what is a learning curve 
a learning curve is a mathematical concept that graphically depicts how a process is improved over time due to learning and increased proficiency the learning curve theory is that tasks will require less time and resources the more they are performed because of proficiencies gained as the process is learned the learning curve was first described by psychologist hermann ebbinghaus in 1885 and is used as a way to measure production efficiency and to forecast costs 1a learning curve is typically described with a percentage that identifies the rate of improvement in the visual representation of a learning curve a steeper slope indicates initial learning that translates into higher cost savings and subsequent learnings result in increasingly slower more difficult cost savings understanding a learning curvethe learning curve also is referred to as the experience curve the cost curve the efficiency curve or the productivity curve this is because the learning curve provides cost benefit measurements and insight into all the above aspects of a company the idea behind this is that any employee regardless of position takes time to learn how to carry out a specific task or duty the amount of time needed to produce the associated output is high then as the task is repeated the employee learns how to complete it quickly and that reduces the amount of time needed for a unit of output that is why the learning curve is downward sloping in the beginning with a flat slope toward the end with the cost per unit depicted on the y axis and total output on the x axis 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 gained 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 2learning curve formulathe learning curve has a formula to identify a target cumulative average time per unit or batch the formula for the learning curve is y a x b where y cumulative average time per unit or batch a time taken to produce initial quantity x the cumulative units of production or the cumulative number of batches b the slope or learning curve index calculated as the log of the learning curve percentage divided by the log of 2 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 per unit or batcha time taken to produce initial quantityx the cumulative units of production or the cumulative number of batchesb the slope or learning curve index calculatedas the log of the learning curve percentagedivided by the log of 2 learning curve calculationlet s use an 80 learning curve as an example this means that every time we double the cumulative quantity the process becomes 20 more efficient in addition the first task we complete took 1 000 hours y 1000 1 log 80 log 2 1000 1 an average of 1 000 hours per task to complete one task 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 1 000 hours per task to complete one task now let s double our manufacturing output the initial time spent on the first task will stay 1 000 hours however our value for x will now change from one to two y 1000 2 log 80 log 2 1000 8 an average of 800 hours per task to complete two tasks 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 hours per taskto complete two tasks this means that the total cumulative amount of time needed to perform the task twice was 1 600 since we know the total amount of time taken for one task was 1 000 hours we can infer that the incremental time to perform the second task was only 600 hours this diminishing average theoretically continues as you advance along the learning curve for example the next doubling of tasks will occur at four tasks completed y 1000 4 log 8 log 2 1000 64 an average of 640 hours per task to complete four tasks 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 average of 640 hours per taskto complete four tasks in this final example it took a total of 2 560 hours 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 in theory the third and fourth task in the example above would have taken different amounts of time due to the fourth task being theoretically more efficient than the third task however the time taken for each of these two units is often shown as the average i e 960 hours two units 480 hours for each of the third and fourth unit learning curve tablethe learning curve can become complicated when trying to distinguish between the cumulative quantity the cumulative production time the cumulative average production time and the incremental production time therefore it is common to see a learning curve table that summarizes and neatly organizes each value this type of information is very useful in cost accounting the example above would have table as follows note that the cumulative quantity must double between rows to continue the table the next row must be calculated using a quantity of eight in addition note that 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 the 960 hours in the next row is the time it took to yield two additional tasks learning curve graphsbecause learning curve data easily creates trend lines it s fairly common to see learning curve data depicted graphically there are several data 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 the 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 slowing 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 shapes types of learning curveslearning curves can be depicted visually in different ways they can be represented in a chart with linear coordinates like the charts above in which the shape is an actual curve a learning curve can also be depicted between axis points in a chart as a straight line or a band of points lower learning curve percentages mean higher degrees of improvement as a result the lower the learning curve percentages the steeper the slope of graphs benefits of using the learning curvecompanies know how much an employee earns per hour and can derive the cost of producing a single unit of output based on the number of hours needed a well placed employee who is set up for success should decrease the company s costs per unit of output over time businesses can use the learning curve to inform production planning cost forecasting and logistics schedules the slope of the learning curve represents the rate in which learning translates into cost savings for a company the steeper the slope the higher the cost savings per unit of output this standard learning curve is known as the 80 learning curve it shows that for every doubling of a company s output the cost of the new output is 80 of the prior output as output increases it becomes harder and harder to double a company s previous output depicted using the slope of the curve which means cost savings slow over time learning curve examplethe learning curve has many applications within the realm of business it can help assess the true cost of undertaking a project for example the learning curve can play a fundamental part in understanding production costs and cost per unit consider a new hire who is placed on a manufacturing line as the employee becomes more proficient at their job they will be able to manufacture more goods in a smaller amount of time all else being equal in this example a 90 learning curve would mean there is a 10 improvement every time the number of repetitions doubles in the long run a company can use this information to plan financial forecasts price goods and anticipate whether it will meet customer demand 