2.3.2.2 Learning curve calculation

Achievable CMA Part 1

2. Planning, budgeting, and forecasting

2.3. Forecasting techniques

2.3.2. Learning curve analysis

Our CMA Part 1 course is currently in development and is a work-in-progress.

Learning curve calculation

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Calculating the learning curve

The cumulative average-time learning model is one of the most commonly used models in learning curve analysis. It calculates the average time or cost per unit based on the cumulative number of units produced.

In a learning curve, the production time decreases as cumulative production increases. For instance, if a company operates with a 70% learning curve, each time the total number of units produced doubles, the cumulative production time for all units drops to 70% of what it would have been if there were no learning effect. In the absence of learning, doubling production would simply double the time required.

Graph showing cumulative production time decreasing as cumulative units produced doubles, illustrating a learning curve. — Learning curve illustration

The cumulative average-time learning model can be applied to calculate the following metrics:

Total production time or cost: This is the total time (or cost) required to produce the entire quantity of units, from the first unit to the last. It takes into account the efficiency improvements gained as production increases.
Cumulative average time per unit: This refers to the average time taken to produce each unit, calculated from the very first unit produced to the final unit in the total quantity. This average reflects the efficiency gained across all units due to the learning process.

Example: See the following summary of production capacities for a company that manufactures model cars. The first unit takes $20 hours$ to produce and the company has determined that an $80% learning curve$ is applicable.

Calculating cumulative average and incremental hours for units produced under an 80% learning curve. — Learning Curve Example

In terms of the total production time and incremental time, the following interpretations can be inferred from the table:

If the company produces only one unit, it will take 20 hours.
Producing the second unit (the first doubling of production) will take a total of 32 hours, or an additional 12 hours from the original 20 hours it took to produce the first car. As a result, instead of 20 hours, it will only take 12 hours to produce the 2nd car.
Producing a total of 4 units (the second doubling of the production) will take only a total of 51.2 hours, or an additional 19.2 hours from the first 2 units produced. As a result, 19.2 hours would be the hours required to produce the 3rd and 4th cars.
Producing a total of 8 units (the third doubling of the production) will take a total of 81.92 hours, or an additional 30.72 hours from the first 4 units produced. As a result, it will take 30.72 hours to produce the 5th to 8th cars.

In terms of the cumulative average time per unit, you will notice that the average time decreased as the production is doubled. By the time 8 cars are produced, the cumulative average time per unit falls to 10.24 hours ( $81.92 \div 8$ ), compared with 20 hours for the first unit - keep in mind that this 10.24 hours is the average across all 8 cars, not the time to build the 8th car by itself.

Don’t mix up average and incremental time: the cumulative average time is the average time (or cost) per unit across all units produced so far - never the time for one specific unit or batch. When a question asks for the time (or cost) to produce an additional batch (for example, units 5-8), find the total at the higher cumulative level minus the total at the lower cumulative level, as shown in the table above. A separate incremental unit-time model, in which the time for the very last unit alone falls to the learning curve percentage with each doubling, gives different numbers - use it only if a question specifically names it.

All the calculations above can be represented in the following formula:

$Y = a (2 \cdot L C)^{n}$

Where:

Y = Total production time (or cost) to produce all units
a = the time or cost to produce the first unit
LC = the learning curve in decimals
n = the number of doublings to date

Applying the formula to the model car example, where $2 \times 0.80 = 1.60$ is the per-doubling factor and $a = 20 hours$ is the time to produce the first car, $n = 3$ for the third doubling gives $Y = 20 (1.60)^{3} = 81.92$ hours, the same cumulative total shown earlier. Keep in mind that $Y$ is the total production time for all units - to get the cumulative average time per unit, divide $Y$ by the number of units produced (for example, $81.92 \div 8 = 10.24$ hours per unit).

Applying the learning curve formula to calculate hours per unit as production doubles. — Learning Curve Formula

The learning curve analysis can manifest in different ways in the exam but the key is understanding the concepts behind it. CMA candidates can be asked about:

the total production time
the average time per unit; or
the incremental time required to produce additional batches.

