Supplement G  Learning Curve Analysis
Supplement
G
Learning Curve Analysis
TRUE/FALSE
1. The learning effect can be represented by a line called a learning curve.
Answer: True
Reference: The Learning Effect
Difficulty: Easy
Keywords: learning, effect, curve
2. The first learning curve was developed by the aircraft industry.
Answer: True
Reference: The Learning Effect
Difficulty: Moderate
Keywords: learning, curve
3. The simpler the product, the more pronounced the learning rate.
Answer: False
Reference: Managerial Considerations in the Use of Learning Curves
Difficulty: Moderate
Keywords: learning, rate
4. Learning curves provide their greatest advantage in the early stages of new service or product
production.
Answer: True
Reference: Managerial Considerations in the Use of Learning Curves
Difficulty: Moderate
Keywords: learning, curve, new, product, service
611
Supplement G  Learning Curve Analysis
MULTIPLE CHOICE
5. Which of the following statements about learning curves is generally TRUE?
a. Management can decide to achieve a certain rate of learning.
b. Learning curves were first quantified by the U.S. Postal Service.
c. Using the “doubling” model, a learning curve with a rate of learning of 70 percent means the tenth
unit takes 70 percent of the time that the twentieth unit will take.
d. Learning curves are recognition of the concept that the time a task takes usually decreases with
experience.
Answer: d
Reference: The Learning Effect
Difficulty: Moderate
Keywords: learning, curve, repetition
6. Which one of the following statements about learning curves is TRUE?
a. A learning curve assumes that the direct labor requirements per unit will decrease at an increasing
rate as cumulative production increases.
b. Learning at a capital-intensive operation usually will be less than it is for a labor-intensive
operation.
c. Learning for a simple product will usually be greater than it is for complex products.
d. Learning curves can be used only for individuals, not for the whole organization.
Answer: b
Reference: Multiple sections
Difficulty: Moderate
Keywords: learning, curve, capital
7. Which one of the following statements is TRUE about the relationship between learning curves and
competitive strategy?
a. Knowing where your process is on the learning curve will enable you to make frequent product
modifications.
b. Firms that emphasize low cost in their competitive strategy strive to move down the learning curve
by increasing volume.
c. Learning curves enable managers to project fixed manufacturing costs for future production
quantities.
d. Projecting the impact of learning curves into the future is one effective way of reducing the impact
of environmental uncertainty.
Answer: b
Reference: Multiple sections
Difficulty: Moderate
Keywords: learning, curve, strategy
612
Supplement G  Learning Curve Analysis
8. Which one of the following is an assumption of learning curves?
a. The cumulative time of production decreases as production increases.
b. Time reduction per unit increases as cumulative production increases.
c. The same learning curve should be used when a company increases its level of automation.
d. The reduction in time per unit follows an exponential curve.
Answer: d
Reference: Multiple sections
Difficulty: Moderate
Keywords: learning, curve, assumption, exponential
9. Which one of the following statements is NOT a typical assumption related to developing learning
curves?
a. The total direct labor hours needed to produce the first 100 units will be double the amount of
hours needed to build the first 50 units.
b. The direct labor needed per unit will decrease at a declining rate as cumulative production
increases.
c. The direct labor hours per unit will decrease according to an exponential curve as cumulative
production increases.
d. The direct labor needed to produce the 50th unit will always be more than the direct labor needed
to produce the 51st unit.
Answer: a
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, double
10. The annual report for Luddite Corporation boasted of their ERP implementation and noted that,
“while there were initially some growing pains, our learning rate for this system has been calculated
at 100%.” What are the implications of this statement?
a. Luddite Corporation is twice as fast processing transactions now.
b. Luddite Corporation is twice as slow processing transactions now.
c. Luddite Corporation processes transactions at the same rate now.
d. Luddite Corporation processes transactions instantaneously (takes zero time) now.
Answer: c
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, rate
11. Under learning curve theory, with a learning rate of 70 percent:
a. the time to produce the second unit will be 70 percent less than the time to produce the first unit.
b. the time to produce the second unit will be 30 percent less than the time to produce the first unit.
c. the cumulative average time per unit after producing the first 100 units will be 70 percent less than
the average time per unit of the first 50 units.
d. the average time per unit will be cut in half for every 70 units.
