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?

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

Explanation:

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