Let’s take the following example problem:

Example 1: EcoDrive Technologies is launching a new line of electric motors for eco-friendly vehicles. As the production team gains experience, EcoDrive expects a reduction in production time due to improved efficiency. Based on past experience, the company projects an 80% learning curve. The cost to produce the first motor is estimated at $10,000.

Required: What is the estimated cost of manufacturing an additional seven (7) motors after the first one has been completed (8 total units)?

Solution: Manufacturing an additional seven (7) motors mean that production has already doubled thrice from the original one that was produced.

Doubling of Production
Achievable

Using the formula:

$Y = a (2 \cdot L C)^{n}$

where:

$Y$ is the total cost of producing 8 units,

$n = 3$ , which is the number of doublings at the production level of 8 units

$a = $10, 000$ which is the cost of producing the first motor; and

$LC = 80%$ which is EcoDrive’s learning curve,

we can compute the total cost of producing 8 units.

$Cost to manufacture 8 units = a (2 \cdot L C)^{n} = ($10, 000) (2 \times 80%)^{3} = ($10, 000) (1.60)^{3} = ($10, 000) (4.096) = $40, 960$

This means that if the first unit costs $10,000 to produce, then the cost of the next seven units will be:

$Cost of the next seven (7) units = $40, 960 - $10, 000 = $30, 960$

The base quantity $a$ doesn’t have to be a single unit - it can be a batch, as the next example shows, where $a$ is the time to produce the first batch of 100 units, and doublings are counted from that batch.

CMA candidates can also be asked to do a simple estimation of the learning curve percentage like as follows:

Example 2: Nova Robotics took 10,000 hours to produce its first batch of 100 units. When production doubled to 200 units, the total labor time amounted to 16,000 hours.

Required: What is the learning curve percentage of Nova Robotics?

Explanation: The hours without efficiency would have been: $2 \times 10, 000 hours = 20, 000 hours$ .

To calculate the learning curve, divide the time for 200 units (after the efficiency gains) by the time for 200 units (without the efficiency gains): $16, 000 hours /20, 000 hours = 80%$ .

Conclusion

Learning curve analysis offers several benefits:

more accurate labor-cost and pricing estimates for new products
more realistic budgets and cost standards as production ramps up
better-informed bid and pricing decisions on new contracts

It also has shortcomings:

assumes the learning rate stays constant, which rarely holds exactly in practice
learning levels off once a process matures, so the model works best early in production
only fits labor-intensive, repetitive work - it doesn’t apply to automated or one-off processes
staff turnover or process changes can disrupt or reset the learning effect
the learning curve percentage itself can be difficult to estimate accurately

It is important to recognize the limitations of the learning curve percentage used in these models. The learning curve should ideally be above 50% and below 100%. A percentage of 50% or below would indicate unrealistically high efficiency gains, while a percentage of 100% or higher suggests no improvement at all. Businesses typically use learning curves between 70% and 90% to reflect realistic improvements based on industry and process complexity.

Cumulative average-time learning model

Calculates average time/cost per unit based on cumulative units produced
Learning curve % = portion of time remaining each time cumulative production doubles (e.g., 70% curve → time drops to 70% of no-learning level at each doubling)
Produces two key metrics: total production time/cost, and cumulative average time per unit (total ÷ units)

Average vs. incremental time

Cumulative average time = average across all units so far, never a single unit/batch’s time
To find incremental cost/time for a specific batch (e.g., units 5-8): subtract total at lower cumulative level from total at higher cumulative level
Don’t confuse with a separate “incremental unit-time model” (last unit only) - use only if specifically named

Learning curve formula

$Y = a (2 \cdot L C)^{n}$
- $Y$ = total production time/cost for all units
- $a$ = time/cost for first unit (or first batch)
- $L C$ = learning curve as a decimal
- $n$ = number of doublings from the base unit/batch
$a$ can represent a single unit or a starting batch; doublings counted from that base
To get incremental cost of additional units: compute $Y$ at higher doubling level, subtract $Y$ (or base cost) at lower level

Estimating the learning curve percentage

Compare actual total time at doubled production to the hypothetical no-learning total (simple doubling of first-batch time)
$L C = \frac{actual time at doubled production}{time without learning (2 \times first batch time)}$

