Question

The first of a group of 100 machines requires 75 hours to build. If you expect 80% learning curve, how much time would it take to complete the 60th machine?

Answer 1

The first of a group of 100 machines requires 75 hours to build. If you expect 80% learning curve, how much time would it take to complete the 60th machine?

The theory of learning curve is based on the idea that the time required to perform a task decreases as worker gains experience. One of the models widely used in learning curve is Wright's Cumulative Average Model

which states that Y = aX^b

where

Y = the cumulative average time per unit
X = the cumulative number of machines produced
a = time required to produce the first machine
b = slope of the function when plotted on log-log paper.
   = log of the learning rate/log of 2.

here b = log 0.8/log 2 = -0.09691/.301 = -.32196

Also a = 75 hrs

So Y = 75X^(-0.322)

Now when X = 60 we get Y = 75 X 60^(-0.322) = 20.07 hours which is the cumulative average time per unit for 60 machines

i,e cumulative time for 60 machines = 60X20.07 = 1204.2 hrs

Similary, when X = 59, Y = 75X 59^(-0.322) = 20.18 hrs which is cumulative average time per unit for 59 machines

i.e. cumulative time for 59 machines = 59X20.18 = 1190.62 hrs

Therefore, time taken to complete the 60th machine = 1204.2 - 1190.62 = 13.58 hrs