Learning Curve Modeling Approaches

Wright learning curve method.

struct WrightMethod <: LearningCurveMethod end

Introduced by T.P. Wright in 1936 in his seminal work on airplane production cost analysis (Wright, 1936). This model observes that with each doubling of cumulative production, the unit cost decreases by a fixed percentage. It is well‐suited for processes where learning is continuous and gradual.

$\text{Cost} = \text{InitialEffort} \times \text{TotalUnits}^{\frac{\log(\text{Learning})}{\log(2)} + 1}$

When to Use:

• When historical data show a smooth, predictable decline in unit costs as production doubles.

When to Avoid:

• When cost reductions occur in discrete steps or when the production process experiences structural changes.

Crawford learning curve method.

struct CrawfordMethod <: LearningCurveMethod end

Derived from discrete cumulative cost analysis methods found in operations research, the Crawford learning curve (e.g., Crawford, 1982) aggregates individual unit costs—which decrease according to a power‐law function of the unit index—to yield a total cost. Unlike the smooth curves of Wright and Experience, the Crawford method sums unit‐by‐unit costs that are reduced based on their position in the production sequence.

$\text{Cost} = \sum_{i=1}^{\text{TotalUnits}} \text{InitialEffort} \times i^{\frac{\log(\text{Learning})}{\log(2)}}$

When to Use:

• When you have detailed unit cost data and need a granular, discrete analysis of learning effects.

When to Avoid:

• When the overall cost trend is continuous and best represented by a smooth curve, in which case Wright’s or the Experience model might be preferable.

Experience learning curve method.

    struct ExperienceMethod <: LearningCurveMethod end

Popularized by Bruce Henderson of the Boston Consulting Group in the 1970s, the experience curve expands on Wright’s observation to encompass total cost reductions (including overhead and other factors) as cumulative production increases. It suggests that as cumulative output doubles, total costs fall by a constant percentage, reflecting economies of scale and learning effects throughout an organization.

$\text{Cost} = \text{InitialEffort} \times (\text{TotalUnits}^{\text{Learning}})$

When to Use:

• For strategic analysis and competitive planning when broad organizational efficiency improvements are observed.

  When to Avoid:

• When cost behavior is highly non-linear or when improvements are due to sudden technological breakthroughs.

Generate a learning curve as a DataFrame for a given method.

lc_curve(method::LearningCurveMethod, InitialEffort, TotalUnits, Learning; LotSize=1)

The DataFrame columns are:

• Units: Production unit number.
• CurvePoint: Cumulative cost/effort at that unit.
• IncrementalCost: Difference in cumulative cost from the previous step.
• AvgCost: Average cost per unit up to that point.
• Method: A string identifier for the method.

lc_fit(::ExperienceMethod, InitialEffort, Units; EstLC=0.8)

Fit the learning rate for the Experience method by adjusting the rate until its analytic cumulative cost converges to that computed using Wright's model.

lc_fit(::CrawfordMethod, InitialEffort, Units; EstLC=0.8)

Fit the learning rate for the Crawford method by adjusting the rate until its analytic cumulative cost converges to that computed using Wright's model.

lc_fit(::WrightMethod, InitialEffort, Units; EstLC=0.8)

Wright's method is taken as the baseline model so no fitting is performed. Returns the provided estimated learning rate.

Estimate the learning rate using Wright's method from two production data points.

learn_rate(::WrightMethod, TotalUnitsA, WorkUnitA, TotalUnitsB, WorkUnitB)

This method can be used as a starting point for the Crawford and Experience curves because no closed form solutions exist for these methods

Generate a comparison of cumulative costs for a range of learning rates (0 to 1) across the three methods: Wright, Crawford, and Experience.

learn_rates(InitialEffort, Units; LC_Step=0.1)

Returns a DataFrame with columns:

• LC: The learning rate.
• Wright: Cumulative cost from Wright's model.
• Crawford: Cumulative cost from Crawford's model.
• Experience: Cumulative cost from the Experience model.