Benefits and limitations

Benefits: better labor-cost/pricing estimates, more realistic budgets/standards, improved bid decisions
Limitations: assumes constant learning rate (rarely true), learning flattens as process matures, only applies to labor-intensive/repetitive tasks (not automated/one-off work), turnover/process changes disrupt the curve, LC % hard to estimate accurately
Valid LC range: above 50% and below 100%; typical real-world range 70%-90%
- ≤50% = unrealistically high efficiency gains
- ≥100% = no improvement at all

Next | 2.3.3 Expected value

Learning curve calculation

Calculating the learning curve

The cumulative average-time learning model can be applied to calculate the following metrics:

Total production time or cost: This is the total time (or cost) required to produce the entire quantity of units, from the first unit to the last. It takes into account the efficiency improvements gained as production increases.
Cumulative average time per unit: This refers to the average time taken to produce each unit, calculated from the very first unit produced to the final unit in the total quantity. This average reflects the efficiency gained across all units due to the learning process.

In terms of the total production time and incremental time, the following interpretations can be inferred from the table:

If the company produces only one unit, it will take 20 hours.
Producing the second unit (the first doubling of production) will take a total of 32 hours, or an additional 12 hours from the original 20 hours it took to produce the first car. As a result, instead of 20 hours, it will only take 12 hours to produce the 2nd car.
Producing a total of 4 units (the second doubling of the production) will take only a total of 51.2 hours, or an additional 19.2 hours from the first 2 units produced. As a result, 19.2 hours would be the hours required to produce the 3rd and 4th cars.
Producing a total of 8 units (the third doubling of the production) will take a total of 81.92 hours, or an additional 30.72 hours from the first 4 units produced. As a result, it will take 30.72 hours to produce the 5th to 8th cars.

All the calculations above can be represented in the following formula:

$Y = a (2 \cdot L C)^{n}$

Where:

Y = Total production time (or cost) to produce all units
a = the time or cost to produce the first unit
LC = the learning curve in decimals
n = the number of doublings to date

The learning curve analysis can manifest in different ways in the exam but the key is understanding the concepts behind it. CMA candidates can be asked about:

the total production time
the average time per unit; or
the incremental time required to produce additional batches.

Let’s take the following example problem:

Example 1: EcoDrive Technologies is launching a new line of electric motors for eco-friendly vehicles. As the production team gains experience, EcoDrive expects a reduction in production time due to improved efficiency. Based on past experience, the company projects an 80% learning curve. The cost to produce the first motor is estimated at $10,000.

Required: What is the estimated cost of manufacturing an additional seven (7) motors after the first one has been completed (8 total units)?

Solution: Manufacturing an additional seven (7) motors mean that production has already doubled thrice from the original one that was produced.

Using the formula:

$Y = a (2 \cdot L C)^{n}$

where:

$Y$ is the total cost of producing 8 units,

$n = 3$ , which is the number of doublings at the production level of 8 units

$a = $10, 000$ which is the cost of producing the first motor; and

$LC = 80%$ which is EcoDrive’s learning curve,

we can compute the total cost of producing 8 units.

$Cost to manufacture 8 units = a (2 \cdot L C)^{n} = ($10, 000) (2 \times 80%)^{3} = ($10, 000) (1.60)^{3} = ($10, 000) (4.096) = $40, 960$

This means that if the first unit costs $10,000 to produce, then the cost of the next seven units will be:

$Cost of the next seven (7) units = $40, 960 - $10, 000 = $30, 960$

CMA candidates can also be asked to do a simple estimation of the learning curve percentage like as follows:

Example 2: Nova Robotics took 10,000 hours to produce its first batch of 100 units. When production doubled to 200 units, the total labor time amounted to 16,000 hours.

Required: What is the learning curve percentage of Nova Robotics?

Explanation: The hours without efficiency would have been: $2 \times 10, 000 hours = 20, 000 hours$ .

To calculate the learning curve, divide the time for 200 units (after the efficiency gains) by the time for 200 units (without the efficiency gains): $16, 000 hours /20, 000 hours = 80%$ .

