Operations management 12th stevenson ch07 learning curves

Supplement 7
Learning Curves

McGraw-Hill/Irwin

Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.


Supplement 7: Learning Objectives

You should be able to:
1.

Explain the concept of a learning curve

2.

Make time estimates based on learning curves

3.

List and briefly describe some of the main applications of learning curves

4.

Outline some of the cautions and criticisms of learning curves

5.

Estimate learning rates from data on job times

Instructor Slides

7S-2


Learning Curves

Learning curve
 The time required to perform a task decreases with increasing repetitions
The degree of improvement is a function of the task being done
 Short, routine tasks will show modest improvement relatively quickly
 Longer, 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 selection
 Product design
 Methods analysis
 Effort expended prior to the start of work


Changes made after production has begun

 Changes in work methods
 Changes 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 predictable
 The learning percentage is constant

Every doubling of repetitions results in a constant percentage decrease in the
time per repetition

 Typical decreases range from 10 to 20 percent

Instructor Slides

7S-6


Learning Curves: On a Log-Log Graph

Instructor Slides

7S-7


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?


Learning Curves

nth
unit

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

Unit Time
(hours)
Calculations

10
8 (.8) x (10) = (.8)1(10)
6.4 (.8)(8) = (.8)(.8)(10) = (.8)2(10)

5.12 (.8)(6.4) = (.8)(.8)(.8)(10) = (.8)3(10)

4
4.096 (.8)(5.12) = (.8)(.8)(.8)(.8)(10) = (.8) (10)

Improvement

2
1.6

1.28

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

Instructor Slides

= 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

7S-10

Unit Times: Formula Approach

Tn = T1 × n b
where
Tn = Time for nth unit
T1 = Time for first unit
ln r
b=
ln 2
r = learning rate percentage
ln stands for the natural logarithm
Instructor Slides

7S-11


Example: Formula Approach

If the learning rate is 90, and the first unit took 100 hours to complete, how
long would it take to complete the 25

th

unit?

T25 = 100 × 25

ln .90
ln 2

= 100 × 25−.15200
= 61.3068 hours

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)

Tn = T1 × Unit time factor
 Cumulative value, which enables us to compute the total time required to
complete a given number of units.

∑T

n

Instructor Slides

= T1 × Total time factor

7S-13

Example: Learning Factor Approach

If the learning rate is 90, and the first unit took 100 hours to complete, how
long would it take to complete the 25

th

unit?

T25 = 100 × .613
= 61.3 hours

How long would it take to complete the first 25 units?

∑T

25

Instructor Slides

= 100 × 17.713
= 1,771.3 hours
7S-14


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%.

Learning Curves Example S-2

Q1: Calculate the time of the 5th unit
 Approach 1 – using the formula

b = ln(.8) / ln(2) = -.3219
b
(-.3219)
n =5
= .5956
T5 = (400)(.5956) = 238.24
7S-16


Learning Curves Example S-2

Q1: Calculate the time of the 5th unit
 Approach 2
 using the learning Curve Coefficients table (7S-1, page 346)

b

n = .596 (Unit Time for 85% and n = 5)
T5 = (400)(.596) = 238.4

7S-17

Learning Curve Coefficients
Unit
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

28
29
30

70%
Unit
Total
Time
Time
1.000
0.700
0.568
0.490
0.437
0.398
0.367
0.343
0.323
0.306
0.291
0.278
0.267
0.257
0.248
0.240
0.233
0.226
0.220
0.214
0.209

0.204
0.199
0.195
0.191
0.187
0.183
0.180
0.177
0.174

1.000
1.700
2.268
2.758
3.195
3.593
3.960
4.303
4.626
4.932
5.223
5.501
5.769
6.026
6.274
6.514
6.747
6.973
7.192
7.407

7.615
7.819
8.018
8.213
8.404
8.591
8.774
8.954
9.131
9.305

75%
Unit
Total
Time
Time
1.000
0.750
0.634
0.563
0.513
0.475
0.446
0.422
0.402
0.385
0.370
0.357
0.345
0.334

