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Learning Curves
Supplement 7
McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Supplement 7: Learning ObjectivesYou should be able to:
1. Explain the concept of a learning curve2. Make time estimates based on learning curves3. List and briefly describe some of the main
applications of learning curves4. Outline some of the cautions and criticisms of
learning curves5. Estimate learning rates from data on job
times
Instructor Slides 7S-2
Learning CurvesLearning curve
The time required to perform a task decreases with increasing repetitionsThe degree of improvement is a function of the
task being doneShort, routine tasks will show modest improvement
relatively quicklyLonger, more complex tasks will show improvement
over a longer interval
Instructor Slides 7S-3
Learning
Instructor Slides 7S-4
The Learning Effect The learning effect is attributed to a variety of
factors: Worker learning Preproduction factors
Tooling and equipment selectionProduct designMethods analysisEffort expended prior to the start of work
Changes made after production has begunChanges in work methodsChanges in tooling and equipment
Managerial factors Improvements in planning, scheduling, motivation, and
control
Instructor Slides 7S-5
Interesting Characteristics of Learning
The learning effect is predictableThe learning percentage is constant
Every doubling of repetitions results in a constant percentage decrease in the time per repetitionTypical decreases range from 10 to 20 percent
Instructor Slides 7S-6
Learning Curves: On a Log-Log Graph
Instructor Slides 7S-7
7S-8
Learning Percentage
90% learning percent means 10% decrease in unit time with each doubling of repetition
80% learning percent means 20% decrease in unit time with each doubling of repetition
Question: What does 100% learning percent imply?
7S-9
Learning Curvesnth unit
Unit Time (hours) Calculations Improvement
1 10
2 8 (.8) x (10) = (.8)1(10) 23
4 6.4 (.8)(8) = (.8)(.8)(10) = (.8)2(10) 1.6567
8 5.12 (.8)(6.4) = (.8)(.8)(.8)(10) = (.8)3(10) 1.289
101112131415
16 4.096 (.8)(5.12) = (.8)(.8)(.8)(.8)(10) = (.8)4(10) 1.024
Learning Illustrated Each time cumulative output doubles, the time per unit for
that amount should be approximately equal to the previous time multiplied by the learning percentage.
If the first unit of a process took 100 hours and the learning rate is 90%:
Unit Unit Time (hours)
1 = 100
2 .90(100) = 90
4 .90(90) = 81
8 .90(81) = 72.9
16 .90(72.9) = 65.61
32 .90(65.61) = 59.049
Instructor Slides 7S-10
Unit Times: Formula Approach
logarithm natural for the standsln
percentage rate learning 2ln
ln
unitfirst for Time
unitth for Time
where
1
1
r
rb
T
nT
nTT
n
bn
Instructor Slides 7S-11
Example: Formula ApproachIf the learning rate is 90, and the first unit
took 100 hours to complete, how long would it take to complete the 25th unit?
hours 3068.61
25100
2510015200.
2ln
90.ln
25
T
Instructor Slides 7S-12
Unit Times: Learning Factor Approach
The learning factor approach uses a table that shows two things for selected learning percentages:Unit value for the number of repetitions (unit
number)
Cumulative value, which enables us to compute the total time required to complete a given number of units.
factor Unit time1 TTn
factor timeTotal1TTn
Instructor Slides 7S-13
Example: Learning Factor ApproachIf the learning rate is 90, and the first unit
took 100 hours to complete, how long would it take to complete the 25th unit?
How long would it take to complete the first 25 units?
hours 3.61
613.10025
T
hours 3.771,1
713.7110025
T
Instructor Slides 7S-14
7S-15
Learning Curves Example S-2
A contract calls for the production of 20 jets. The initial unit required 400 days of direct labor. The learning percent is 80%.
