# Talk:Experience curve effects

## Sharpening the axe vs. chopping the tree

A related, but subtly different, I think, idea, is the relationship between efficiency for a method compared to another method on different time scales. For instance, a macintosh one-button mouse and GUI is much more efficient on short time scales but a complicated keystroke-based thingy like vim is more efficient on long timescales after becoming comfortable with it. (I don't like either.) Similarly, a chording keyboard can theoretically be used more quickly than a regular computer keyboard, but the time it takes to learn makes it unusable in the short term, compared to hunt and peck typing. Is there a word for this concept? - Omegatron 23:11, May 8, 2005 (UTC)

This is spoken about as the difference between the "learning phase" and the "automated phase" in this article: http://jef.raskincenter.org/humane_interface/summary_of_thi.html - Omegatron 02:47, Jun 17, 2005 (UTC)
A relevant quote from Abraham Lincoln:

If I had six hours to chop down a tree, I'd spend the first four hours sharpening the axe.

This illustrates the tradeoff between preparation time vs. execution time for a given task. The more trees one needs to chop, the greater the return on a unit of axe-sharpening time. — Teratornis 14:52, 23 August 2006 (UTC)
Another is (paraphrasing) "Given ten hours to accomplish a task, an engineer will spend nine hours learning to do it in one hour." - 209.130.150.117 04:58, 4 March 2007 (UTC)

## Power law or exponential law?

The article states "Each time cumulative volume doubles, ... costs ... fall by a constant ... percentage". This would imply that mathematically the effect approximates a power law:

${\displaystyle c=Bv^{-\alpha }\,}$

where v is volume, c is cost, and B and ${\displaystyle \alpha >0}$ are constants. In fact it is more likely that

${\displaystyle c=A+Bv^{-\alpha }\,}$

where A is an asymptotic unit cost greater than zero.

Another possibility is that "each time cumulative volume increases by a fixed amount, costs fall by a constant percentage": this would imply that costs decay exponentially, with formula

${\displaystyle c=A+Be^{-\beta v}\,}$

Is there evidence for one of these "laws" over another?

Note that for the related area of response time in individual learning of repeated tasks, Heathcote, Brown and Mewhort in their paper The Power Law repealed: the case for an Exponential Law of Practice make a case via statistical analysis that an exponential law usually gives a better approximation to the observed data than a power law does. - JimR 06:57, 14 July 2005 (UTC)

## Cumulative average cost?

Note that http://www.maaw.info/LearningCurveSummary.htm states that in Wright's original model the cost involved is not the unit cost of the last unit, but the cumulative average unit cost. The article does not mention this point at present. I'm not sure if this makes a big enough difference to need remedying. Any ideas? (More generally, in the apparent absence of pointers to evidence of experimental verification of the effect in practice, I wonder whether the precision of the numerical form of the curve is really justified.) - JimR 07:18, 16 July 2005 (UTC)

In the aerospace industry, production estimators use, if not swear by, improvement curve theories. Wright's model, also known as the Cumulative Average Curve, Wright Curve, or Northrop Curve, predicts the cumulative average unit cost while a competing theory, known as the Unit Curve (aka. Crawford Curve, Boeing Curve), is based on the individual unit cost. The government accepts both for proposals, and their usage tends to be dictated by what the given corporation traditionally uses.

You can find out more from the US DoD Defense Procurement site: http://www.acq.osd.mil/dpap/contractpricing/vol2chap7.htm Koreantoast 17:24, 4 October 2006 (UTC)

## Moore's Law

Isn't Moore's law a special case of this?