Conclusion

Learning curve analysis offers several benefits:

more accurate labor-cost and pricing estimates for new products
more realistic budgets and cost standards as production ramps up
better-informed bid and pricing decisions on new contracts

It also has shortcomings:

assumes the learning rate stays constant, which rarely holds exactly in practice
learning levels off once a process matures, so the model works best early in production
only fits labor-intensive, repetitive work - it doesn’t apply to automated or one-off processes
staff turnover or process changes can disrupt or reset the learning effect
the learning curve percentage itself can be difficult to estimate accurately

Achievable CMA Part 1

2. Planning, budgeting, and forecasting

2.3. Forecasting techniques

2.3.2. Learning curve analysis

Our CMA Part 1 course is currently in development and is a work-in-progress.

Learning curve calculation

9 min read

Font

Discuss

Feedback

Calculating the learning curve

The cumulative average-time learning model can be applied to calculate the following metrics:

Total production time or cost: This is the total time (or cost) required to produce the entire quantity of units, from the first unit to the last. It takes into account the efficiency improvements gained as production increases.
Cumulative average time per unit: This refers to the average time taken to produce each unit, calculated from the very first unit produced to the final unit in the total quantity. This average reflects the efficiency gained across all units due to the learning process.

In terms of the total production time and incremental time, the following interpretations can be inferred from the table:

If the company produces only one unit, it will take 20 hours.
Producing the second unit (the first doubling of production) will take a total of 32 hours, or an additional 12 hours from the original 20 hours it took to produce the first car. As a result, instead of 20 hours, it will only take 12 hours to produce the 2nd car.
Producing a total of 4 units (the second doubling of the production) will take only a total of 51.2 hours, or an additional 19.2 hours from the first 2 units produced. As a result, 19.2 hours would be the hours required to produce the 3rd and 4th cars.
Producing a total of 8 units (the third doubling of the production) will take a total of 81.92 hours, or an additional 30.72 hours from the first 4 units produced. As a result, it will take 30.72 hours to produce the 5th to 8th cars.

All the calculations above can be represented in the following formula:

$Y = a (2 \cdot L C)^{n}$

Where:

Y = Total production time (or cost) to produce all units
a = the time or cost to produce the first unit
LC = the learning curve in decimals
n = the number of doublings to date

The learning curve analysis can manifest in different ways in the exam but the key is understanding the concepts behind it. CMA candidates can be asked about:

the total production time
the average time per unit; or
the incremental time required to produce additional batches.

Let’s take the following example problem:

Example 1: EcoDrive Technologies is launching a new line of electric motors for eco-friendly vehicles. As the production team gains experience, EcoDrive expects a reduction in production time due to improved efficiency. Based on past experience, the company projects an 80% learning curve. The cost to produce the first motor is estimated at $10,000.

Required: What is the estimated cost of manufacturing an additional seven (7) motors after the first one has been completed (8 total units)?

Solution: Manufacturing an additional seven (7) motors mean that production has already doubled thrice from the original one that was produced.

Doubling of Production
Achievable

Using the formula:

$Y = a (2 \cdot L C)^{n}$

where:

$Y$ is the total cost of producing 8 units,

$n = 3$ , which is the number of doublings at the production level of 8 units

$a = $10, 000$ which is the cost of producing the first motor; and

$LC = 80%$ which is EcoDrive’s learning curve,

we can compute the total cost of producing 8 units.

$Cost to manufacture 8 units = a (2 \cdot L C)^{n} = ($10, 000) (2 \times 80%)^{3} = ($10, 000) (1.60)^{3} = ($10, 000) (4.096) = $40, 960$

This means that if the first unit costs $10,000 to produce, then the cost of the next seven units will be:

$Cost of the next seven (7) units = $40, 960 - $10, 000 = $30, 960$

CMA candidates can also be asked to do a simple estimation of the learning curve percentage like as follows:

Example 2: Nova Robotics took 10,000 hours to produce its first batch of 100 units. When production doubled to 200 units, the total labor time amounted to 16,000 hours.

Required: What is the learning curve percentage of Nova Robotics?

Explanation: The hours without efficiency would have been: $2 \times 10, 000 hours = 20, 000 hours$ .

