Question 1

To use the table of learning-curve coefficients,you must specify ________ and ________.

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Question 2

In the formula approach to learning curve calculations,you have used the formula TN = T1 (Nb).For a problem with a 92 percent learning curve,what is b?

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Question 3

Your firm has expertise with a special type of hand-finished furniture.The learning curve is known to be 82%.If the first piece of furniture took 6 hours,estimate (using the doubling approach)how long it will take to complete the third unit.

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Question 4

The first unit of a product took 50 hours to build,and the learning curve is 80%.How long will it take to make the third unit? (Use at least three decimals in the exponent if you use the formula approach. )
A)under 30 hours
B)about 32 hours
C)about 35 hours
D)about 50 hours
E)about 75 hours

Accepted Answer

Using the learning curve formula, we can calculate the time it takes to build the nth unit: 
Tn = T1*(n^log(0.8))
For the third unit, n = 3 and T1 = 50. 
T3 = 50*(3^log(0.8)) 
T3 ≈ 35.27 
Therefore, the best choice is C, which approximates the calculated value to the nearest hour.

Question 5

Your firm has expertise with a special type of hand-finished furniture.The learning curve is known to be 82%.If the first piece of furniture took 6 hours,use the formula approach to determine how long it will take to make the third unit.

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Question 6

A defense 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?
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

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Question 7

A defense contractor has just started producing turbines for a new government contract.The first turbine took 7000 hours to produce.If the learning curve is 90%,how long will it take to produce the 10th turbine? (Use at least three decimals in the exponent if you use the formula approach. )
A)less than 4800 hours
B)from 4800 to 4900 hours
C)from 4900 to 5000 hours
D)from 5000 to 5100 hours
E)over 5100 hours

Accepted Answer

Using the learning curve formula: 
Y = aX^b, 
where Y is the time required to produce the Xth unit, a is the time to produce the first unit, and b is the learning rate factor. 
We know that the first turbine took 7000 hours to produce (a = 7000) and the learning curve is 90% (b = log(0.9)/log(2) = -0.152). 
So, for the 10th turbine, we can calculate: 
Y = aX^b = 7000(10)^(-0.152) = 4872.6 hours. 
Therefore, the answer is C) from 4900 to 5000 hours.

Question 8

The first unit of a product took 832 hours to build,and the learning curve is 90%.How long will it take to make the 25th unit? (Use at least three decimals in the exponent if you use the formula approach. )
A)time ≤ 500 hours
B)500 < time ≤ 525
C)525 < time ≤ 530
D)530 < time ≤ 550
E)time > 550

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The answer of The first unit of a product took...

Question 9

The Learning-Curve Coefficients table reports that for 70 percent learning,the eighth unit has a unit time value of 0.343.Verify that table entry by use of the doubling method.

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Question 10

In the Learning-Curve Coefficients table for 70 percent learning,the sixth unit has a unit time value of 0.398.Verify that table entry by use of the formula approach.Use five decimals in your work.

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Question 11

The ________ is the simplest approach to learning curve problems.

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Question 12

A manager is trying to estimate the appropriate learning curve for a certain job.The manager notes that the first four units had a total time of 30 minutes.Which learning curve would yield approximately this result if the first unit took 9 minutes? (Use Table E.3. )
A)0.70
B)0.75
C)0.80
D)0.85
E)0.90

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Question 13

The first unit of a product took 80 work days.The learning curve is estimated to be 90%.The time for the fourth unit will be about ________ work days and the time for the first four units will be about ________ work days.(Use Table E.3)
A)51;250
B)250;51
C)65;285
D)51;cannot be determined
E)65;cannot be determined

Accepted Answer

Using Table E.3 and the given 90% learning curve estimate, we can find the following:

- For the second unit, we multiply the time of the first unit by 0.9: 80 * 0.9 = 72 work days
- For the third unit, we multiply the time of the second unit by 0.9: 72 * 0.9 = 64.8 rounded to 65 work days
- For the fourth unit, we multiply the time of the third unit by 0.9: 65 * 0.9 = 58.5 rounded to 59 work days

To find the time for the first four units, we simply add the times together: 80 + 72 + 65 + 59 = 276 work days, which is closest to choice C of 285 work days. Therefore, the answer is C.

Question 14

The first unit of a product took 1,000 hours to build and the learning curve is 85%.How long will it take to make the first 5 units? (Use Table E.3)
A)less than 4,005 hours
B)from 4,005 to 4,015 hours
C)from 4,015 to 4,025 hours
D)from 4,025 to 4,035 hours
E)from 4,035 to 4,045 hours

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The answer of The first unit of a product took...

Question 15

The first unit of a product took 900 hours to build and the learning curve is 90%.How long will it take to make the first 3 units? (Use Table E.3)
A)less than or equal to 2,470 hours
B)from 2,470 to 2,472 hours
C)from 2,472 to 2,475 hours
D)from 2,475 to 2,478 hours
E)from 2,478 to 2,481 hours

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The answer of The first unit of a product took...