From the consumer's point of view, sort of (except that the consumer is getting different products as Moore's law grinds ahead, not exactly the same product at successively lower costs). From the producer's point of view, not quite. A quote from the Moore's law article:

As the cost to the consumer of computer power falls, the cost for producers to achieve Moore's Law has the opposite trend: R&D, manufacturing, and test costs have increased steadily with each new generation of chips. As the cost of semiconductor equipment is expected to continue increasing, manufacturers must sell larger and larger quantities of chips to remain profitable. (The cost to tape-out a chip at 0.18um was roughly $300,000 USD. The cost to tape-out a chip at 90nm exceeds$750,000 USD, and the cost is expected to exceed \$1.0M USD for 65nm.)

Teratornis 15:11, 23 August 2006 (UTC)

## The "steep" learning curve misnomer

Learning a Task When I first met the phrase 'learning curve' in the 1950's it was in a book by an industrial phsycologist who said that individuals or small groups learning a job progress slowly at first (getting the fundamentals), then quickly (applying them) and finally slowly (long practice tends toward extra high skill). This leads to an 'S' shaped graph of skill against time. On this basis having "a steep learning curve" implies easy to learn: the opposite what is usually meant.

In any case the "Steep learning curve" is much more commom than other usages and it should be highlighted in the article and given precedence over the more esoteric applications of the phrase. 82.38.97.206 17:23, 11 February 2006 (UTC)mikeL

Actually, I was about to say that "steep learning curve" should indeed be mentioned, but as a misuse of the term. -cp 03:19, 17 April 2006 (UTC)
I will add this to the misnomer article's list of examples. Also, the learning curve article could use an illustrative graph comparing a steep learning curve to a shallow one, to show how a steep curve implies rapid (easy) learning. Perhaps a better descriptor for a difficult learning problem would be stiff, to imply that a given learning curve resists being driven down. Too bad we can't get the word out to millions of people who use the misnomer. — Teratornis 15:11, 23 August 2006 (UTC)
I have little experience with the psychological definition, but according to merriam-webster's Dictionary, "learning curve" means either:
1. a curve plotting performance against practice; especially : one graphing decline in unit costs with cumulative output
2. the course of progress made in learning something
so wouldn't the common usage "steep learning curve" just refer to the second, more colloquial, definition? Note that the two definitions refer to different things: Def. 1 (the subject of the current article) is a measure of efficiency versus experience. Def. 2 (subject of the colloquialism) is a measure of effort versus learning. "Millions of people" do use the idiomatic term "steep learning curve" to mean "difficult to learn", probably simply drawing an analogy from a steep hill being hard to climb. I would suggest that the introductory segment disputing the colloquial usage be removed, but I'll leave it to someone with more experience with the term to decide. — Talyian 08:54, 12 April 2007 (UTC)

I first encountered the learning curve concept in an article in either Dr. Dobb's Journal or Creative Computing around 1990. The article discussed hypothetical decisions made by a software development firm relating to choosing a new compiler, programming language, programming paradigm, or something similar. If the amount of resources expended to achieve a given level of expertise is measured along the vertical axis, and expertise gained is measured along the horizontal axis, then a more "expensive" learning curve will indeed be steeper (ie, it will have a greater positive slope). I was flabbergasted when first reading this "Experience curve effects" Wikipedia article! The "experience curve" concept seems to me to be virtually unrelated to the "learning curve" concept. The "Learning Curve" idea is this: different approaches to solving a problem (ie, writing a computer program) may be more or less expensive; the "Experience Curve" idea is: using the same problem-solving method over and over gets less and less expensive (ideally).GrouchyDan 20:57, 30 September 2006 (UTC)

STEEP misnomer. I've rewritten the Learning curve lede with a summary of steep is GOOD -- and a separate section on the use of "steep learning curve" in product reviews. And added a couple of clear diagrams. Alanf777 (talk) 23:55, 15 March 2013 (UTC)

## Ebbinghaus?

see de:Lernkurve --Espoo 20:58, 29 June 2006 (UTC)

Interesting. Can somebody please translate this?