Answer: b
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve
613
Supplement G  Learning Curve Analysis
12. Which one of the following statements about learning curves is FALSE?
a. The direct labor for the n+1st unit will always be less than the direct labor required for the nth unit.
b. The reduction in time will follow an exponential curve.
c. A benefit of learning curves is that they are unaffected by factors such as product complexity and
the rate of capital additions.
d. The cumulative average number of direct labor hours per unit for a given product after the tenth
unit with an 80 percent learning rate will be less than that for the same product with a 70 percent
learning rate.
Answer: c
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, capital, complexity
13. The first unit took 12 hours to produce and the learning rate is expected to be 85 percent. How long
will it take to produce the tenth unit?
a. Fewer than or equal to 7.0 hours
b. Greater than 7.0 hours but fewer than or equal to 7.5
c. Greater than 7.5 but fewer than or equal to 8.0
d. Greater than 8.0
Answer: a
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, labor
14. The first unit produced in 15 hours has an estimated learning rate of 90 percent. At what level of
output will the average production time per unit fall below 11 hours?
a. Fewer than or equal to 15 units
b. Greater than 15 units but fewer than or equal to 17 units
c. Greater than 17 units but fewer than or equal to 19 units
d. Greater than 19 units
Answer: d
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, average
15. How long will it take to make 25 units if the first one took 8 hours and there is a 90 percent learning
rate? Refer to the copy of Table G.1appended to this exam.
a. Fewer than or equal to 130 hours
b. Greater than 130 hours but fewer than or equal to 140 hours
c. Greater than 140 hours but fewer than or equal to 150 hours
d. Greater than 150 hours
Answer: c
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve
614
Supplement G  Learning Curve Analysis
16. The fifth unit took 10 hours to produce and the learning rate is expected to be 85 percent. How long
will it take to produce the tenth unit?
a. Fewer than or equal to 8.0 hours
b. Greater than 8.0 hours but fewer than or equal to 8.5
c. Greater than 8.5 hours but fewer than or equal to 9.0
d. Greater than 9.0
Answer: b
Reference: Developing Learning Curves
Difficulty: Easy
Keywords: learning, curve, labor
17. The fifth unit of a long production run was produced in 15 hours. The process has an estimated
learning rate of 90 percent. What is the lowest level of output at which the average production time
per unit falls below 15 hours?
a. Fewer than or equal to 8 units
b. Greater than 8 units but fewer than or equal to 11 units
c. Greater than 11 units but fewer than or equal to 14 units
d. Greater than 14 units
Answer: c
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, average
18. How long will it take to make 25 units if the third one took 6.5 hours and there is a 90 percent
learning rate? Refer to the copy of Table G.1 appended to this exam.
a. Fewer than or equal to 130 hours
b. Greater than 130 hours but fewer than or equal to 140 hours
c. Greater than 140 hours but fewer than or equal to 150 hours
d. Greater than 150 hours
Answer: b
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve
19. The fourth unit took 10 hours to produce and the learning rate is expected to be 80 percent. How long
will it take to produce the tenth unit?
a. Fewer than or equal to 7.0 hours
b. Greater than 7.0 hours but fewer than or equal to 8.0
c. Greater than 8.0 hours but fewer than or equal to 9.0
d. Greater than 9.0
Answer: b
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, labor
615
Supplement G  Learning Curve Analysis
20. The seventh unit of a long production run was produced in 3 hours. The process has an estimated
learning rate of 90 percent. At what level of output will the cumulative production time exceed 40
hours?
a. Fewer than or equal to 8 units
b. Greater than 8 units but fewer than or equal to 10 units
c. Greater than 10 units but fewer than or equal to 12 units
d. Greater than 12 units
Answer: d
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, average
21. How long will it take to make units 11through 20 if the first one took 8 hours and there is a 90
percent learning rate? Refer to the copy of Table G.1 appended to this exam.
