Learning curves

When a complex and repetitive process is done by humans the time taken to complete one iteration of the task will reduce by a fixed amount as the number of times its repeated increases. In simpler words, when a task is done over and over again, if can be done faster.

Analyzing this phenomenon is done under learning curves with the use of a mathematical model

Learning percentage is the percentage by which the total cumulative time taken would reduce when the output level is doubled

Example, If the time taken to produce one unit is ‘t’ and the learning curve is 80%

According to the definition above when producing 2 units, the average time taken for one unit would be,           

It is important to understand that this is the average of producing the 2 units

So the total time taken to produce both units would be, t * 80% * 2

Using this method we are able to calculate the times taken to produce when the output level is doubled only. 

Learning curve plotted in respect with cum.average time per unit versus number of units

If both axis variables log values are plotted again, it can be seen to have a linear relation

This linear relation could be used to derive the formula below

Learning curve formula

           

Where Y – Cumulative average time taken per unit

            a = Total time taken for the first unit

            X = total number of units

            b = index of learning

 

Learning curve becomes essential when calculating time taken when the output level cannot be achieved by doubling the first output level (as done previously)

It is important to keep in mind that, the solution we get to Y is the cumulative average of the time taken for one unit,

It is NOT the time taken to produce the last unit

If the time taken to produce the last unit is needed, we will have to follow the bellow method,

Example: Assume we need to calculate the time taken to produce the n’th unit, the first unit took t’ amount of time. And the leaning curve is 80%

           

            Cumulative average time for producing n units =

            Total time taken for producing n units = unit time * number of units =  

Now we know the time taken to produce n units. If we find the time to produce n-1 units, the difference between them should effectively give us the time taken to produce the n’th unit. 

            Cumulative average time for producing (n-1) units =

            Total time taken for producing (n-1) units = unit time * number of units 
                                                                           =

There for the time taken to produce the nth unit = time taken for n units – time taken for n-1 units

                       

This done by variables would seem quiet comprehensive, but when solving a question with given figures following these steps logically is quite simple. Try to grasp the concept of how we arrived at the solution.

Uses of the learning curve

• In circumstances where the learning curve is likely to apply like complex assembly operations
• When preparing budgets the effect of the learning curve should be considered
• Can be used as a rational basis for price negotiation and cost control 

Important points to keep in mind when faced with a learning curve problem

• Learning curve is concerning the reduction of time per unit, NOT the cost per unit
• If labour is working in a machine set phase, for an example in a belt driven lineup, there is no possibility for learning curve to exist
• Learning is assumed to automatic, but the attitudes of the management and the commitment of the workforce would have a great impact in achieving this