.
3. How is cumulative total time calculated?
Multiply cumulative output by cumulative average time.
4. How is a new batch’s time calculated?
Subtract the earlier cumulative total from the new cumulative total.
5. Can the cumulative-average and incremental-unit models be mixed?
No. Their percentage labels do not make their results interchangeable.
6. Must the unit definition stay consistent?
Yes. A change in product or batch scope can invalidate the assumed learning history.
7. Does a falling average guarantee lower total production time?
No. More units can require more total time even while average time declines.
8. Can every cost be reduced by the learning percentage?
No. Assess materials, fixed capacity and other costs separately.
9. Is an absorbed labour-hour rate always relevant cash cost?
No. Determine what the rate contains and whether those costs change.
10. Can wage inflation offset learning?
Yes. Keep the hour improvement and rate change separate in the cost bridge.
11. Why test a fifty-per-cent input?
It implies zero additional time at doubling under this model, showing an invalid positive-production assumption.
12. What does a factor of one indicate?
No learning improvement in the model.
13. Should the model be extrapolated forever?
No. Review plateaus, process resets and supported operating limits.
14. Can a long production gap affect the assumption?
It can. Reassess actual crew, process and retained learning rather than assuming continuity.
15. Does the last cumulative average become future unit time automatically?
No. Determine future marginal-time assumptions from appropriate evidence.
16. What should the quotation file preserve?
Model type, unit definition, starting output, learning evidence, incremental hours, rate assumptions and the actual-outcome review.
Conclusion
Keep the learning model, production history and new batch distinct. Budget incremental hours from total differences, then apply supported cost rates and review the model against actual outcomes.