What Is a Learning Curve?

A learning curve graphically depicts how a process improves through learning and increased proficiency. Tasks will require less time and resources the more they are performed. The learning curve was first described by psychologist Hermann Ebbinghaus in 1885 and is used to measure production efficiency and to forecast costs.

Role In Business

Companies can derive the cost of producing a single unit of output based on the number of hours needed, based on an employee's hourly rate. As a task is repeated, the employee learns how to complete it quickly and reduces the amount of time needed per unit. A well-placed employee should decrease the company's costs over time. Businesses can use the learning curve to inform production planning, cost forecasting, and 澳洲幸运5开奖号码历史查询:logistics schedules.

The learning curve is also referred to as the experience curve, the cost curve, the efficiency curve, or the productivity curve because it provides 澳洲幸运5开奖号码历史查询:cost-benefit measurements. The learning curve is downward sloping in the beginning, with a flat slope toward the end. As learning increases, it decreases the cost per unit of output initially ꧟before flattening out, as it becomes harder to increase the efficiencies gained through learning.

Learning curves are often associated with percentages that identify the rate of improvement. For example, a 90% learning curve means that for every time the cumulative quantity is doubled, there is a 10% efficiency gain in the cumulative average production time per unit. The percentage states the percentage of time that will carry over to future iterations of the task when production is doubled.

Learning Curve Formula

The learnin𝓰g curve has📖 a formula to identify a target cumulative average time per unit or batch:

$\begin{aligned}&{\bf Y = aX^b}\\&\textbf{where:}\\&\textbf{Y} = \text{Cumulative average time per unit or batch}\\&\textbf{a} = \text{Time taken to produce initial quantity}\\&\textbf{X} = \text{The cumulative units of production or the}\\&\qquad\ \text{cumulative number of batches}\\&\textbf{b} = \text{The slope or learning curve index, calculated}\\&\qquad\text{as the log of the learning curve percentage}\\&\qquad\text{divided by the log of 2}\end{aligned}$​Y=aXbwhere:Y=Cumulative average time&ཧnbsp;per unit or&n𓆉bsp;batcha=Timཧe taken to produce initial quantityX=The cumulative units&nb💟sp;of production&nbs♔p;or the cumulative number of batchesb=The slope&n𝓀bsp;or learning&nbs🌞p;curve index, calculatedas the log&𝔉nbsp;of the learni🎐ng curve percentagedivided by the log of 2​

Example

Assume an 80% learning curve. Every time the cumulative quantity is doub🌊led, the process becomes 20% more efficient. Assume the first task takeꦏs 1,000 hours.

$\begin{aligned}Y &= 1000\times1^{\frac{\text{log}\, .80}{\text{log}\, 2}} \\&= 1000\times 1\\& = \text{an average of 1,000 hours per task}\\&\quad\ \,\text{to complete one task}\end{aligned}$Y​=1000×1log2log.80​=1000×1=an average of 1,0✃00 h🐲ours per task to complete one task​

Now let's double the manufacturing output. The initial time spent on the first task will be 1,000 hours. However, the value for X will now change fr♛om one to two:

$\begin{aligned}Y&= 1000\times2 ^{\frac{\text{log}\, .80}{\text{log}\, 2}}\\&= 1000\times .8\\& = \text{an average of 800 hours per task}\\&\quad\,\,\,\text{to complete two tasks}\end{aligned}$Y​=1000×2log2log.80​=1000×.8=an average of 🌠800 hour💦s per taskto complete two tasks​

The total cumulative amount of time needed to perform the task twice was 1,600. Since the total amount of time taken forℱ one task was 1,000 hours, it can be inferred that the incremental time to perform the second task was 600 hours. This diminishing average theoretically continues along the learning curve. For example, the next doubling of tasks will occur at four tasks completed:

$\begin{aligned}Y &= 1000 \times 4^{\frac{\text{log}\, .8}{\text{log}\, 2}}\\& = 1000 \times .64\\& = \text{an average of 640 hours per task}\\&\quad\,\,\,\text{to complete four tasks}\end{aligned}$Y​=1000×4log2log.8​=1000×.64=an avera𒊎ge of 640 hours per taskto complete four tasks​
In this final example, it took a total of 2,560 hou♚rs to produce 4 tasks. Knowing it took 1,600 hours to produce the first two tasks, the learning curve indicates it will only take a total of 960 hours to produce the third and fourth task.

The cumulative quantity must double between rows—to continue the table, the next row must be calculated using a quantity of eight. The incremental time is a cumulation of more and more units as the table is extended. For example, the 600 hours of incremental time for task No. 2 is the time it took to yield one additional task. However, th🧸e 960 hours in the next row is the ti🍷me it took to yield two additional tasks.

Graphing Data

Because learning curve data easily creates trend lines, learning curve data is depicted graphically. There are several ꦏdata points to choose from, one of which is the total cumulative time needed to produce a given number of tasks or units. In the graph below, th💦e learning curve shows that more time is needed to generate more tasks.

However, the graph above fails to demonstrate how the process is becoming more efficient. Because of the graph's upward sloping curve, it appears it takes incrementally more time to perform more tasks. However, due to the nature of the learning curve, the x-axis is doubling and incrementally taking less time per unit. For example, consider the graph below that demonstrates the approximate average time needed to perform a given number of tasks.

The Bottom Line

The time and resources spent to perform a task the first time are probably hig🎶her than the time and resources spent on performing the same task for the 100th time. This idea of continual improvemen🅷t is measured through the learning curve.