Question 16

In the formula approach to learning curve calculations,you have used the formula TN = T1 (Nb).Your manager shows you a problem for which b is specified as -.18443.What learning curve does that value represent?

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The answer of In the formula approach to learning curve...

Question 17

The first unit of a product took 50 hours to build,and the learning curve is 85%.How long will it take to make the 10th unit? (Use at least three decimals in the exponent if you use the formula approach. )
A)less than 24 hours
B)from 25 to 30 hours
C)from 30 to 35 hours
D)from 35 to 40 hours
E)more than 40 hours

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Question 18

It took 60 hours to make the first unit of a product.After the second and third units were made,the learning curve was estimated to be 80%.At $10 per hour,estimate the labor bill for the fourth unit.(Use at least three decimals in the exponent if you use the formula approach. )
A)$400 or less
B)from $400 to $420
C)from $420 to $440
D)from $1800 to $2000
E)over $2000

Accepted Answer

The labor time for the fourth unit can be calculated using the learning curve formula: T_n = T_1 * n^(log(b)/log(2)), where T_n is the time required to produce the nth unit, T_1 is the time required to produce the first unit, n is the unit number, and b is the learning rate (in decimal form). For the fourth unit (n=4) with an 80% learning curve (b=0.8), the formula becomes T_4 = 60 * 4^(log(0.8)/log(2)). This calculates to approximately 38.4 hours. At $10 per hour, the labor bill for the fourth unit is $384, which is $400 or less.

Question 19

Your firm has a contract to make 20 specialty lenses for night vision equipment.The first one took 40 hours.Learning is expected at the 85% learning curve.How long will it take to finish all 20 units?

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Question 20

Identify one advantage and one disadvantage of the doubling approach over the formula approach to learning curve calculations.

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Quiz 26: Learning Curves

To use the table of learning-curve coefficients,you must specify and .

In the formula approach to learning curve calculations,you have used the formula TN = T1 (Nb).For a problem with a 92 percent learning curve,what is b?

Your firm has expertise with a special type of hand-finished furniture.The learning curve is known to be 82%.If the first piece of furniture took 6 hours,estimate (using the doubling approach)how long it will take to complete the third unit.

The first unit of a product took 50 hours to build,and the learning curve is 80%.How long will it take to make the third unit? (Use at least three decimals in the exponent if you use the formula approach. )

Your firm has expertise with a special type of hand-finished furniture.The learning curve is known to be 82%.If the first piece of furniture took 6 hours,use the formula approach to determine how long it will take to make the third unit.

A defense 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?

A defense contractor has just started producing turbines for a new government contract.The first turbine took 7000 hours to produce.If the learning curve is 90%,how long will it take to produce the 10th turbine? (Use at least three decimals in the exponent if you use the formula approach. )

The first unit of a product took 832 hours to build,and the learning curve is 90%.How long will it take to make the 25th unit? (Use at least three decimals in the exponent if you use the formula approach. )

The Learning-Curve Coefficients table reports that for 70 percent learning,the eighth unit has a unit time value of 0.343.Verify that table entry by use of the doubling method.

In the Learning-Curve Coefficients table for 70 percent learning,the sixth unit has a unit time value of 0.398.Verify that table entry by use of the formula approach.Use five decimals in your work.

The ________ is the simplest approach to learning curve problems.

A manager is trying to estimate the appropriate learning curve for a certain job.The manager notes that the first four units had a total time of 30 minutes.Which learning curve would yield approximately this result if the first unit took 9 minutes? (Use Table E.3. )

The first unit of a product took 80 work days.The learning curve is estimated to be 90%.The time for the fourth unit will be about work days and the time for the first four units will be about work days.(Use Table E.3)

The first unit of a product took 1,000 hours to build and the learning curve is 85%.How long will it take to make the first 5 units? (Use Table E.3)

The first unit of a product took 900 hours to build and the learning curve is 90%.How long will it take to make the first 3 units? (Use Table E.3)

In the formula approach to learning curve calculations,you have used the formula TN = T1 (Nb).Your manager shows you a problem for which b is specified as -.18443.What learning curve does that value represent?

The first unit of a product took 50 hours to build,and the learning curve is 85%.How long will it take to make the 10th unit? (Use at least three decimals in the exponent if you use the formula approach. )

It took 60 hours to make the first unit of a product.After the second and third units were made,the learning curve was estimated to be 80%.At $10 per hour,estimate the labor bill for the fourth unit.(Use at least three decimals in the exponent if you use the formula approach. )

Your firm has a contract to make 20 specialty lenses for night vision equipment.The first one took 40 hours.Learning is expected at the 85% learning curve.How long will it take to finish all 20 units?

Identify one advantage and one disadvantage of the doubling approach over the formula approach to learning curve calculations.