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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?

(post is archived)

[–] • 3 pts

You're right. The problem is most people are stupid. A steep curve implies rapid skill acquisition, a shallow curve means slow skills acquisition. The problem you're running into is people mistaking colloquial speech for a mathematical meaning. People are familiar with steep hills, so intuitively think a steep curve implies greater difficulty. This is retarded. The only way they'd be correct is if they flipped the axis of the graph, with ability along the X axis and time along the Y axis. But that's not how we do graphs on earth.

https://www.valamis.com/hub/steep-learning-curve

If someone says, "that there thing has a steep learning curve" they probably mean it's difficult to learn, but they're actually saying that it can learned relatively quickly.

[–] [deleted] • 1 pt (edited )

The common expression "a steep learning curve" is a misnomer suggesting that an activity is difficult to learn and that expending much effort does not increase proficiency by much, although a learning curve with a steep start actually represents rapid progress.[2][3] In fact, the gradient of the curve has nothing to do with the overall difficulty of an activity, but expresses the expected rate of change of learning speed over time.

In other words, the common usage of the phrase has no relation to the technical meaning.

[–] [deleted] • 1 pt
[–] [deleted] • 0 pt

Good stuff, but I usually also include a penalty based on batch sizes and time between runs... "Forget factor". Otherwise,this is exactly what I've used.

But "steep" in my usage has always meant "gets easier faster."

That seems to be the issue.

[–] [deleted] • 1 pt

It looks like TP Wright's Cost of Airplanes, PDF linked in my link, agrees with you. He even takes into account nonconsecutive orders or your forget factors.

I learned something new at least by reading through it.

[–] [deleted] • 1 pt

Me, too!

I took over estimating here about 10 years ago when the last guy retired. He explained the concept, but admitted he usually winged it.

I added it to a spreadsheet, gave it some realistic numbers, and never had an issue... Until I said "Software X has a pretty steep learning curve if you've used software Y, so you'll be fine."

Apparently people get hateful when you get that term wrong.

[–] [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.

[–] • 0 pt

Learning is exponential. Experiments with neural nets show that learning is exponential. Also it depends on how you plot performance over time, as that will shape the curve. Then you have to define the behavior, or behavior group. Learning curves are like climbing a mountain, the steeper it is the harder it is to make progress. Take for example a martial art like Bagua, or something like that. Those arts have very steep learning curves because it takes a lot of effort and time to make progress, vs something like boxing where you can make progress quickly, that means the curve is less steep. A steep curve takes a lot of effort to make progress, but when you do make progress, it's a more dramatic improvement.

Another example, let's say you are practicing a jab vs a side kick. You can repeat the jab much faster and it takes less energy and the difference between the first and 1,000th jab won't be very high. Whereas it takes much more energy and effort to throw a side kick, and the difference between the 1st and 1,000th kick will be much more noticable.

[–] • 1 pt

I agree. In this one horizontal would be progress, and vertical the accumulated effort spent. For a steep task, you put a lot of effort in and see little progress (horizontal axis). This makes people drop out before they reach the top. Once they reach the top, they suddenly can reach the right side. Whereas something more gradual gives continual progress from effort, so it's easier to stay in the game. The curve is thus illustrating psychological difficulty, not reward for effort.

[–] • 1 pt

BOOM goes the dynamite!

[–] • 1 pt

No, while parts of what you're talking about may be true, they have nothing to do with a graph showing learning (skills acquisition) over time. Just go through the task of building a graph that represents how well something has been learned over some period of time. Look at the different curves you've drawn, and try to think about what they'd mean.

[–] • 1 pt

They're all either logarithmic or exponential. Learn to cooperate instead of competing for the glory of being right.

[–] • 0 pt

Just read the first two paragraphs of the wikipedia article: https://en.wikipedia.org/wiki/Learning_curve

Note that the third paragraph references what you are talking about, the "experience curve".

[–] • 0 pt

I think you need to look at more quality control/assurance lingo.

You're looking at a quality/timliness dependant on batch size.

Part of what youd be looking at is setup time to get the process going divided by batch size.

[–] [deleted] • 0 pt

I don't understand what quality lingo has to do with the original question.

Batch sizes are based on other factors... Minimum (and maximum) dollar value per lot, outside service lot sizes, maximum hours per operation, raw material yield, etc. and are not driven by setup time or quality concerns.

Setup times are calculated based on work center, fixturing, quantity of tools, number of machine axes, and so on.

Dividing setup time by quantity does give a minutes per part number, but we charge setup and teardown times as a separate nre line item.

I am applying a learning curve factor to setup times as well, but my original question still applies... if it gets considerably easier to do something over time, then my cost to produce drops quickly over time... a steep curve. If it does not get easier to do something over time, then the cost to produce is relatively horizontal... a very shallow curve.

The question has nothing to do with "figuring out how to do a new thing," it has to do with "getting better at doing that new thing the next time you do it" and then the next time, and the times after that.

[–] • 0 pt

Steep to me would mean the learning curve is more difficult, thus a steep learning curve to me, would mean that its a more difficult task. I always thought of it as just an expression and not really a term with an express definition like you're saying. I'm not sure.

[–] • 1 pt

A learning curve is literally a graph of how well something has been learned over some period of time. Your Y axis should represent ability, and your X axis should represent time. As you go up on the Y axis, you've learned more, as you go along the X axis, you've taken more time. Try drawing a few curves and think about what the different shapes would mean.

[–] [deleted] • 0 pt

There is the crux of the discussion.

I'm not interested in the time to figure something out for the first time. That's just a starting point.

What I'm looking at is the time it takes to figure it out the second time. And all the next times.

Like this:

"Go to the store and get me a bottle of water."

It may take you an hour to drive around looking for the store, find the aisle with water, get caught by the speed trap on the main road on the way back, and so on. Whatever, you don't know my neighborhood.

But tomorrow, when I send you back for another bottle, you will be faster because you remember where the store is, and which aisle has the water.

After a week, you have found a shortcut that saves you another 30 seconds, after a month you just buy a 6 pack every 6 days, after 6 months you know which register checks you out faster, after a year you know which traffic lights are 3 seconds faster, and so on.

Just because it is harder the first time isn't really the point, it's all about how much of an improvement can be made over subsequent times repeating the process.