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I posted this question in the math forum on redddit, but it was deleted because it is not a math question.

I am hoping someone here can enlighten me.

In my life as an estimator for a machine tool builder, I have always used a learning curve model to estimate future repeat production.

That model is: Every time a quantity of parts is ran, the time to complete should improve; that improvement will be seen every time the quantity is doubled. In other words - with a 95% learning curve, a 5% improvement (100-95) will be seen between the first and second part, and again from the 2nd to the 4th, from the 4th to the 8th, etc. Every time the quantity doubles, the same percentage improvement is realized. (There is a little more to it, batch sizes and a 'forget factor' and so on, but I think you get the point.)

Every time a job is repeated, it is expected to go faster/cheaper because of experience and lessons learned.

If a job is able to be improved considerably every time it is re-ran, then the cost/time goes down considerably on subsequent runs. That is, a plot of cycle times or costs vs quantity, would show a very big drop from part 1 to part 2, from part 2 to part 4, from 4 to 8, etc. A big drop = a steep curve. Going down that curve happens quickly.

If a job is very difficult to improve upon, then the curve is considerably shallower, because the time to produce does not get better over time = shallow learning curve.

I have always used 'steep learning curve' to denote 'rapid improvement over time' but am now being told that is the opposite; apparently my definition is backward, and a SHALLOW learning curve means rapid improvement over time.

Could someone please set me straight on this?

I posted this question in the math forum on redddit, but it was deleted because it is not a math question. I am hoping someone here can enlighten me. In my life as an estimator for a machine tool builder, I have always used a learning curve model to estimate future repeat production. That model is: Every time a quantity of parts is ran, the time to complete should improve; that improvement will be seen every time the quantity is doubled. In other words - with a 95% learning curve, a 5% improvement (100-95) will be seen between the first and second part, and again from the 2nd to the 4th, from the 4th to the 8th, etc. Every time the quantity doubles, the same percentage improvement is realized. (There is a little more to it, batch sizes and a 'forget factor' and so on, but I think you get the point.) Every time a job is repeated, it is expected to go faster/cheaper because of experience and lessons learned. If a job is able to be improved considerably every time it is re-ran, then the cost/time goes down considerably on subsequent runs. That is, a plot of cycle times or costs vs quantity, would show a very big drop from part 1 to part 2, from part 2 to part 4, from 4 to 8, etc. A big drop = a steep curve. Going down that curve happens quickly. If a job is very difficult to improve upon, then the curve is considerably shallower, because the time to produce does not get better over time = shallow learning curve. I have always used 'steep learning curve' to denote 'rapid improvement over time' but am now being told that is the opposite; apparently my definition is backward, and a SHALLOW learning curve means rapid improvement over time. Could someone please set me straight on this?

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[–] [deleted] • 1 pt

steep learning curve = rapid improvement over time

The expression is not used like that, but rather to indicate that you have to learn a lot in the beginning. Front-end-heavy would be another expression.

In any case, I've never heard the expression used about productivity or margins of scale. As someone else mentioned, the scenario that you describe is something of the form f(x) = a{bx} + c, where a > 0, b < 0, and c > 0 (say, f is cost and g(x) is time, defined similarly)

a and b determine the shape/steepness of the graph. c is like the cheapest or fastest that it could physically/feasibly get.

[–] • 1 pt

No, that's not what a learning curve implies at all. Just think it through instead if typing out your stupid F of X. What would the axis on your graph look like? How would you label them? What would the curve look like? If you go through that thought process, you'll see you're wrong and that a front end heavy learning model would have a shallow curve when compared to something with a light learning load.

[–] [deleted] • 0 pt

I think you missed something.

My functions f and g are about cost and time, respectively, to produce a unit (these are the y-axes). The x axis is total units produced (which will be chronological, but not strictly time). These represent exponential decay.

A steep learning curve is not exponential. If anything it would be logarithmic. The x-axis IS time in this situation, and the y-axis is something like "amount learned."

Again - I think you missed something, but apparently my functions are stupid and I am stupid so I'm probably just stupid and wrong.

[–] • 1 pt

What you missed is the initial question. Would a steep curve imply faster(easier) learning, or slower (more difficult) learning. There is absolutely no reason to drag high school level calculus into the conversation.

[–] [deleted] • 0 pt

You assumed that "having to learn a lot in the beginning" has anything to do with the question.

I don't care if it's hard to figure out the first time. That just means I start with a high cycle time.

But over time, it should get easier, because (hopefully) you don't have to repeat the initial learning process.

How much easier is the point of the learning curve.

[–] [deleted] • 0 pt

I don't care how hard it is to figure something out for the first time. That's the time to produce the first part, or whatever the activity is. That's just the starting point.

The learning curve begins the next time you repeat that process. If you remember all the problems you had the first time, and can get through them better the second time, and every time after that, then the rate of improvement can be applied to that process.

"Hard to figure out" doesn't matter. "Hard to get better at it" does matter.