Historisch gesehen stammt der Begriff der Lernkurve von Hermann Ebbinghaus (1885), der das Konzept der Lernkurve in seiner Monografie "Über das Gedächtnis" vermutlich als Erster verwendete und somit als Erfinder gelten dürfte. In der Psychologie wird der Begriff der Lernkurve mitunter ohne strikte Definition der x- und y-Achsenzuordnung angewandt, sodass die Frage der Steilheit anhand konkreter Beispiele betrachtet werden muss. Eine erste strikte Definition des Begriffs für die Anwendung in der Betriebswirtschaft stammt von Wright (1927).

It seems to state that the idea of the Learning Curve (Lernkurve) stems from Ebbinghaus in 1885, long before Wright in 1927. But what's the difference between de:Lernkurve and de:Erfahrungskurve? -- JimR 05:57, 1 July 2006 (UTC)

"Historically, the term learning curve comes from Hermann Ebbinghaus(1885), in whose monograph "Über das Gedächtnis [On Memory]" it was probably first used and thus he might be considered the inventor of the concept. In psychology the term "learning curve" is used from time to time without any definition of the x and y axes, so that the the slope of the curve is [supposed to be derived from non-numerical values]. The first strict definition of the term for use in marketing and management is due to Wright(1927)". That, in any event, is the gist, the nub, the kernel.SpikeMolec 22:01, 4 March 2007 (UTC)

## Why two articles?

Should this be merged into Learning curve? --Jcbutler (talk) 20:31, 19 September 2008 (UTC) fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

As this article and the one on "experience curve" addresses the same topic. A merge would (and redirect of learning curve to here, or vice versa) produce a more comprehensive article to the benefit of all Wikipedia readers. Editor br (talk) 11:37, 9 January 2009 (UTC)

I wrote the section on General Learning Limits on the Learning curve page. I think Learning curve is the more general term, but I don't mind merging if both terms are in the title on the page and there's a redirect link. I think the top of the page should be about learning, as a phenomenon experience, and cultures and systems development in general. I think learning and experience don't follow formulas, though they have natural limits, but occurs by interaction with unmapped environments, and so the analogy of economic models needs to clearly presented. I'd find some time to do a little work on it if it happened with something like the above generality in the approach. --Pfhenshaw (talk) 01:43, 21 January 2009 (UTC)

I'd say too that they could be merged. Just this article is more exact, as it talks in math, theories & numbers, whereas the learning curve is more abstract way without much exactness... But they both talk about more or less the same! Kazkaskazkasako (talk) 16:04, 23 January 2009 (UTC)

Maybe keep two articles -- one as a summary without much Math (based on the present Learning curve) and another concentrating on the Math (more like this one) ? I'd be happy to tackle the former. Alanf777 (talk) 00:06, 16 March 2013 (UTC)

## "Cumulative" is misspelled twice as "Cumulatve" in the chart labels.

"Cumulative" is misspelled twice as "Cumulatve" in the chart labels. —Preceding unsigned comment added by Firebird (talkcontribs) 17:48, 24 January 2010 (UTC)

Fix it maybe? The time it took you to tell everyone you could have just fixed it. --122.148.94.52 (talk) 10:50, 9 November 2014 (UTC)

## Unit curve confusion

I find confusing and partially incorrect the following text from the "Unit curve" section as of 2016-12-24:

This equation describes the basis for what is called the unit curve. In this equation, Y represents the cost of a specified unit in a production run. For example, If a production run has generated 200 units, the total cost can be derived by taking the equation below and applying it 200 times (for units 1 to 200) and then summing the 200 values. This is cumbersome and requires the use of a computer or published tables of predetermined values. [The following information may be helpful: When the equation for Yx below is associated with a unit improvement curve it is called a Crawford unit curve. When exactly the same equation for Yx below is called a cumulative average learning curve, it is called a Wright cumulative average. To calculate a Wright xth unit cost, Px, from its cumulative average, we have

