Question

Assume that it takes 49.61 min to produce the 20th unit and 40.03 min to produce the 50thunit. What is the learning curve? How many cycles are needed to reach a standard time of 35?

Answer 1

The formula that will be used here is: Tn = T1*C

where Tn = time required for nth unit, T1 = time required for 1st unit and C = learning curve coefficient

For the 20th unit: T20 = T1*C for 20 or 49.61 = T1*C for 20. Thus T1 = 49.61/C for 20

For 50th unit: T50 = T1*C for 50 or 40.03 = T1*C for 50. Thus T1 = 40.03/C for 50

Now 49.61/C for 20 = 40.03/C for 50

or 1.2393 = C for 20/C for 50

We know that C = N ^b where b is the log of the learning rate/log of 2

Thus 20^b/50^b = 1.2393

or b = -0.2342

also b = log of learning rate/log 2

Solving we get learning rate = 0.85

Thus learning curve = 85%

Let the no. of cycles be "x".

Thus 35 = T1*C

Now 49.61 = T1*C for 20 at 85%

or 49.61 = T1*0.495

or T1 = 49.61/0.495 = 100.22 minutes

So 35 = T1*C

or 35 = 100.22*C

or C = 35/100.22 = 0.349

C = N^b

Thus 0.349 = N^-0.2342

or N = 89

Thus standard time of 35 will be reached in the 89th unit.