The Learning Curve

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MANAGEMENT ACCOUNTING APPLICATIONS

The learning curve: from aircraft to spacecraft?
instructions, the components, and how to assemble them. In addition, you may also lack confidence in your ability to produce an acceptable product. The second one, however, will take you less time, as you will be more familiar with the instructions, the components, and the assembly procedures. You will also be confident of your ability to assemble this product. The third one will take even less time, as you will have learned from your earlier mistakes and determined more efficient assembly procedures. That is the learning effect. complete tasks in space etc. The phenomenon observed by Wright and Crawford is now being used for extra terrestrial activities!

This article on the learning curve: • explains the learning effect; • identifies sectors where it can be used; • explains how it is calculated; • explains, with examples, how it can be used for planning, control and decision-making; • discusses the other factors that have to be considered in relation to its use.

Learning curve model
Wright observed that the cumulative average time per unit decreases by a fixed percentage each time cumulative production doubles over time. The following table illustrates this effect: Cumulative output 1 unit 2 units 4 units 8 units Cumulative time 1,000 hrs 1,800 hrs 3,240 hrs 5,832 hrs Average time 1,000 hrs 900 hrs 810 hrs 729 hrs

Cost reduction tool?
It is important to appreciate that the learning curve is not a cost-reduction technique since the rate of future time reduction can be predicted accurately by the learning curve model. Cost reduction only occurs if management action is taken, for example, to increase the rate of time reduction by providing additional training, provision of better tools etc. The learning effect occurs because people are inventive, learn from earlier mistakes, and are (generally) keen to take less time to complete tasks, for a variety of reasons. It should also be noted that the learning process may be done consciously and/or intuitively. The learning curve consequently reflects human behaviour.

hile this article was principally written for Management Accounting Applications, it is also relevant for Management Science Applications (MSA). MSA students, however, are only expected to have knowledge of this technique, i.e. no calculations are required for this technique at Stage 2.

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The above table indicates that the cumulative average time per unit falls by 10% each time cumulative production doubles, i.e. it is depicting a 90% learning curve. The above relationship between cumulative output and time can be represented by the following formula: Yx = axb where Yx = cumulative average time to produce a cumulative number of units a = time to produce the first unit x = cumulative number of units b = index of learning The index of learning is the log of the learning curve divided by the log of 2. NB: At present, CIMA does not require students to calculate the index of learning. Use your calculator to confirm that b = -0.152 for a learning rate of 90%; Calculator instructions Press LOG Enter 0.9 Press DIVIDE Press LOG Enter 2 Press EQUALS to obtain answer, i.e. -0.152 NB: The above instructions may not apply to all types of scientific calculator and the cumulative average time per unit is 7,329 hours for a cumulative output of eight units.

Introduction
The learning curve was first observed by Wright in the 1930s in the American aircraft industry, and his pioneering work was confirmed by Crawford in the 1940s. But what is the learning effect? Where can it be used? What can it be used for? And is it relevant for the modern business environment?

Learning curve sectors
While the learning curve can be applied to many sectors, its impact is most pronounced in sectors which have repetitive, complex operations where the pace of work is principally determined by people, not machines. If the pace of work is...
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