Learning Curve

Improvement by learning, gaining experience & skill by learning are the way of life. A person (or) an organization performs a task again & again, with the passage of time. They become more proficient, efficient at the task i.e they improve the skill of doing the task which lead to reduction in the performance time (or) cost. This can be stated as more the no. of time doing the same job, less the time required to complete the job. Based on this concept learning curve theory is developed. It states that everything the quantity produced is doubled, the cumulative average time decreases at fixed rate.

Terms associated with the study

• Learning curve ratio

This ratio indicates that every time the production is doubled, the cumulative average time declines at a particular fixed ratio known as learning curve ratio (or learning rate. For eg: LC ratio i.e LC rate is 90% indicates that for every time if the production is doubled, the cumulative average time reduced to 90% of the previous.

Illustration:

Production	cumulative avg. time	Total time
1st 1 unit	100hrs	100hrs
1st 2 unit	90% on 100 = 90x	180hrs
1st 4 units	90% on 90= 81*4	324hrs
1st 8 units	90% on 81= 72.9*8	593.2rs

• Learning coefficient (or) index of the learning curve (or) slope of learning curve:

 It is an improvement co-efficient & calculated using {log (LC Ratio)/log2}. This co efficient is denoted by S or B. We can remember the values for standard levels.

if

LC ratio = 90%	S = -0.152
LC ratio = 80%	S = -0.322
LC ratio = 70%	S = -0.5146

The relation among cumulative average time, index of learning curve etc

If K= the time required for producing the 1st unit (or) 1st lot (or) 1st batch

   S = Index of learning curve

   X = cumulative no. of units produced

   Y= cumulative avg. time for producing X units

Then we have: log(Y)= log(K) + (S)log(X)

The learning curve concept can be used to find out the cumulative average time (cumulative avg. cost) for the specified production level.

There are two situation namely

1. If the production quantity is successively doubled namely unit 2, unit 4, 8, 16, 32.....
2. If the production quantity is not in the form of doubling.