To calculate the learning curve, divide the time for 200 units (after the efficiency gains) by the time for 200 units (without the efficiency gains): $16, 000 hours /20, 000 hours = 80%$ .

Conclusion

Learning curve analysis offers several benefits:

more accurate labor-cost and pricing estimates for new products
more realistic budgets and cost standards as production ramps up
better-informed bid and pricing decisions on new contracts

It also has shortcomings:

assumes the learning rate stays constant, which rarely holds exactly in practice
learning levels off once a process matures, so the model works best early in production
only fits labor-intensive, repetitive work - it doesn’t apply to automated or one-off processes
staff turnover or process changes can disrupt or reset the learning effect
the learning curve percentage itself can be difficult to estimate accurately

Cumulative average-time learning model

Calculates average time/cost per unit based on cumulative units produced
Learning curve % = portion of time remaining each time cumulative production doubles (e.g., 70% curve → time drops to 70% of no-learning level at each doubling)
Produces two key metrics: total production time/cost, and cumulative average time per unit (total ÷ units)

Average vs. incremental time

Cumulative average time = average across all units so far, never a single unit/batch’s time
To find incremental cost/time for a specific batch (e.g., units 5-8): subtract total at lower cumulative level from total at higher cumulative level
Don’t confuse with a separate “incremental unit-time model” (last unit only) - use only if specifically named

Learning curve formula

$Y = a (2 \cdot L C)^{n}$
- $Y$ = total production time/cost for all units
- $a$ = time/cost for first unit (or first batch)
- $L C$ = learning curve as a decimal
- $n$ = number of doublings from the base unit/batch
$a$ can represent a single unit or a starting batch; doublings counted from that base
To get incremental cost of additional units: compute $Y$ at higher doubling level, subtract $Y$ (or base cost) at lower level

Estimating the learning curve percentage

Compare actual total time at doubled production to the hypothetical no-learning total (simple doubling of first-batch time)
$L C = \frac{actual time at doubled production}{time without learning (2 \times first batch time)}$

Benefits and limitations

Benefits: better labor-cost/pricing estimates, more realistic budgets/standards, improved bid decisions
Limitations: assumes constant learning rate (rarely true), learning flattens as process matures, only applies to labor-intensive/repetitive tasks (not automated/one-off work), turnover/process changes disrupt the curve, LC % hard to estimate accurately
Valid LC range: above 50% and below 100%; typical real-world range 70%-90%
- ≤50% = unrealistically high efficiency gains
- ≥100% = no improvement at all

Next | 2.3.3 Expected value

Learning curve calculation

Calculating the learning curve

The cumulative average-time learning model can be applied to calculate the following metrics:

Total production time or cost: This is the total time (or cost) required to produce the entire quantity of units, from the first unit to the last. It takes into account the efficiency improvements gained as production increases.
Cumulative average time per unit: This refers to the average time taken to produce each unit, calculated from the very first unit produced to the final unit in the total quantity. This average reflects the efficiency gained across all units due to the learning process.

In terms of the total production time and incremental time, the following interpretations can be inferred from the table:

If the company produces only one unit, it will take 20 hours.
Producing the second unit (the first doubling of production) will take a total of 32 hours, or an additional 12 hours from the original 20 hours it took to produce the first car. As a result, instead of 20 hours, it will only take 12 hours to produce the 2nd car.
Producing a total of 4 units (the second doubling of the production) will take only a total of 51.2 hours, or an additional 19.2 hours from the first 2 units produced. As a result, 19.2 hours would be the hours required to produce the 3rd and 4th cars.
Producing a total of 8 units (the third doubling of the production) will take a total of 81.92 hours, or an additional 30.72 hours from the first 4 units produced. As a result, it will take 30.72 hours to produce the 5th to 8th cars.

All the calculations above can be represented in the following formula:

$Y = a (2 \cdot L C)^{n}$

Where:

Y = Total production time (or cost) to produce all units
a = the time or cost to produce the first unit
LC = the learning curve in decimals
n = the number of doublings to date

The learning curve analysis can manifest in different ways in the exam but the key is understanding the concepts behind it. CMA candidates can be asked about:

the total production time
the average time per unit; or
the incremental time required to produce additional batches.

