Learning curves model the relationship between the cumulative number of units produced and the time it takes to produce each additional unit. There are three main assumptions of learning curve theory: 1) time to complete a task decreases each time it is done; 2) the decrease in time occurs at a decreasing rate; and 3) the reduction in time follows a predictable pattern. Learning curves can be used to estimate time and costs for production. Both individual learning, from repeated practice, and organizational learning, from changes to processes, affect learning curves.

2. Chapter 6: Learning Curves
McGraw-Hill/Irwin

3. What are Learning Curves?
• Learning curve: a line displaying the relationship between unit
production time and the cumulative number of units produced
• Wide range of applications
• Can be used to estimate time and cost
• One of the trade-offs in JIT
• Individual learning: improvement that results when people repeat a
process and gain skill or efficiency from their own experience
• Practice makes perfect
• Organizational learning: also comes from changes in administration,
equipment, and product design
• Expect to see both simultaneously
6-3

4. Three Assumptions of Learning Curve Theory
1. Time required to complete a given task will be less each time the
task is undertaken
2. Unit time will decrease at a decreasing rate
3. Reduction in time will follow a predictable pattern
6-4

5. Finding the Learning Rate
1. Arithmetic tabulation
2. Logarithms
3. Some other curve-fitting method
6-5

6. Learning Curves Plotted as Times and
Numbers of Units
6-6

7. Plotting Learning Curves
• In practice, learning curves are plotted using a graph with logarithmic
scales
• The unit curves become linear throughout their entire range
• The cumulative curve becomes linear after the first few unit
• Direct logarithmic analysis is more efficient because it does not
require a complete enumeration of successive time–output
combinations
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8. Data for an 80 Percent Learning Curve
6-8
Exhibit 6.2

9. Resulting Learning Curve Plots
6-9
Exhibit 6.3

10. Logarithmic Analysis
• 𝑌𝑥 = 𝐾𝑥𝑛
• x = Unit number
• Yx = Number of direct labor hours required to produce the xth unit
• K = Number of direct labor hours required to produce the first unit
• 𝑛 =
𝑙𝑜𝑔 𝑏
𝑙𝑜𝑔 2
• b = Learning percentage
6-10

11. Example
• First unit takes 100,000 hours
• 80 percent learning curve
• Find hours for eighth unit
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12. Example
• First unit takes 100,000 hours
• 80 percent learning curve
• Find hours for eighth unit
𝑌8 = 100,000 8 𝑛
= 100,000(8)log 0.8 log 2
= 100,000 8 −0.322 =
100,000
8 −0.322
=
100,000
1.9534
= 51,193
6-12

13. Improvement Curves: Table of Unit Values
6-13
Exhibit 6.4 (Partial)

14. Improvement Curves: Table of Cumulative
Values
6-14
Exhibit 6.5 (Partial)

15. Estimating the Learning Percentage
1. Assume that the learning percentage will be the same as it has been for
previous applications within the same industry
2. Assume that it will be the same as it has been for the same or similar
products
3. Analyze the similarities and differences between the proposed start-up and
previous start-ups and develop a revised learning percentage that appears
to best fit the situation
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16. Individual Learning
1. Proper selection of workers
2. Proper training
3. Motivation
4. Work specialization
5. Do one or very few jobs at a time
6. Use tools that support performance
7. Provide quick and easy access for help
8. Allow workers to help redesign tasks
6-16

17. Test Results of Two Job Applicants
6-17
Exhibit 6.6

18. Organizational Learning
• Organizations learn as well
• A main source is individual learning
• An organization also acquires knowledge in its technology, its
structure, documents it retains, and standard operating procedures
• Knowledge can also be embedded in the organizational structure
• Knowledge can depreciate if individuals leave the organization
• Knowledge can depreciate if technologies become inaccessible or
difficult to use
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19. Managerial Considerations
• Workers and organization must have adequate incentives to enhance
learning
Individual learning and incentives
• The newer the job, the greater the improvements possible
Learning on new jobs versus old jobs
• Better methods and support systems, not increased effort, are the source of
gains
Improvement comes from working smarter, not harder
• Learning rate becomes a goal instead of an independent phenomenon
Suggesting a learning rate leads to a built-in bias
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20. Managerial Considerations
•High levels of preproduction planning mean early units will already incorporate a significant
amount of learning
Preproduction versus postproduction adjustments
•Changes to production conditions can influence the learning rate
Changes in indirect labor and supervision
•Significant adjustments to any of these factors can affect production rate
Changes in purchasing practices, methods, and organizational structure
•As a contract nears completion, learning curve may begin to turn upward
Contract phase-out
6-20