a. Fewer than or equal to 50 hours
b. Greater than 50 hours but fewer than or equal to 55 hours
c. Greater than 55 hours but fewer than or equal to 60 hours
d. Greater than 60 hours
Answer: b
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve
22. Suppose the average time for the first 1,000 units you have manufactured is 2.375 minutes. Your rate
of learning is 90 percent, and you need to find the total time required to manufacture the next 1,000
units. Refer to the copy of Table G.1 appended to this exam. The total time is:
a. not more than 2,000 minutes.
b. greater than 2,000 minutes but not more than 2,700 minutes.
c. greater than 2,700 minutes but not more than 3,300 minutes.
d. greater than 3,300 minutes.
Answer: a
Reference: Developing Learning Curves
Difficulty: Hard
Keywords: learning, curve, time
23. Given that the third unit took 100 minutes and the rate of learning is 80 percent, how much time will
it take to build unit 96?
a. Fewer than or equal to 30 minutes
b. Greater than 30 minutes but fewer than or equal to 35 minutes
c. Greater than 35 minutes but fewer than or equal to 40 minutes
d. Greater than 40 minutes
Answer: b
Reference: Developing Learning Curves
Difficulty: Hard
Keywords: learning, curve, time
616
Supplement G  Learning Curve Analysis
24. It took 100 hours to produce the first unit and 95 hours to produce the second unit. How many hours
are required to produce the eighth unit?
a. Fewer than or equal to 60 hours
b. Greater than 60 hours but fewer than or equal to 75 hours
c. Greater than 75 hours but fewer than or equal to 90 hours
d. Greater than 90 hours
Answer: c
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, time
25. It took 100 hours to produce the first unit and the learning rate is 80 percent. How much time will it
take to produce units 16 through 20? Refer to the copy of Table G.1 appended to this exam.
a. Fewer than or equal to 160 hours
b. Greater than 160 but fewer than or equal to 170 hours
c. Greater than 170 but fewer than or equal to 180 hours
d. Greater than 180 hours
Answer: d
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, time
26. Given that the fifth unit took 10 hours to build and the learning rate is 90 percent, how much time will
it take to build units 11 through 15? Refer to the copy of Table G.1 appended to this exam.
a. Fewer than or equal to 38 hours
b. Greater than 38 hours but fewer than or equal to 40 hours
c. Greater than 40 hours but fewer than or equal to 42 hours
d. Greater than 42 hours
Answer: d
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, time
617
Supplement G  Learning Curve Analysis
27. A company is introducing a new product. The first unit took 1,000 hours to complete, and the fourth
unit took 750 hours to complete. What is the rate of learning for this product?
a. Less than 40 percent
b. Greater than or equal to 40 percent but less than 60 percent
c. Greater than or equal to 60 percent but less than 80 percent
d. Greater than 80 percent
Answer: d
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, rate
Case G.1
The production schedule for a new product follows.
The first unit took 100 hours to complete, and the rate of learning is 80 percent. Each
employee works 40 hours per month. Refer to the copy of Table G.1 appended to this exam.
28. Using the information in Case G.1, how much time will it take to produce the units in month 1?
a. Fewer than 800 hours
b. Greater than or equal to 800 hours but fewer than 1,100 hours
c. Greater than or equal to 1100 hours but fewer than 1,500 hours
d. Greater than 1,500 hours
Answer: b
Reference: Using Learning Curves
Difficulty: Moderate
Keywords: learning, curve, time
29. Using the information in Case G.1, what is the minimum number of employees needed in month 3?
a. Fewer than 20 employees
b. Greater than or equal to 20 employees but fewer than 30 employees
c. Greater than or equal to 30 employees but fewer than 40 employees
d. Greater than 40 employees
Answer: b
Reference: Using Learning Curves
Difficulty: Moderate
Keywords: learning, curve, employees
618
Supplement G  Learning Curve Analysis
30. The production for a new product follows:
The first unit will take 2,000 hours to produce and the learning rate is 90 percent. Currently, the
company employs 40 workers, who each work 200 hours regular time per month. In which
months will overtime be needed for the production schedule shown? Refer to the copy of Table
G.1 appended to this exam.
a. Month 4 only
b. Months 3 and 4 only
c. Months 1 and 2 only
d. Month 1 only
Answer: b
Reference: Using Learning Curves
Difficulty: Moderate
Keywords: learning, curve, overtime
31. As the cumulative number of units produced becomes large:
a. the learning effect is more noticeable.
b. the learning effect increases.
c. the learning effect is less noticeable.
d. the learning effect decreases.
