391. Learning Curves
The empirical observation that cost or time per unit decreases by a constant percentage every time cumulative production doubles. Discovered by T. P. Wright (1936) studying aircraft production at Curtiss-Wright.
391.1. Wright’s formula
Time (or cost) for the -th unit:
where:
- : time for the first unit
- : learning exponent
- : cumulative unit number
The learning rate — the proportion of time the -th unit takes relative to the -th:
So .
391.2. Common learning rates
| Learning rate | Exponent | Example industry |
|---|---|---|
| 80% | 0.322 | Aircraft assembly (Wright’s original) |
| 85% | 0.234 | Automotive |
| 90% | 0.152 | Electronics, software |
| 95% | 0.074 | Highly automated; little learning |
| 70% | 0.515 | Complex assembly, lots of skill |
Lower → faster learning. means no learning.
391.3. Crawford’s unit model vs cumulative average
Two conventions:
Wright (unit model): is the time for the -th unit specifically.
Crawford (cumulative average): is the average time across all units to . Same , but different curves and different interpretations.
| Wright unit | Crawford cumulative average | |
|---|---|---|
| Formula | ||
| Interpretation | time of the -th unit | average time over first units |
Crawford’s average always overstates per-unit improvement vs Wright (averaging includes early high-time units). Industries vary in which they use.
391.4. Cumulative cost
Total time / cost for the first units:
For Crawford model: .
391.5. Strategic implications (BCG, 1960s)
Boston Consulting Group famously generalized learning curves to experience curves — all costs (not just labor) decline with cumulative volume.
Strategic implications:
- Cost leadership through scale: the highest-volume producer has the lowest unit cost
- Predatory pricing: price below current cost to grab share, ride the curve to profitability
- First-mover advantage: head start on the curve is hard to overtake
Famous critiques (Henderson, BCG): treat learning as a strategic asset and a barrier to entry.
391.6. Limitations
- Empirical, not causal: explains pattern, doesn’t explain why learning happens
- Discontinuities: new product / process resets the curve
- Diminishing returns: long-run learning saturates
- Stanford-B / DeJong adjustments: include an “incompressibility factor” — costs can’t fall below some floor
DeJong’s model:
where is the incompressibility floor.
391.7. See also
- Factory Physics
- Takt Time — performance target as learning advances