Editing Learning curve (section)

== Examples  and mathematical modeling ==
A learning curve is a plot of proxy measures for implied [[learning]] ([[Uncertainty coefficient|proficiency]] or progression toward a limit) with [[experience]].
* The horizontal axis represents experience either directly as time (clock time, or the time spent on the activity), or can be related to time (a number of trials, or the total number of units produced).
* The vertical axis is a measure representing 'learning' or 'proficiency' or other proxy for "efficiency" or "productivity". It can either be increasing (for example, the score in a test), or decreasing (the time to complete a test).

For the performance of one person in a series of trials the curve can be erratic, with proficiency increasing, decreasing or leveling out in a [[Plateau (mathematics)|plateau]].

When the results of a large number of individual trials are [[average]]d then a smooth curve results, which can often be described with a [[Function (mathematics)|mathematical function]]. 
<gallery class="center" widths="220" heights="140" style="line-height:130%">
File:Alanf777 Lcd fig07.png|S-curve or sigmoid function 
File:Alanf777 Lcd fig04.png|Exponential growth
File:Alanf777 Lcd fig05.png|Exponential rise or fall to a limit
File:Alanf777 Lcd fig06.png|Power law
</gallery>
Several main functions have been used:<ref>Newell, A. (1980) [http://repository.cmu.edu/cgi/viewcontent.cgi?article=3420&context=compsci Mechanisms of skill acquisition and the law of practice]. University of Southern California
</ref><ref>Ritter, F. E., & Schooler, L. J. (2002) [http://ritter.ist.psu.edu/papers/ritterS01.pdf "The learning curve"]. In ''[[International Encyclopedia of the Social and Behavioral Sciences]]'', pp. 8602–8605. Amsterdam: Pergamon. {{ISBN|9780080430768}}</ref><ref>{{cite journal |doi=10.1016/j.jmp.2010.01.006 |url=http://www.bgu.ac.il/~akarniel/pub/LeibowitzetalJMP2010.pdf |title=The exponential learning equation as a function of successful trials results in sigmoid performance |year=2010 |last1=Leibowitz |first1=Nathaniel |last2=Baum |first2=Barak |last3=Enden |first3=Giora |last4=Karniel |first4=Amir |journal=Journal of Mathematical Psychology |volume=54 |issue=3 |pages=338–340}}</ref>

* The [[Sigmoid function|S-Curve or Sigmoid function]] is the idealized general form of all learning curves, with slowly accumulating small steps at first followed by larger steps and then successively smaller ones later, as the learning activity reaches its limit. That idealizes the normal progression from discovery of something to learn about followed to the limit of learning about it. The other shapes of learning curves (4, 5 & 6) show segments of S-curves without their full extents. In this case the improvement of proficiency starts slowly, then increases rapidly, and finally levels off.
* Exponential growth; the proficiency can increase without limit, as in [[Exponential growth]]
* Exponential rise or fall to a Limit; proficiency can exponentially approach a limit in a manner similar to that in which a capacitor charges or discharges ([[exponential decay]]) through a resistor. The increase in skill or retention of information may increase rapidly to its maximum rate during the initial attempts, and then gradually levels out, meaning that the subject's skill does not improve much with each later repetition, with less new knowledge gained over time.
* [[Power law]]; similar in appearance to an [[exponential decay]] function, and is almost always used for a decreasing performance metric, such as cost. It also has the property that if plotted as the [[logarithm]] of proficiency against the [[logarithm]] of experience the result is a straight line, and it is often presented that way.

The specific case of a plot of Unit Cost versus Total Production with a power law was named the [[experience curve]]: the mathematical function is sometimes called Henderson's Law. This form of learning curve is used extensively in industry for cost projections.<ref>{{cite web |url=http://classweb.gmu.edu/aloerch/LearningCurve%20Basics.pdf |title=Learning Curve Basics |access-date=2013-03-17 |url-status=dead |archive-url=https://web.archive.org/web/20130718044848/http://classweb.gmu.edu/aloerch/LearningCurve%20Basics.pdf |archive-date=2013-07-18 }} U.S. Department of Defense Manual Number 5000.2-M, mandates the use of learning curves for costing of defense programs (variable costs of production)</ref>