Learning Curve Theory
Learning Curve Theory is based upon the observation that repetition of a task promotes improvement in performance through learning. Each time an operator assembles an electronic chassis the operator becomes better at it. Each time a material move person walks a part through the factory floor Iess time is taken. A few ways that learning can manifest itself are an increase in hand-eye coordination in a manual process, new and faster machining processes as a numerically controlled workstation's programming is refined, improved machinability resulting from trial of new materials, less in-line rejects due to increasing operator awareness of critical points in processing, and refinement of tooling and fixturing. Unlike Quantity Curve Theory, Learning Curve Theory recognizes that learning is a continuous process. It is a cumulative phenomenon, increasing with each repetition of a task.
Learning Curve Theory also recognizes that the amount of improvement will decrease with each repetition. The first time an operator assembles a new type of chassis the operator is slow and the assembly is prone to errors. The second chassis assembled takes much less time than the first and errors are fewer. The amount of improvement from the first chassis to the second is dramatic. Less dramatic will be the amount of learning between the assembly of the second to the third chassis. As the number of assembled chassis increases the improvement rate decreases until improvement is hardly noticeable.
Learning Curve Theory can be mathematically quantified with the use of logarithmic curves. The learning curve formula is expressed as:
y = axb where
y = cumulative average unit price
a = coefficient
x = cumulative quantity
b = logarithmic slope expression
The logarithmic slope is closely related to the Learning Curve Percent. The Learning Curve Percent can be defined as the amount of the cost of the first unit the second unit will cost to produce. In fact, the percent is the amount to multiply the cumulative average price of a prior cumulative quantity by whenever the cumulative quantity doubles to arrive at the cumulative average cost of the new cumulative quantity. For example, a 90% Learning Curve Percent indicates that the cumulative average cost of the 2nd unit will be 90% of the cost of the first unit, the cumulative average cost of the 4th unit will be 90% of the cumulative average cost of the 2nd unit, and the cumulative average cost of the 8th unit will be 90% of the cumulative average cost of the 4th unit. To illustrate, a 90% Learning Curve and an 80% Learning Curve have the following data points.
|
Unit Number |
Price 90% Learning Curve |
Price 80% Learning Curve |
|
|
|
|
|
1 |
$100.00 |
$100.00 |
|
2 |
$90.00 |
$80.00 |
|
4 |
$81.00 |
$64.00 |
|
8 |
$72.90 |
$51.20 |
|
16 |
$65.61 |
$40.96 |
|
32 |
$59.05 |
$32.77 |
|
64 |
$53.14 |
$26.21 |
Since we are constantly multiplying the cumulative average unit price by a fraction (the Learning Curve Percent) every time we double the cumulative quantity the learning curve tends to flatten out. This reflects the nature of manufacturing or processing an item. Repetition provides increased efficiency at an ever-decreasing rate.
Various factors influence the Learning Curve Percent. They include the length of the production run, the initial manufacturability of the item, the quality and automation of the initial tooling, the training of the manpower, and the nature of the item itself. For example, an item requiring a great deal of assembly will tend to have a lower Learning Curve Percent than an item that is totally processed complete.
As a general guideline, percents of 90 are applicable to most procurements. A percent of 70 would be applicable during the pre-production phase of a major system or assembly. A percent of 98 would be applicable to an item that has been mass produced for a great length of time. The most rapid improvement, thus a low Learning Curve Percent, would be associated with items requiring a large proportion of assembly and fabrication. The greater the labor content, the lower the percent.