# Learning Curve (2) by reb83169

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```									Learning Curve (2)

Learning curve theory suggests that as output doubles (ie 1 batch becomes 2
batches becomes 4 batches becomes 8 and so on), the average time taken to
produce each batch (known as the cumulative average time in the text books)
falls at a constant rate.

In the previous article, it was shown that the production of widgets had a learning
rate of 90% (ie as output doubles, the average time taken to produce each batch
- or cumulative average time - fell to 90% of what it had been previously).

This is only useful, however, if you are aiming to budget for production at output
levels 2, 4, 8, 16, 32 and so on.

How can we use learning curve theory if you want to know how long it will take to
produce the first 7 or 31 batches etc?

There is, of course, a formula as follows…..

y = axb

…where

y = cumulative average time
a = time taken to produce the first batch
x = number of batches produced to date
b = log learning rate/log 2

So, using the example of widgets from the previous article, where the first batch
took 100 hours and the learning rate was 90%, let’s calculate the time taken to
produce the first 7 batches.

Approach:

i.   Calculate the average time per batch for the first 7 batches (y in the
formula above)
ii.   Multiply the average by 7 to give the total time for 7

To use the formula, you need to be able to use your scientific calculator. You do
not need to understand what is meant by the term ‘log’. Somewhere on you
calculator there is a function that has written the word ‘log’. If you are still holding
onto your GCSE calculator because it has sentimental value, now is the time to
part with it. The modern scientific calculators are far more user friendly (I would
advise a CASIO fx-83), and will help enormously with the later subjects of F9 and
P4.
So, for our example, b = log 0.9/log 2

Using your calculator, hit the following keys… (You may have to use a shift or
function key to access the log function on older calculators)

log – 0.9 – divide – log – 2 and finally =

the answer should be -0.152 (to 3 decimal places).

Beware if your calculator automatically opens brackets, you must close after the
0.9 and after the 2.

So, the average time per batch for the first 7 batches is…

y = 100 x 7-0.152

y = 74.395 (to 3dps)

Therefore, the total time for the first 7 batches is…..

7 x 74.395 = 520.765 hours (I would round this to 520.8 hours)

In the final article we will investigate how to calculate the actual time for a
particular batch, rather than the average time. This is useful in exam based
questions to work out the time it takes to produce a batch once learning has
ceased.

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