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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
Batches Total Time CAT
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
Batches Total Time CAT
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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Learning Curves 16: formulae
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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Learning Curves 17: formulae
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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Learning Curves 18: formulae
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
This means that at 64 batches, CAT = 26.2141
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
This means that at 32 batches, CAT = 35.4298
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
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, 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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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 our
Experiments can not confirm that we are.
Heres why
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Learning Curves: follow up 3
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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Learning Curves: follow up 4
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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Learning Curves: follow up 5
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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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
200.0000
250.0000
300.0000
350.0000
400.0000
450.0000
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%