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11 April, 23:37

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?

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  1. 12 April, 01:46
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    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
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