CIMA Student 8
MANAGEMENT ACCOUNTING APPLICATIONS
The learning curve:
from aircraft to spacecraft?
G.J. Steven, Napier University
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.
W
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.
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?
Economies of scale
Most students will be familiar with economies of
scale. However, it is important to appreciate that
the learning effect is not concerned with
reduction in unit cost as production increases
and/or production facilities are scaled up to
manufacture larger batches of products. So what
is the learning effect?
Learning effect
The learning effect is concerned with cumulative
production over time—not the manufacture of a
single product/batch at a particular moment in
time—and recognises that it takes less time to
assemble a product the more times that product is
made by the same worker, or group of workers.
The most effective way of describing the
learning effect is to consider the assembly of selfassembly furniture in your own home! Let’s
assume that you decide to purchase three selfassembly chests of drawers for your home.
The first chest of drawers will take considerable
time to assemble since you are unfamiliar with the
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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.
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.
complete tasks in space etc. The phenomenon
observed by Wright and Crawford is now being
used for extra terrestrial activities!
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
Cumulative
time
Average
time
1 unit
2 units
4 units
8 units
1,000 hrs
1,800 hrs
3,240 hrs
5,832 hrs
1,000 hrs
900 hrs
810 hrs
729 hrs
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
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
determined by machines, the learning effect will
not be observed since (at present!) people learn,
not machines.
Examples of sectors where the learning effect is
pronounced include:
• aerospace;
• electronics;
• shipbuilding;
• construction;
• defence.
The learning curve is also being utilised by the
refurbishment sectors. Rail operators, for example,
seek to extend cost-effectively the lives of their
assets, e.g. London Underground, privatised rail
companies etc.
Another sector which makes considerable use
of this technique is the space industry. NASA, for
example, uses the learning curve to estimate costs
for the production of space shuttles, time to
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.
Management Accounting May 1999
NB: The above instructions may not apply to all
types of scientific calculators.
CIMA Student 9
Calculator instructions
Enter a, i.e. 1000
Press MULTIPLY
Enter x, i.e. 8
Press XY
Enter b as a positive, i.e. 0.152
Change b to -b with +/-, i.e. 0.152
Press EQUALS to obtain answer, i.e. 729
capable of flying outside the earth’s atmosphere.
The company has been asked to submit a tender
to install ten guidance systems for this project.
While a tender would take account of all costs
that would apply to a particular project, one of
the key costs for a high-technology project is
labour time, as highly skilled personnel (who are
highly paid) are required to assemble and test
such systems. The following analysis will focus on
the labour time required for this project.
Aurora project
NASA’s web site—see below for URL—contains a
learning curve calculator based on Wright’s and
Crawford’s models. Unfortunately, students do
not have access to this resource in CIMA’s
examinations! Please note that the preceding
calculations are based on Wright’s model.
Budgeting and control
While the learning curve can be used for a
number of purposes as it predicts time reduction,
it is normally associated with budgeting. This is
because budgets and standards will only provide
reliable benchmarks to measure actual
performance against if account is taken of the
learning effect.
For example, if it is assumed that the above
data covered the first year’s production of this
product, and demand in year 2 was expected to
be 24, a simplistic analysis which ignored the
learning effect would produce an estimate of
17,496 hours to produce 24 additional items. This
would produce a large favourable variance if the
actual time taken to produce these 24 items was
13,800 hours.
Additional production (24 items)
Multiplied by
Cumulative average time for last year’s
production (729 hours)
Equals
17,496
A very different picture emerges, however, if
account is taken of the learning effect since the
expected time to produce the additional 24 items
would be 13,064 hours. That is, it would generate
a significant adverse variance which would
provide a more accurate indication of
performance.
Cumulative average time for 32 items x 32
(= 18,896 hours)
Less
Cumulative average time for 8 items x 8
(= 5,832 hours)
Equals
13,064 hours
Decision-making
While a great deal has been written about the use
of the learning curve for control purposes, this
technique can also be used to determine costs for
potential contracts in sectors which exhibit the
learning effect.
