The cumulative average labor hours to assemble the first five units of product A were 15.882 hours. If the learning curve, based on the previous experience with similar products, is 85%, what is the estimated time (labor hours) that will be required to assemble the 20th unit?

The learning curve theory states that as the cumulative output doubles the cumulative average time taken till date is reduced to a certain percentage of the previous time. This percentage is called learning rate; and is given as 85% in this question.

The cumulative average time is determined using the formula below:

Y= aX^b

a - time taken for the first unit produced

b = log LR/Log 2

X- cumulative units till date

Y - cumulative average time taken for X units

LR- Learning rate

So we can apply this formula to our question

b = Log 0.85%/Log 2 = -0.23446

15.882 = a * 5^(-0.23446)

15.882 = a * 0.685671

a =15.882/0.685671

a =23.16271007

Time taken for the first unit =23.16 hours

Estimated time taken to assemble 20th units:

= Total time for 20units -Total time for 19units

= (23.16×(20^-0.23446)×20) - (23.16×(19^-0.23446)×19)

= 229.4949 -229.4949

= 8.836 hours

Note: total time = Cumulative average time × Cumulative number of units

Estimated time required to assemble the 20th unit= 8.836 hours