7S-16
Learning Curves Example S-2
Q1: Calculate the time of the 5th unitApproach 1 – using the formula
b = ln(.8) / ln(2) = -.3219
nb = 5(-.3219) = .5956T5 = (400)(.5956) = 238.24
7S-17
Learning Curves Example S-2
Q1: Calculate the time of the 5th unitApproach 2
using the learning Curve Coefficients table (7S-1, page 346)
nb = .596 (Unit Time for 85% and n = 5)
T5 = (400)(.596) = 238.4
7S-18
Learning Curve Coefficients
Unit Number
Unit Time
Total Time
Unit Time
Total Time
Unit Time
Total Time
Unit Time
Total Time
Unit Time
Total Time
Unit Time
Total Time
1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0002 0.700 1.700 0.750 1.750 0.800 1.800 0.850 1.850 0.900 1.900 0.950 1.9503 0.568 2.268 0.634 2.384 0.702 2.502 0.773 2.623 0.846 2.746 0.922 2.8724 0.490 2.758 0.563 2.946 0.640 3.142 0.723 3.345 0.810 3.556 0.903 3.7745 0.437 3.195 0.513 3.459 0.596 3.738 0.686 4.031 0.783 4.339 0.888 4.6626 0.398 3.593 0.475 3.934 0.562 4.299 0.657 4.688 0.762 5.101 0.876 5.5387 0.367 3.960 0.446 4.380 0.534 4.834 0.634 5.322 0.744 5.845 0.866 6.4048 0.343 4.303 0.422 4.802 0.512 5.346 0.614 5.936 0.729 6.574 0.857 7.2619 0.323 4.626 0.402 5.204 0.493 5.839 0.597 6.533 0.716 7.290 0.850 8.111
10 0.306 4.932 0.385 5.589 0.477 6.315 0.583 7.116 0.705 7.994 0.843 8.95411 0.291 5.223 0.370 5.958 0.462 6.777 0.570 7.686 0.695 8.689 0.837 9.79212 0.278 5.501 0.357 6.315 0.449 7.227 0.558 8.244 0.685 9.374 0.832 10.62413 0.267 5.769 0.345 6.660 0.438 7.665 0.548 8.792 0.677 10.052 0.827 11.45114 0.257 6.026 0.334 6.994 0.428 8.092 0.539 9.331 0.670 10.721 0.823 12.27415 0.248 6.274 0.325 7.319 0.418 8.511 0.530 9.861 0.663 11.384 0.818 13.09216 0.240 6.514 0.316 7.635 0.410 8.920 0.522 10.383 0.656 12.040 0.815 13.90717 0.233 6.747 0.309 7.944 0.402 9.322 0.515 10.898 0.650 12.690 0.811 14.71718 0.226 6.973 0.301 8.245 0.394 9.716 0.508 11.405 0.644 13.334 0.807 15.52519 0.220 7.192 0.295 8.540 0.388 10.104 0.501 11.907 0.639 13.974 0.804 16.32920 0.214 7.407 0.288 8.828 0.381 10.485 0.495 12.402 0.634 14.608 0.801 17.13021 0.209 7.615 0.283 9.111 0.375 10.860 0.490 12.892 0.630 15.237 0.798 17.92922 0.204 7.819 0.277 9.388 0.370 11.230 0.484 13.376 0.625 15.862 0.796 18.72423 0.199 8.018 0.272 9.660 0.364 11.594 0.479 13.856 0.621 16.483 0.793 19.51724 0.195 8.213 0.267 9.928 0.359 11.954 0.475 14.331 0.617 17.100 0.790 20.30725 0.191 8.404 0.263 10.191 0.355 12.309 0.470 14.801 0.613 17.713 0.788 21.09526 0.187 8.591 0.259 10.449 0.350 12.659 0.466 15.267 0.609 18.323 0.786 21.88127 0.183 8.774 0.255 10.704 0.346 13.005 0.462 15.728 0.606 18.929 0.784 22.66528 0.180 8.954 0.251 10.955 0.342 13.347 0.458 16.186 0.603 19.531 0.781 23.44629 0.177 9.131 0.247 11.202 0.338 13.685 0.454 16.640 0.599 20.131 0.779 24.22630 0.174 9.305 0.244 11.446 0.335 14.020 0.450 17.091 0.596 20.727 0.777 25.003
90% 95%70% 75% 80% 85%
7S-19
Learning Curves Example S-2
Q2 – Expected time for the 20th jet
T20 = (400) X (.381) = 152.4 labor days
Q3 – Expected total time for all 20 jets
T1-20 = (400) X (10.485) = 4,194 labor days
Q4 – Average time per jet:
Average time = 4,194/20 = 209.7 labor days
7S-20
Learning Curves Example
Given T2 = 10 and 80% learning percent, find the expected time for the 5th unit
T2 = 10 = T1 X (.8)
T1 = 10 / .8 = 12.5
T5 = 12.5 X 0.596 = 7.45
Learning Curve ApplicationsUseful application areas:
1. Manpower planning and scheduling2. Negotiated purchasing3. Pricing new products4. Budgeting, purchasing, and inventory
planning5. Capacity planning
Instructor Slides 7S-21
Cautions and Criticisms
1. Learning rates may differ from organization to organization and by type of workBase learning rates on empirical studies rather than
assumptions where possible
2. Projections based on learning curves should be regarded as approximations of actual times
3. Because time estimates are based on the first unit, care should be taken to ensure that the time is valid
4. It is possible that at some point the curve might level off or even tip upward
Instructor Slides 7S-22
Cautions and Criticisms
5. Some of the improvements may be more apparent than real: improvements in times may be caused by increases in indirect labor costs
6. In mass production situations, learning curves may be of initial use in predicting how long it will take before the process stabilizes
The concept does not usually apply because improvement in time per unit is almost imperceptible
Instructor Slides 7S-23
Cautions and Criticisms
7. Users of learning curves fail to include carryover effects from previous experiences
8. Shorter product life cycles, flexible manufacturing, and cross-functional workers can affect the ways in which learning curves may be applied
Instructor Slides 7S-24
Operations StrategyLearning curves have strategic
implications for:Market entry when trying to rapidly gain
market shareAs volume increases, operations is able to move
quickly down the learning curveReduced cost improved competitive advantage
Useful for capacity planningCan lead to more realistic time estimates, thus
leading to more accurate capacity needs assessment
Instructor Slides 7S-25