0.325
0.316
0.309
0.301
0.295
0.288
0.283
0.277
0.272
0.267
0.263
0.259
0.255
0.251
0.247
0.244

1.000
1.750
2.384
2.946
3.459
3.934
4.380
4.802
5.204
5.589
5.958
6.315
6.660

6.994
7.319
7.635
7.944
8.245
8.540
8.828
9.111
9.388
9.660
9.928
10.191
10.449
10.704
10.955
11.202
11.446

80%
Unit
Total
Time
Time
1.000
0.800
0.702
0.640
0.596
0.562
0.534

0.512
0.493
0.477
0.462
0.449
0.438
0.428
0.418
0.410
0.402
0.394
0.388
0.381
0.375
0.370
0.364
0.359
0.355
0.350
0.346
0.342
0.338
0.335

1.000
1.800
2.502
3.142
3.738
4.299

4.834
5.346
5.839
6.315
6.777
7.227
7.665
8.092
8.511
8.920
9.322
9.716
10.104
10.485
10.860
11.230
11.594
11.954
12.309
12.659
13.005
13.347
13.685
14.020

85%
Unit
Total
Time
Time

1.000
0.850
0.773
0.723
0.686
0.657
0.634
0.614
0.597
0.583
0.570
0.558
0.548
0.539
0.530
0.522
0.515
0.508
0.501
0.495
0.490
0.484
0.479
0.475
0.470
0.466
0.462
0.458
0.454
0.450

1.000
1.850
2.623
3.345
4.031
4.688
5.322
5.936
6.533
7.116
7.686
8.244
8.792
9.331
9.861
10.383
10.898
11.405
11.907
12.402
12.892
13.376
13.856
14.331
14.801
15.267
15.728
16.186
16.640

17.091

90%
Unit
Total
Time
Time
1.000
0.900
0.846
0.810
0.783
0.762
0.744
0.729
0.716
0.705
0.695
0.685
0.677
0.670
0.663
0.656
0.650
0.644
0.639
0.634
0.630
0.625
0.621

0.617
0.613
0.609
0.606
0.603
0.599
0.596

1.000
1.900
2.746
3.556
4.339
5.101
5.845
6.574
7.290
7.994
8.689
9.374
10.052
10.721
11.384
12.040
12.690
13.334
13.974
14.608
15.237
15.862

16.483
17.100
17.713
18.323
18.929
19.531
20.131
20.727

95%
Unit
Total
Time
Time
1.000
0.950
0.922
0.903
0.888
0.876
0.866
0.857
0.850
0.843
0.837
0.832
0.827
0.823
0.818
0.815

0.811
0.807
0.804
0.801
0.798
0.796
0.793
0.790
0.788
0.786
0.784
0.781
0.779
0.777

1.000
1.950
2.872
3.774
4.662
5.538
6.404
7.261
8.111
8.954
9.792
10.624
11.451
12.274
13.092

13.907
14.717
15.525
16.329
17.130
17.929
18.724
19.517
20.307
21.095
21.881
22.665
23.446
24.226
25.003


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


Learning Curves Example

Given T2 = 10 and 80% learning percent, find the expected time for
th
the 5
unit
T2 = 10 = T1 X (.8)
T1 = 10 / .8 = 12.5
T5 = 12.5 X 0.596 = 7.45


Learning Curve Applications

Useful application areas:
1.

Manpower planning and scheduling

2.

Negotiated purchasing

3.

Pricing new products

4.

Budgeting, purchasing, and inventory planning

5.

Capacity planning

Instructor Slides

7S-21


Cautions and Criticisms

1.

Learning rates may differ from organization to organization and by type of work

 Base 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 Strategy

Learning curves have strategic implications for:
 Market entry when trying to rapidly gain market share
As volume increases, operations is able to move quickly down the learning curve
 Reduced cost  improved competitive advantage

 Useful for capacity planning
Can lead to more realistic time estimates, thus leading to more accurate capacity needs
assessment

Instructor Slides

7S-25