Answer: c
Reference: Managerial Considerations in the Use of Learning Curves
Difficulty: Moderate
Keywords: learning, curve, effect
32. Which statement regarding the effect of automating some of the direct labor in a process is best?
a. The overall learning rate should be unaffected.
b. The overall learning rate will probably decrease.
c. The overall learning rate will probably increase.
d. The learning rate for the automated portion of the process should be higher than the learning rate
for the portion that is not automated.
Answer: b
Reference: Managerial Considerations in the Use of Learning Curves
Difficulty: Moderate
Keywords: learning, curve, rate, automation
619
Supplement G  Learning Curve Analysis
33. Which statement regarding learning rates is best?
a. A more complicated process offers more room for improvement.
b. A simpler process has a more pronounced learning rate.
c. Typically, the effect of each capital addition on the learning curve is significant.
d. Regardless of output volume. the estimate for the time required to produce the first unit is less
important than the estimate of the learning rate.
Answer: a
Reference: Managerial Considerations in the Use of Learning Curves
Difficulty: Moderate
Keywords: learning, curve, rate, process
FILL IN THE BLANK
34. The ____________ can be represented by a line called a learning curve.
Answer: learning effect
Reference: The Learning Effect
Difficulty: Moderate
Keywords: learning, effect
35. The mathematical model that is used to generate a learning curve is ____________.
Answer: logarithmic
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, logarithm
36. The learning rate depends on factors such as ____________ and ____________.
Answer: complexity; rate of capital addition, automation
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, rate, capital, complexity, automation
SHORT ANSWERS
37. What are the three major assumptions of the learning curve?
Answer: (1) Direct labor required for the n+1st unit will always be less than that required for the
nth unit. (2) Direct labor requirements will decrease at a declining rate as cumulative production
increases. (3) Reductions in time will follow an exponential curve.
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, assumptions
38. How are learning curves useful in financial planning?
Answer: Learning curves help the financial planner determine the amount of cash needed to
finance operations and provide a basis for comparing prices and costs. They can be used to help
determine a contract price by identifying the average direct labor cost per unit.
Reference: Using Learning Curves
Difficulty: Moderate
Keywords: learning, curves, financial, planning
620
Supplement G  Learning Curve Analysis
39. A manager of a company producing computer chips knows that in the early stages of production for a
new product, the expenditures exceed receipts, whereas in the latter stages, the reverse is true. Give
an explanation for this phenomenon.
Answer: The learning curve theory states that the direct labor costs will exceed the average in the
early stages of production, whereas the reverse is true in the latter stages. Pricing is often
predicted on average costs.
Reference: Using Learning Curves
Difficulty: Moderate
Keywords: learning, curves, direct, labor
40. An industrial engineer observes a brand new process and develops time standards for several of the
manual components of the production line. What are the implications of learning effects on the time
standards and the line balance? What could be done to address this situation?
Answer: The learning curve theory states that the labor requirement will be greater in the early
stages of production and lower as workers enjoy several repetitions of their jobs. A line balance
that is performed using inflated times will have increased idle time and decreased efficiency as
learning effects occur. The industrial engineer can compensate for learning effects by applying a
smaller performance rating factor (or allowance factor if downtime is an issue). If the industrial
engineer is unsure of the workers’ learning rate, the line can be balanced, and then a second study
performed to rebalance it.
Reference: Using Learning Curves
Difficulty: Moderate
Keywords: learning, curves, labor, output, rate, time, standard, line, balance
41. Why is the learning rate more pronounced for complex products than for simple products?
Answer: Complex products offer more opportunity for improving work methods, materials, and
processes.
