Learning Curves: introduction

I hope you will enjoy and profit from this overview of learning curves.

As always, I enjoy your feedback …

duncan.williamson@tesco.net at any time!

April 2001

Dun

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Will

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Apri

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Learning Curves 1

Learning curves are a vital aspect of the work of many 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 50.00

2 80.00

4 128.00

8 204.80

… …

128 1,342.18

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Learning Curves 4

80% Learning Rate

Batches Total Time

CAT

1 50.00 50.00

2 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

Batches Total Time

CAT

1 50.00 50.00

2 100.00 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 opposed to no learning taking place …

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Learning Curves 7: £1/hour

80% Learning Rate

Batches Total Time Labour Cost

1 50.00 50.00

2 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 50.00

2 100.00 100.00

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 5 units …

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Learning Curves 10

Average Cost/unit

Units 80% Learning

No Learning

5 10.00 10.00

10 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 11Learning 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

CA

T

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Learning Curves 12Learning curve: 90%

0.000

10.000

20.000

30.000

40.000

50.000

60.000

0 100 200 300 400 500 600

Batch Number

CA

T

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Learning Curves 13Learning 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

CA

T

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Learning Curves 14: overlays

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Learning Curves 15: formulae

It’s very difficult to calculate or predict the CAT for anything other than the CAT at the DOUBLING POINT: 1, 2, 4, 8, 16 … 128 …

Now it gets mathematical!

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Learning Curves 16: formulae

baX Y

where Y = CAT or CACa = time/cost of the 1st unit or batchX = cumulative production or batches producedb = learning exponent (rate)

and

ln2

Rate lnLearning b

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Learning Curves 17: formulae

Now we can calculate or predict the CAT for any number 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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Learning Curves 18: formulae

10.48576 128*50 aX Y -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 hours

X = 64 batches

learning rate = 80%

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Learning Curves 19b: solution

This means that at 64 batches, CAT = 26.2141

So total time = 26.2141 * 64 = 1,677.71

26.2141 64*100 aX Y -0.32193b

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Learning Curves 20: exercise

Try again …

eg a = 60 hours

X = 32 batches

learning rate = 90%

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Learning Curves 20b: solution

This means that at 32 batches, CAT = 35.4298

So total time = 35.4298 * 32 = 2,125.787

35.4298 32*60 aX Y -0.15200b

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Learning Curves 21

In general terms, the following guidelines might be useful for us

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

50% hand assembly/50% machining = 85% learning

25% hand assembly/75% machining = 90% 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, we’ll look at ways of assessing our own learning rates

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Learning Curves 24: results

Trial No Time Taken

1

2

3

4

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 week’s learning curve experimentsInteresting and informative.

Let’s just review what we found and some implicationsOf that.

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Learning Curves: follow up 2

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 ourExperiments can not confirm that we are.

Here’s why …

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Learning Curves: follow up 3

Remember, I set up the experiments to demonstrateHow 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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Learning Curves: follow up 4

I tried to make the experiments are similar to eachOther 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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Learning Curves: follow up 5

Some other points that we should think about and getOur 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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Learning Curves: follow up 6

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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Learning Curves: follow up 7

Suppose you were to carry out the experiments again.

What would you expect to find?

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Learning Curves: follow up 8

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 Curves: follow up 9

Learning Exercise:Trials 1 - 14 done on day 1

Trials 15 - 28 done on day 4

0.0000

50.0000

100.0000

150.0000

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400.0000

450.0000

0 5 10 15 20 25 30

trials

CA

T

session 1 session 2

Learning rate 1 68.19%

Learning rate 2 92.07%

Learning rate 1+2

66.33%

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Learning Curves: conclusion

I hope you have enjoyed and will profit from this overview of learning curves.

I like learning curves and find all students like doing what I’ve shown here. Do the experiments, do the calculations, draw the graphs and discuss what you find … there’s a lot to discover!

Write to me: duncan.williamson@tesco.net at any time to discuss these slides. April 2001

Dun

can

Will

iam

son

Apri

l 2001