9.8 The Learning Curve

When we estimate the cost or price of an item, whether it is based on a detailed cost build-up, an analogy, catalog price, or a cost estimating relationship, the cost or price may not address the effect of quantity or of learning. The learning curve (cost improvement curve, or experience curve) is a well-known approach to modeling the effect of quantity on cost. This technique was first discussed in the journals of the 1930's and continues as an industry standard today both in commercial and non-commercial (government) applications.

Figure 9-8 Learning Curve

Learning curve theorizes that people and organizations learn to do things more efficiently when performing repetitive tasks. The more often the task is performed or repeated, the more efficient the worker becomes and the less time it takes to perform those task. There is a usable pattern (Figure 9-8 learning curve) to the learning. And that pattern is different for different conditions. For that reason a number of different learning curves have been developed. Learning curves are generally drawn showing that as the number of units produced doubles, the unit cost decreases in a predictable pattern.

The learning curve was adapted from the historical observation that individuals performing repetitive tasks exhibit an improvement in performance as the task is repeated a number of times. Empirical studies of this phenomenon yielded three conclusions on which the current theory and practice is based:

1. The time required to perform a task decreases as the task is repeated.
2. The amount of improvement decreases as more units are produced.
3. The rate of improvement has sufficient consistency to allow its use as a prediction tool.

Theodore P. Wright created the "learning curve" math model in 1936 and the model was used during World War I to estimate aircraft production costs. The initial studies attributed the improved productivity or efficiency to improved motor skills as the workers repeated their tasks. Thus tasks with a lot of touch labor tended to get the most attention. However, worker learning is just one of the components which contribute to efficiencies and it was later realized that management could also be a contributor to the achievement of efficiencies. From Table 9-3 it can be seen that the total improvement is a combination of personnel learning and management action. While some study has been done, there is no general rule concerning the relative contribution of the specific elements.

Table 9-3 Factors Leading to Manufacturing Improvement

While learning is found in almost all elements of the defense industry, its impact is most pronounced when certain characteristics are present.

1. The first characteristic is the building of a large complex product. requiring a large number of direct labor hours.
2. The second is continuity of manufacturing to preclude loss of accrued improvements during production breaks.
3. The third characteristic is an element of continuing change in the product. This third characteristic can present some problems in analysis using the manufacturing improvement curve.

The historical data on which a company's improvement curve is based contain the effects of an engineering change activity which can be characterized as "normal." During the analysis of the program of interest, changes which are developed need to be evaluated to determine whether they are "normal" and already accounted for by the learning curve, or major changes which must be the subject of a contract modification. The decision needs to be made on the basis of the unique situation involved in the program. This should be done in the context of the nature of the historical contractor activity which was used to develop the learning curve used in the contract negotiation.

To utilize learning curve theory, certain key phrases listed below are of importance:

Figure 9-9 Learning Curve Comparisons

• Slope of the Curve — Is a percentage figure that represents the steepness (Figure 9-9 shows the slopes of three different learning curves) of the curve. Using the unit curve theory, this percentage represents the value (e.g., hours or cost) at a doubled production quantity in relation to the previous quantity. For example, with an learning curve having an 80 percent slope, the value at unit two is 80 percent of the value of unit one; the value at unit four is 80 percent of the value at unit two; the value at unit 1,000 is 80 percent of the value at unit 500.
• Unit One — The first unit of product actually completed during a production run, This is not to be confused with a unit produced in any preproduction phase of the overall acquisition program.
• Cumulative Average Hours — The average hours expended per unit for all units produced through any given unit.
• Unit Hours — The total direct labor hours expended to complete any specific unit.
• Cumulative Total Hours — The total hours expended for all units produced through any given unit.

There are two fundamental models of the learning curve in general use:

1. The cumulative average curve, and
2. The unit curve.

The cumulative average curve's (T. P. Wright) underlying hypothesis is that the direct labor man-hours necessary to complete a unit of production will decrease by a constant percentage each time the production quantity is doubled. If the rate of improvement is 20 percent between doubled quantities, then the learning percent would be 80 percent (100-20=80). The cumulative average combines each sequential lot with the preceding lots and calculates an average cost. This is sometimes referred to as smoothing the data. This technique helps to reduce the effect of variation in the data and produces better statistical models. While the learning curve emphasizes time, it can be easily extended to cost.

The unit curve was developed by James R. Crawford in 1947 and used by the Army Air Corps to study airframe production. The unit curve focuses on the hours or cost involved in specific units of production and treats each lot as a separate reference point. The theory can be stated as follows:

• As the total quantity of units produced doubles, the cost per unit decreases by some constant rate.
• The constant rate by which the costs of doubled quantities decrease is called the rate of learning.
• The "slope" of the learning curve is related to the rate of learning. It is the difference between 100 and the rate of learning. For example, if the hours between doubled quantities are reduced by 20 percent (rate of learning) it would be described as a curve with an 80 percent slope.

The difference or amount of labor-hour reduction is not constant. Rather, it declines by a continually diminishing amount as the quantities are doubled. The amount of change over the "doubling" period has been found to be a constant percentage of cost at the beginning of the doubling period.