${\displaystyle P_{x}=xY_{x}-(x-1)Y_{x-1}}$

because in this case

${\displaystyle Y_{x}={\frac {P_{1}+P_{2}+\cdots +P_{x}}{x}}.}$

Now the equation for the unit curve is given by:[1]

${\displaystyle Y_{x}=Kx^{\log _{2}(b)}}$

where

• K is the number of direct labour hours to produce the first unit
• Yx is the number of direct labour hours to produce the xth unit
• x is the unit number
• b is the learning percentage (expressed as a decimal)
In particular, in the first two set-off lines of math, Yx is the cumulative average learning cost with Px being the cost of unit x. However in the last set-off line of math, Yx is the cost of unit x. I propose to delete the reference to Yx and leave the following:
Empirical research has validated the following mathematical form for the unit cost, Px, producing unit number x starting with P1:
${\displaystyle P_{x}=P_{1}x^{\log _{2}(b)}}$,
where (1-b) is the proportion reduction in the unit cost with each doubling in the cumulative production. To see this, not the following:
${\displaystyle P_{2}x=P_{1}(2x)^{\log _{2}(b)}=P_{x}2^{\log _{2}(b)}=P_{x}b}$
Of course, this is only a statistical average and will rarely if ever exactly predict the unit cost of producing any future product. However, it has been found to be useful in many contexts.
I apologize if this creates other problems with this article. If it does, I trust someone will correct those problems. However, I hope no one will just revert these edits and restore the above text that I found erroneous. Thanks, DavidMCEddy (talk) 03:02, 25 December 2016 (UTC)

## Errors in discussion of Cumulative Average Curve

I'm deleting the subsection of "Learning curve and learning curve effect" discussing "Cumulative Average Curve", because it seems to contain fundamental errors that I'm not able to fix at this time. As of 2016-12-24 it read as follows:

This equation describes the basis for the cumulative average or cum average curve. In this equation, Y represents the average cost of different quantities (X) of units. The significance of the "cum" in cum average is that the average costs are computed for X cumulative units. Therefore, the total cost for X units is the product of X times the cum average cost. For example, to compute the total costs of units 1 to 200, an analyst could compute the cumulative average cost of unit 200 and multiply this value by 200. This is a much easier calculation than in the case of the unit curve.

${\displaystyle {\overline {Y_{x}}}=K{\frac {{\frac {1}{1+\log _{2}(b)}}x^{1+\log _{2}(b)}}{x}}}$

where

• K is the number of direct labour hours to produce the first unit
• Yx is the average number of direct labour hours to produce first x units
• x is the unit number
• b is the learning percentage
• My concern: Consider the case x = 1: By the definition of k, we should have the following:
${\displaystyle {\overline {Y_{1}}}=K}$

${\displaystyle {\overline {Y_{1}}}=K{\frac {1}{1+\log _{2}(b)}}}$

This is only true of b = 1, not for arbitrary positive b less than 1.

As I wrote in the previous section a few minutes ago, I apologize if this creates other problems with this article. If it does, I trust someone will correct those problems. However, I hope no one will just revert these edits and restore the above text that I found erroneous. Thanks, DavidMCEddy (talk) 03:54, 25 December 2016 (UTC)

## Equations 1 and 2

One more edit: I'm deleting the reference to "Equations 1 and 2" from the following line: "The Learning Curve model posits that for each doubling of the total quantity of items produced, costs decrease by a fixed proportion, as described by Equations 1 and 2." Wikipedia style does not use equation numbers. I don't know what these refer to. I hope this makes the article easier to read and more intelligible.

Thanks to all who brought the article to this point. It's generally quite useful, I think -- averaging 200 page views per day over the past 90 days. It's worth trying to make it easier to read. I hope I've done that (and not the opposite). Thanks, DavidMCEddy (talk) 04:00, 25 December 2016 (UTC)

1. ^ Chase, Richard B. (2001), Operations management for competitive advantage, ninth edition, International edition: McGraw Hill/ Irwin, ISBN 0-07-118030-3