Learning Curves Introduction

8/3/2019 Learning Curves Introduction

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Learning Curves: introduction


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Learning Curves 1

Learning curves are a vital aspect of the work ofmany business and commercial settings.

The more we do a job, the quicker we do it the man who made 6 million boxes!


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Learning Curves 2

Learning applies to people, machinery, systems

80% learning curve usually assumed but


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Learning Curves 3

80% Learning Rate

Batches Total Time CAT

1 50.002 80.00

4 128.00

8 204.80

128 1,342.18


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Learning Curves 4

80% Learning Rate


1 50.00 50.002 80.00 40.00

4 128.00 32.00

8 204.80 25.60

128 1,342.18 10.49


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Learning Curves 5

No Learning


1 50.00 50.002 100.00 50.00

4 200.00 50.00

8 400.00 50.00

128 6,400.00 50.00


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Learning Curves 6

Implications of learning taking place as opposedto no learning taking place


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Learning Curves 7: 1/hour

80% Learning Rate

Batches Total Time Labour Cost

1 50.00 50.002 80.00 80.00

4 128.00 128.00

8 204.80 204.80

128 1,342.18 1,342.18


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Learning Curves 8: 1/hour

No Learning

Batches Total Time Labour Cost

1 50.00 50.002 100.00 100.00

4 200.00 200.00

8 400.00 400.00

128 6,400.00 6,400.00


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Learning Curves 9

Imagine now that each batch is made up of 5units


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Learning Curves 10

Average Cost/unit

Units 80% Learning No Learning

5 10.00 10.0010 16.00 20.00

20 25.60 40.00

40 40.96 80.00 - -

640 268.44 1,280.00


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Learning Curves 11

Learning curve: 80%

0.000

10.000

20.000

30.000

40.000

50.000

60.000

0 100 200 300 400 500 600

Batch Number

CAT


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Learning Curves 13

Learning curve: 60%

0.000

10.000

20.000

30.000

40.000

50.000

60.000

0 100 200 300 400 500 600

Batch Number

CAT


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Learning Curves 14: overlays


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Learning Curves 15: formulae

Its very difficult to calculate or predict the CATfor anything other than the CAT at theDOUBLING POINT: 1, 2, 4, 8, 16 128

Now it gets mathematical!


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baXY

where Y = CAT or CAC

a = time/cost of the 1st unit or batch

X = cumulative production or batches produced

b = learning exponent (rate)

and

ln2

RatelnLearningb


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Now we can calculate or predict the CAT for anynumber of batches.

eg a = 50 hours

X = 128 batches

learning rate = 80%

b = ln0.8/ln2 = -0.22314/0.69315

= -0.32193


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10.48576128*50aXY -0.32193b

This means that at 128 batches, CAT = 10.48576

So total time = 10.48576 * 128 = 1,342.18


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Learning Curves 19: exercise

Your turn

eg a = 100 hoursX = 64 batches

learning rate = 80%


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Learning Curves 19b: solution


So total time = 26.2141 * 64 = 1,677.71

26.214164*100aXY -0.32193b


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Learning Curves 20: exercise

Try again

eg a = 60 hoursX = 32 batches

learning rate = 90%


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Learning Curves 20b: solution


So total time = 35.4298 * 32 = 2,125.787

35.429832*60aXY -0.15200b


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Learning Curves 21

In general terms, the following guidelines might beuseful for us

75% hand assembly/25% machining = 80% learning




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Learning Curves 22

Alternatively, industry averages:

Aerospace 85%

Shipbuilding 80 85%Raw materials 93 96%

Purchased parts 85 88%


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Learning Curves 23

For the rest of this session, well look at ways ofassessing our own learning rates


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Learning Curves 24: results

Trial No Time Taken

1

2

34

5

6

7

8

9

10


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Learning Curves 25

Activities:

Jigsaw

Finding numbers in a grid (a) and (b)Copying text (a) and (b)


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Learning Curves: follow up 1

I hope you found last weeks learning curve experiments

Interesting and informative.

Lets just review what we found and some implicationsOf that.


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We have learning rates of less than 70% and greater

Than 100%.

Of course, everyone would like to think that they areThe smartest person on the planet; but our

Experiments can not confirm that we are.

Heres why


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Remember, I set up the experiments to demonstrate

How to make learning curve theory come to life; andTo provide ways in which we can practice theMathematics in an interesting way.

My experiments were not wholly scientifically designed,Even if they were good fun!


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I tried to make the experiments are similar to each

Other as possible

eg all the sentences in the writing experiment hadAn average of 33 letters in them

The number grids all had the SAME 20 numbers in them

Each trial was designed to take about 1 minute


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Some other points that we should think about and get

Our students to think about include

The observer will learn from the first guinea pig: weFound that the second person to carry out an

Experiment had a much quicker 1st

trial time thanThe first guinea pig.


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Where on the learning curve was the guinea pig?

If your learning rate is, say, 98% or even 105%, thatCould be because you are already proficient at thatActivity.

eg, the young lady who carried out the beadThreading exercise for me


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Suppose you were to carry out the experiments again.

What would you expect to find?


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Repeating an experiment or a task can lead to a

Perfectly usual learning curve, as we saw last week;Or it could present us with a discontinuousLearning curve


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Learning Exercise:

Trials 1 - 14 done on day 1

Trials 15 - 28 done on day 4

0.0000

50.0000

100.0000

150.0000

200.0000

250.0000

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0 5 10 15 20 25 30

trials

CAT

session 1 session 2

Learning rate 1 68.19%

Learning rate 2 92.07%

Learning rate 1+2 66.33%

Documents

Learning Curves Introduction