When selecting a learning curve model keep in mind the expected production environment. Certain production systems or environments favor one theory over the other:

Figure 9-10 Cum vs Unit Learning Curves

• Unit Curve (Crawford method) is best used if the contractor is starting production with prototype tooling, has an inadequate supplier base established, expects design changes or is subject to short lead times.
• Cumulative Average Curve (Wright method) is best used if the contractor is well prepared to begin production in terms of tooling, suppliers, lead times, etc.

The cum average curve is based on the average cost of a production quantity rather than on the cost of a particular unit. This makes the cum average cost less responsive to cost trends than the unit cost curve. A larger change is needed in the cost of an unit or lot of units before there is a change in the cum average curve. This is the reason the cum average curve is always higher than the unit cost curve (Figure 9-10). Most government negotiators prefer to use the unit cost curve since it is lower than and more responsive to recent trends than is the cum average cost curve.

Research by the Stanford Research Institute revealed that many different slopes were experienced by different manufacturers, sometimes on similar manufacturing programs. In fact, manufacturing data collected from the World War II aircraft manufacturing industry had slopes ranging from 69.7 percent to almost 100 percent. These slopes averaged 80 percent, giving rise to an industry average curve of 80 percent. Other research has developed measures for other industries such as 95.6 percent for a sample of 162 electronics programs. Learning percent is usually determined by statistical analysis of actual cost data for similar products or processes. Figure 9-11 shows typical slopes for a variety of activities. Unfortunately, the industry average curve is frequently misapplied by practitioners who use it as a standard or norm. When estimating slopes without the benefit of data from the plant of the manufacturer, it is better to use learning curve slopes from similar items at the manufacturer's plant, rather than the industry average.

The analyst needs to know the slope of the learning curve for a number of reasons. Accordingly, the slope of the learning curve is usually an issue in production contract negotiation. The slope of the learning curve is also needed to project follow-on costs using either the learning tables or the computational assistance of a computer.

Existing learning curves, by definition, reflect past experience. Trend lines are developed from accumulated data plotted on logarithmic paper (preferably) and "smoothed out" to portray the curve. The data may have been accumulated by product, process, department, or by other functions or organizations. But whichever learning curve or method of data accumulation is selected for use, the data should be applied consistently in order to render meaningful information to management. Consistency in curve concept and data accumulation cannot be overemphasized because existing learning curves play a major role in determining the projected learning curve for a new product. This in turn plays a major role is estimating cost.

When selecting the proper curve for a new production item when only one point of data is available and the slope is unknown, the following, in decreasing order of magnitude, should be considered:

• Similarity between the new item and an item or items previously produced;
• Addition or deletion of processes and components;
• Differences in material, if any;
• Effect of engineering changes in items previously produced;
• Duration of time since a similar item was produced;
• Condition of tooling and equipment;
• Personnel turnover;
• Changes in working conditions or morale;
• Other comparable factors between similar items;
• Delivery schedules;
• Availability of material and components;
• Personnel turnover during production cycle of item previously produced; and
• Comparison of actual production data with previously extrapolated or theoretical curves to identify deviations.

It is feasible to assign weights to these factors as well as to any other factors that are of a comparable nature in an attempt to quantify differences between items. These factors are again historical in nature and only comparison of several existing curves and their actuals would reveal the importance of these factors.

When production is underway, available data can be readily plotted, and the curve may be extrapolated to a desired unit. However, if production has yet to be started, actual unit one data would not be available and a theoretical unit one value would have to be developed. This may be accomplished in one of three ways:

• A statistically derived relationship between the preproduction unit hours and first unit hours can be applied to the actual hours from the preproduction phase.
• A cost estimating relationship (CEA) for first unit cost based upon physical or performance parameters can be used to develop a first unit cost estimate.
• The slope and the point at which the curve and the labor standard value converge are known. In this case a unit one value can be determined. This is accomplished by dividing the labor standard by the appropriate unit value.

A manufacturing or production break is the time lapse between the completion of an order or manufacturing run of certain units of equipment and the commencement of a follow-on order or restart of manufacturing for identical units. This time lapse disrupts the continuous flow of manufacturing and constitutes a definite cost impact. The time lapse under discussion here pertains to significant periods of time (weeks and months) as opposed to the minutes or hours for personnel allowances, machine delays, power failures, and the like.

Since the learning curve has a time/cost relationship, a break will affect both time and cost. Therefore, the length of the break becomes as significant cost factor. It is important to determine the cost of this break in manufacturing. Figure 9-12 graphically depicts how a production break causes the learning curve to shift upwards based on the amount of learning that has been lost. This reset in the learning curve also causes the cost to go up. Take for example what might happen if there were a break in the production of submarines. Welders who work on submarines are required to be specially trained and certified. The training and certification process takes 18-24 months to complete. Imagine what would happen to manpower utilization and cost if the workers lost their certification and had to be recertified before production could restart.

Figure 9-12 Effect of Production Breaks