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- This topic has 3 replies, 2 voices, and was last updated 2 years ago by John Moffat.

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- December 30, 2021 at 10:15 am #645059
I have a question related to example 3 (chapter 12) about the learning curve. If we need to find out the time taken by the next 12 batches in both tabular and formula approaches.

Tabular approach:

Units——Avg time per unit—–Total time

–1—————-200——————–200

–2—————-170——————–340

–4—————-144.5——————578

–8—————-122.825—————982.6

-16—————-104.40125———–1670.42Total time taken by 16 units———1670.42

Total time taken by 4 units———(578)

Total time taken by 12 units———1092.42Formula approach:

Y = ax^b

Y = 200(16)^-0.23446 = 104.402

Y = 200(4)^-0.23446 = 144.501Total time taken by 16 units———-1670.42

Total time taken by 4 units———–(578)

Total time taken by 12 units———-1092.42Is that correct way?

December 30, 2021 at 4:13 pm #645079Yes. Either way is fine for the exam.

December 30, 2021 at 4:48 pm #645085we cannot simply take the average time per unit of 12 batches using the formula (like below) because of doubling rule effect. That’s why we need to first take out the average time per unit of 16 batches less average time per unit of 4 batches.

Y = 200(12)^-0.23446 = 111.687652

Total time for 12 batches = 1340.25

Total time for 12 batches comes out different from the previous total time (so it is wrong!)

Both the Tabular approach and Formula takes the doubling rule assumption (correct?)

December 31, 2021 at 1:19 pm #645118Always, just as I explain in my lectures on this, we can use either the doubling rule or the formula (the formula is based on the doubling rule) but both only give the time for the first so many units. That is why we have to take (in your example) the total time for 16 less the total time for 4. That is always the case.

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