please show work No labor actuals were captured for the first six units manufact
ID: 333154 • Letter: P
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please show work
No labor actuals were captured for the first six units manufactured. It took 160 hours to manufacture the next batch of 8 units (units 7-14) During the next 6 months, an additional 60 units were built for which no labor data was collected.The next batch of 12 units (units 75-86) required 122 hours to produce During the next 6 months, an additional 100 units were produced for which no labor data was collected. It took 117 hours to produce the next batch of 15 units (units 187-201) Calculate the learning curve demonstrated by this organizationExplanation / Answer
As per Wright's Cumulative Average model, Y = aXb , where,
Y = the cumulative average time (or cost) per unit.
X = the cumulative number of units produced.
a = time (or cost) required to produce the first unit.
b = slope of the function when plotted on log-log paper.
= log of the learning rate/log of 2.
Y(7-14) = 14*Y14 - 6*Y6 = 14*a*14b - 6*a*6b = a(14b+1 - 6b+1) = 160 ---(1)
Y(75-86) = 86*Y86 - 74*Y74 = 86*a*86b - 74*a*74b = a(86b+1 - 74b+1) = 122 ---(2)
Y(187-201) = 201*Y201 - 186*Y186 = a*201b+1 - a*187b+1 = a(201b+1 - 186b+1) = 117 ---(3)
Dividing (1) by (2), we get,
Y(7-14) / Y(75-86) = a(14b+1 - 6b+1)/ a(86b+1 - 74b+1) = 160/122
or, (14b+1 - 6b+1)/(86b+1 - 74b+1) = 1.31 (to solve, this we can use Excel Goal seek function)
Solving it for b, we get, b= -0.32
r = e(-0.32*ln(2)) = 0.801
Dividing (2) by (3), we get,
Y(75-86)/Y(187-201) = a(86b+1 - 74b+1)/ a(201b+1 - 186b+1) = 122/117
or, (86b+1 - 74b+1)/(201b+1 - 186b+1) = 1.0427 (to solve, this we can use Excel Goal seek function)
Solving it for b, we get, b= -0.29972
r = e(-0.32*ln(2)) = 0.81241
Average learning rate = (0.801 + 0.81241)/2 = 0.8067 or 80.67 %
Therefore, a learning curve of 80.67% is demonstrated by this organization.
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