Reference: Managerial Consideration in the Use of Learning Curves
Difficulty: Moderate
Keywords: learning, rate, complexity
PROBLEMS
42. A contractor is preparing a bid to install swimming pools at a new housing addition. The estimated
time to build the first pool is 35 hours. The contractor estimates a 90 percent learning rate; what is the
estimated time to install all 30 pools? Refer to the copy of Table G.1 appended to this exam.
Answer:
Using Table G.1, the coefficient for a 90 percent learning rate with n=30 is 0.6909.
The time for all 30 pools would be 35 hours  0.6909  30  725.44 hours
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, rate, curve
621
Supplement G  Learning Curve Analysis
43. The estimated time to produce the first unit is 100 hours. If a 90 percent learning rate is applicable,
what is the estimated time of producing the tenth unit? Refer to the copy of Table G.1 appended to
this exam.
Answer:
Learning rate
90.0%
Time for first unit
Unit number
Time for unit 10
Cumulative average time per unit
100
10
70.47
79.94
Reference: Developing Learning Curves
Difficulty: Moderate
Keywords: learning, curve, rate
44. Two contract labor companies are competing for work being outsourced by Febrero SpA. One
contractor, Terza, has a learning rate governed by a tripling of output at a 90% rate and the other
contractor, Segundo, has a learning rate governed by the conventional doubling of output at a 90%
rate. Both Terza and Segundo take 20 minutes to complete the first unit they are given for bid
estimation purposes. How many more units must Terza make than Segundo before their time per unit
drops below 15 minutes?
Answer:
Segundo :
15  20  n
log(.90)
n
log(2)
Terza :
log(.90)
log(2)
 0.75
log(0.75)
0.152
n  6.63  7th unit
log(n) 
15  20  n
log(.90)
n
log(3)
log(.90)
log(3)
 0.75
log(0.75)
0.0959
n  20.079  21st unit
log(n) 
Depending on rounding, students will determine that the 20th or 21st unit will do the trick for
Terza, a difference of about 14 units.
Reference: Developing Learning Curves
Difficulty: Hard
Keywords: learning, curve, rate
622
Supplement G  Learning Curve Analysis
TABLE G.1
Conversion Factors for the Cumulative Average Number
of Direct Labor Hours per Unit
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
80% Learning Rate
(n = cumulative production)
n
n
1.00000 19
0.53718
37
0.90000 20
0.52425
38
0.83403 21
0.51715
39
0.78553 22
0.51045
40
0.74755 23
0.50410
64
0.71657 24
0.49808 128
0.69056 25
0.49234 256
0.66824 26
0.48688 512
0.64876 27
0.48167 600
0.63154 28
0.47668 700
0.61613 29
0.47191 800
0.60224 30
0.46733 900
0.58960 31
0.46293 1,000
0.57802 32
0.45871 1,200
0.56737 33
0.45464 1,400
0.55751 34
0.45072 1,600
0.54834 35
0.44694 1,800
0.53979 36
0.44329 2,000
0.43976
0.43634
0.43304
0.42984
0.37382
0.30269
0.24405
0.19622
0.18661
0.17771
0.17034
0.16408
0.15867
0.14972
0.14254
0.13660
0.13155
0.12720
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
623
90% Learning Rate
(n = cumulative production)
n
n
1.00000 19
0.73545
37
0.95000 20
0.73039
38
0.91540 21
0.72559
39
0.88905 22
0.72102
40
0.86784 23
0.71666
64
0.85013 24
0.71251 128
0.83496 25
0.70853 256
0.82172 26
0.70472 512
0.80998 27
0.70106 600
0.79945 28
0.69754 700
0.78991 29
0.69416 800
0.78120 30
0.69090 900
0.77320 31
0.68775 1,000
0.76580 32
0.67471 1,200
0.75891 33
0.68177 1,400
0.75249 34
0.67893 1,600
0.74646 35
0.67617 1,800
0.74080 36
0.67350 2,000
0.67091
0.66839
0.66595
0.66357
0.62043
0.56069
0.50586
0.45594
0.44519
0.43496
0.42629
0.41878
0.41217
0.40097
0.39173
0.38390
0.37711
0.37114