Identifying Basic Improvement Curve Theories: Unit Improvement Curve

Since 1936, many different formulations have been proposed to explain and estimate the
improvement that takes place in repetitive production efforts. Of these, the two most popular are
the unit improvement curve and the cumulative average improvement curve
Unit Improvement Curve. The unit improvement curve is the model validated by the postWorld War II SRI study. The formulation is also known by two other names: Crawford curve,
after one of the leaders of the SRI research; and Boeing curve, after one of the firms that first
embraced its use.
Unit curve theory can be stated as follows:
As the total volume of units produced doubles the cost per unit decreases by some constant
percentage.
The constant percentage by which the costs of doubled quantities decrease is called the rate of
learning. The term "slope" in the improvement curve analysis is the difference between 100
percent and the rate of improvement. If the rate of improvement is 20 percent, the improvement
curve slope is 80 percent (100 percent - 20 percent). The calculation of slope is described in
detail later in the chapter.
Unit curve theory is expressed in the following equation:
Y = AX B
Where:
Y = Unit cost (hours or dollars) of the X th unit
X = Unit number
A = Theoretical cost (hours or dollars) of the first unit
B = Constant that is related to the slope and the rate of change of the improvement curve. It is
calculated from the relationship:
In calculating B, the slope MUST be expressed in decimal form rather than percentage form.
Then B will be a negative #, leading to the decreasing property stated above.
7.0.4 Identifying Basic Improvement Curve Theories: Cumulative Average Improvement
Curve
Cumulative Average Improvement Curve. The cumulative average improvement curve is the
model first introduced by Wright in 1936. Like the unit improvement curve, the cumulative
average curve is also known by two other names: Wright Curve, after T.P. Wright; and Northrop
Curve, after one of the firms that first embraced its use.
Cumulative average theory can be stated as follows:
As the total volume of units produced doubles the average cost per unit decreases by some
constant percentage.
As with the unit improvement curve, the constant percentage by which the costs of doubled
quantities decrease is called the rate of improvement. The slope of the improvement curve
analysis is the difference between 100 percent and the rate of learning. However, the rate of
improvement and the slope are measured using cumulative averages rather than the unit values
used in unit improvement curve analysis.
Cumulative average curve theory is expressed in the following equation:
Y = AX B
Where:
= Cumulative average unit cost (hours or dollars) of units
through the X th unit
All other symbols have the same meaning used in describing the unit improvement curve.
Curve Differences. Note that the only difference between definitions of the unit improvement
curve and the cumulative average improvement curve theories is the word average . In the unit
curve, unit cost is reduced by the same constant percentage. In the cumulative average curve, the
cumulative average cost is reduced by the some constant percentage.
The most significant practical difference between the two different formulations is found in the
first few units of production. Over the first few units, an operation following the cumulative
average curve will experience a much greater reduction in cost (hours or dollars) than an
operation following a unit curve with the same slope. In later production, the reduction in cost
for an operation following a cumulative average curve will be about the same as an operation
following a unit curve with the same slope.
Because of the difference in early production, many feel that the unit curve should be used in
situations where the firm is fully prepared for production; and the cumulative average curve
should be used in situations where the firm is not completely ready for production. For example,
the cumulative average curve should be used in situations where significant tooling or design
problems may NOT be completely resolved. In such situations, the production of the first units
will be particularly inefficient but improvement should be rapid as problems are resolved.
In practice, firms typically use one formulation regardless of differences in the production
situation. Most firms in the airframe industry use the cumulative average curve. Most firms in
other industries use the unit curve.
7.1 Identifying Situations for Use
The improvement curve cannot be used as an estimating tool in every situation. Situations that
provide an opportunity for improvement or reduction in production hours are the types of
situations that lend themselves to improvement curve application. Use of the improvement curve
should be considered in situations where there is:
• A high proportion of manual labor.
It is more difficult to reduce the labor input when there is limited labor effort, the labor effort is
machine paced, or individual line workers only touch the product for a few seconds.
• Uninterrupted production.
As more and more units are produced the firm becomes more adept at production and the labor
hour requirements are reduced. If supervisors, workers, tooling, or other elements of production
are lost during a break in production, some improvement will also likely be lost.
• Production of complex items.
The more complex the item the more opportunity there is to improve.
• No major technological change.
The theory is based on continuing minor changes in production and in the item itself. However,
if there are major changes in technology, the benefit of previous improvement may be lost.
• Continuous pressure to improve.
The improvement curve does not just happen; it requires management effort. The management of
the firm must exert continuous pressure to improve. This requires investment in the people and
equipment needed to obtain improvement.
7.1.1 Situations for Use
As you examine situations that appear to have potential for improvement curve application,
consider management emphasis on the following factors affecting the rate of improvement:
• Job Familiarization By Workers.
As noted earlier, many feel that this element has been overemphasized over the years. Still,
workers do improve from repetition and that improvement is an important part of the
improvement curve.
• Improved Production Procedures.
As production continues, both workers and production engineers must constantly be on the
lookout for better production procedures.
• Improved Tooling and Tool Coordination.
Part of the examination of production procedures must consider the tooling used for production.
Tooling improvements offer substantial possibilities for reduction of labor requirements.
• Improved Work Flow Organization.
Improving the flow of the work can substantially reduce the labor effort that does not add value
to the product. Needless movement of work in progress can add significant amounts of labor
effort.