A defence contractor has just started producing engines for a new government contract. The first engine took 800 hours to produce. If the learning curve is 80%, how long will it take to produce the first 20 engines? (Use at least three decimals in the exponent if you use the logarithmic approach, or Use Table E.3 (in the text) cumulative coefficient.)
A) less than or equal to 1000 hours
B) from 1000 to 8000 hours
C) from 8000 to 8500 hours
D) from 8500 to 10000 hours
E) 10,000 or more hours

Question

Quizplus · Accepted Answer

The learning curve formula is:

Y = aX^b

Where:
Y = time to produce a certain number of units
X = number of units produced
a = time to produce the first unit
b = learning rate (log of the learning curve percentage divided by log of 2)

We know that the learning rate is 80%, so

b = log(0.8)/log(2) = -0.3219

For the first engine, X = 1 and Y = 800 hours, so we can solve for a:

800 = a(1)^-0.3219
a = 800/(1^-0.3219)
a = 1746.3 hours

Now we need to find out how long it would take to produce the first 20 engines:

Y = 1746.3(20)^-0.3219
Y = 853 hours (rounded to the nearest hour)

According to the table of cumulative coefficients in the text, a cumulative average time of 853 hours falls between 8000 and 8500 hours. Therefore, the answer is C.

A Defence Contractor Has Just Started Producing Engines for a New