For example, Above & Beyond Ltd, which
produces high-technology guidance systems, is
preparing a tender for the Aurora project, the new
generation of space shuttles. The guidance
systems for the Aurora project will be very similar
to those recently supplied by the company for the
Dark Star project, experimental Stealth aircraft
Management Accounting May 1999
Above & Beyond Ltd’s engineers believe it is
possible to estimate the time required to install
the guidance systems for the new generation of
space shuttles from the learning derived from the
Dark Star project. The same system will be
installed in the space shuttles. The following data
was consequently obtained in respect of the
Stealth project:
• Time to install first system: 12,000 hours;
• Total installed: to date 9 systems;
• Total cumulative time: 69,595 hours.
The first figure to be calculated is b, the index of
learning, and this can be derived from the
learning curve equation, Yx = axb, since all the
other figures are known.
Yx = aXb
69,595/9 = 12,000 x 9b
9b = 7733/12000
9b = 0.6444
b log 9 = log 0.6444
b = log 0.6444 / log 9
b = - 0.2
- 0.2 is equivalent to a learning rate of 87%, i.e.
the antilog of (-0.2 multiplied by log 2).
It may consequently be necessary to take a more
realistic view of the initial efficiency levels that can
be achieved for the Aurora project. It may be
prudent, for example, to use a cumulative total
production of seven to estimate the time required
for this project, i.e. 58,836 hours. While this will
be a subjective judgment, hopefully based on past
experience, it must be made to avoid
underestimating the time required for this project.
it may also be necessary to determine whether or
not the learning rate for Dark Star was affected,
adversely or favourably, by illness, holidays,
changes to work groups etc, to determine
whether or not a reasonable learning rate resulted
from that project.
Conclusion
It is now possible to estimate the time required to
install the guidance systems for this project.
Other factors
The learning effect, which was first recognised by
Wright and Crawford, still applies to today’s
business environment since people haven’t
changed since the 1930s. It is also possible that
the learning curve will be used more widely in the
future due to the demand for sophisticated hightechnology systems, and the increasing interest in
refurbishment to extend asset life. While much has
been written in relation to the use of the learning
curve for budgeting and control, there has been
little recognition of its potential for decisionmaking. The learning curve is a vital decisionmaking tool, however, since it can be used to
prepare competitive tenders by utilising earlier
learning for new contracts for the same, or a
similar, product. Customers are also increasingly
aware of the learning effect, and expect tenders to
take account of this factor. The phenomenon
observed by Wright and Crawford is,
consequently, still relevant for the modem
business environment.
The calculations for the Aurora project assumed it
was possible to continue down the learning curve
from the learning obtained in respect of the Dark
star project. This might not be a realistic starting
point, however, as it may be necessary to take
account of the following factors:
• the guidance system for the Aurora project may
have to be modified for the shuttles since they
have, for example, a different airframe;
• the work teams may be different from those
used for the Dark star project;
• the time lapse since the completion of the Dark
Star project.
References and further reading
DRURY, C. (1996): Management and Cost
Accounting, International Thomson Business Press,
pp.687- 691
DUGDALE, D., KENNEDY, A., SUGDEN, K. and SCARLETT, R.
(1996): Management Accounting
Applications: Practical Elements, pp.61-66
KENNEDY, A. and SUGDEN, K. (1996): Management
Accounting Applications: Knowledge, pp.37-41
NASA http://www,jsc. nasa.gov/bu2/learn.html
UPCHURCH (1998): Management Accounting:
Principles and Practice, pp.78 - 85, Pitman
Cumulative average time for 19 systems x 19
(= 126,527 hours)
Less
Cumulative average time for 9 systems x 9
(= 69,595 hours)
Equals
56,932 hours
Please note that the learning curve would produce
an estimate of 75,715 hours to install the
guidance systems using a learning rate of 87% if
no account was taken of the learning derived from
Dark Star. This difference of 18,783 hours is
extremely significant since the costs of hiring
specialist engineers, and supporting these
engineers, could be £100+ per hour, i.e. £1.8m+.
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