Let’s take the following example problem:

Example 1: EcoDrive Technologies is launching a new line of electric motors for eco-friendly vehicles. As the production team gains experience, EcoDrive expects a reduction in production time due to improved efficiency. Based on past experience, the company projects an 80% learning curve. The cost to produce the first motor is estimated at $10,000.

Required: What is the estimated cost of manufacturing an additional seven (7) motors after the first one has been completed (8 total units)?

Solution: Manufacturing an additional seven (7) motors mean that production has already doubled thrice from the original one that was produced.

Using the formula:

$Y = a (2 \cdot L C)^{n}$

where:

$Y$ is the total cost of producing 8 units,

$n = 3$ , which is the number of doublings at the production level of 8 units

$a = $10, 000$ which is the cost of producing the first motor; and

$LC = 80%$ which is EcoDrive’s learning curve,

we can compute the total cost of producing 8 units.

$Cost to manufacture 8 units = a (2 \cdot L C)^{n} = ($10, 000) (2 \times 80%)^{3} = ($10, 000) (1.60)^{3} = ($10, 000) (4.096) = $40, 960$

This means that if the first unit costs $10,000 to produce, then the cost of the next seven units will be:

$Cost of the next seven (7) units = $40, 960 - $10, 000 = $30, 960$

CMA candidates can also be asked to do a simple estimation of the learning curve percentage like as follows:

Example 2: Nova Robotics took 10,000 hours to produce its first batch of 100 units. When production doubled to 200 units, the total labor time amounted to 16,000 hours.

Required: What is the learning curve percentage of Nova Robotics?

Explanation: The hours without efficiency would have been: $2 \times 10, 000 hours = 20, 000 hours$ .

To calculate the learning curve, divide the time for 200 units (after the efficiency gains) by the time for 200 units (without the efficiency gains): $16, 000 hours /20, 000 hours = 80%$ .

Conclusion

Learning curve analysis offers several benefits:

more accurate labor-cost and pricing estimates for new products
more realistic budgets and cost standards as production ramps up
better-informed bid and pricing decisions on new contracts

It also has shortcomings:

assumes the learning rate stays constant, which rarely holds exactly in practice
learning levels off once a process matures, so the model works best early in production
only fits labor-intensive, repetitive work - it doesn’t apply to automated or one-off processes
staff turnover or process changes can disrupt or reset the learning effect
the learning curve percentage itself can be difficult to estimate accurately

Key points

Cumulative average-time learning model

Calculates average time/cost per unit based on cumulative units produced
Learning curve % = portion of time remaining each time cumulative production doubles (e.g., 70% curve → time drops to 70% of no-learning level at each doubling)
Produces two key metrics: total production time/cost, and cumulative average time per unit (total ÷ units)

Average vs. incremental time

Cumulative average time = average across all units so far, never a single unit/batch’s time
To find incremental cost/time for a specific batch (e.g., units 5-8): subtract total at lower cumulative level from total at higher cumulative level
Don’t confuse with a separate “incremental unit-time model” (last unit only) - use only if specifically named

Learning curve formula

$Y = a (2 \cdot L C)^{n}$
- $Y$ = total production time/cost for all units
- $a$ = time/cost for first unit (or first batch)
- $L C$ = learning curve as a decimal
- $n$ = number of doublings from the base unit/batch
$a$ can represent a single unit or a starting batch; doublings counted from that base
To get incremental cost of additional units: compute $Y$ at higher doubling level, subtract $Y$ (or base cost) at lower level

Estimating the learning curve percentage

Compare actual total time at doubled production to the hypothetical no-learning total (simple doubling of first-batch time)
$L C = \frac{actual time at doubled production}{time without learning (2 \times first batch time)}$

Benefits and limitations

Benefits: better labor-cost/pricing estimates, more realistic budgets/standards, improved bid decisions
Limitations: assumes constant learning rate (rarely true), learning flattens as process matures, only applies to labor-intensive/repetitive tasks (not automated/one-off work), turnover/process changes disrupt the curve, LC % hard to estimate accurately
Valid LC range: above 50% and below 100%; typical real-world range 70%-90%
- ≤50% = unrealistically high efficiency gains
- ≥100% = no improvement at all