Using the cost estimating methods discussed in this chapter can generate the cost of a single item. However, a cost estimator needs to determine whether that cost is for the first unit, the average unit, or every unit. And given the cost for one unit, how should a cost estimator determine the appropriate costs for other units? The answer is in the use of learning curves. Sometimes called progress or improvement curves, learning curve theory is based on the premise that people and organizations learn to do things better and more efficiently when they perform repetitive tasks. A continuous reduction in labor hours from repetitive performance in producing an item often results from more efficient use of resources, employee learning, new equipment and facilities, or improved flow of materials. This improvement can be modeled with a mathematical CER that assumes that as the quantity of units to be produced doubles, the amount of effort declines by a constant percentage.
Workers gain efficiencies in a number of areas as items are repeatedly produced. The most commonly recognized area of improvement is worker learning. Improvement occurs because as a process is repeated, workers tend to become physically and mentally more adept at it. Supervisors, in addition to realizing these gains, become more efficient in using their people, as they learn their strengths and weaknesses. Improvements in the work environment also translate into worker and supervisory improvement: Studies show that changes in climate, lighting, and general working conditions motivate people to improve. Cost improvement also results from changes to the production process that optimize placement of tools and material and simplify tasks. In the same vein, organizational changes can lead to lower recurring costs, such as instituting a just-in-time inventory or centralizing tasks (heat and chemical treatment processes, tool bins, and the like). Another example of organizational change is a manufacturer’s agreeing to give a vendor preferred status if it is able to limit defective parts to some percentage. The reduction in defective parts can translate into savings in scrap rates, quality control hours, and recurring manufacturing labor, all of which can result in valuable time savings. In general, it appears that more complex manufacturing tasks tend to improve faster than simpler tasks. The more steps in a process, the more opportunity there is to learn how to do them better and faster.
Another reason for contractor improvement is that in competitive business environments, market forces require suppliers to improve efficiency to survive. As a result, some suppliers may competitively price their initial product release at a loss, with the expectation that future cost improvements will make up the difference. This strategy can also discourage competitors from entering new markets. For the strategy to work, however, the assumed improvements must materialize or the supplier may cease to exist because of high losses.
In observing production data (for example, manufacturing labor hours), early analysts noted that labor hours per unit decreased over time. This observation led to the formulation of the learning curve equation Y = AXb and the concept of a constant learning curve slope (b) that captures the change in Y given a change in X.41 The unit formulation states that “as the number of units doubles, the cost decreases by a constant percent.” In other words, every time the total quantity doubles, the cost decreases by some fixed percentage. Figure 13 illustrates how a learning curve works.
Figure 13: A Learning Curve
0 20 40 60 80 100 120%
Cumulative number of units
90% ratio curve 1st unit 2nd unit 4th 8th 16th 32nd 64th 128th 80% ratio curve 0 20 40 60 80 100 120 140
Cumulative average hours per unit (as a percent of first unit)
Source: © 1994, R. Max Wideman, FCSCE, “A Pragmatic Approach to Using Resource Loading, Production and Learning Curves on Construction Projects.”
Figure 13 shows how an item’s cost gets cheaper as its quantities increase. For example, if the learning curve slope is 90 percent and it takes 1,000 hours to produce the first unit, then it will take 900 hours to produce the second unit. Every time the quantity doubles—for example, from 2 to 4, 4 to 8, 8 to 16—the resource requirements will reduce according to the learning curve slope.
Determining the learning curve slope is an important effort and requires analyzing historical data. If several production lots of an item have been produced, the slope can be derived from the trend in the data. Another way to determine the slope would be to look at company history for similar efforts and calculate it from those efforts. Or the slope could be derived from an analogous program. The analyst could look at slopes for a particular industry—aircraft, electronics, shipbuilding—sometimes reported in organizational studies, research reports, or estimating handbooks. Slopes can be specific to functional areas such as manufacturing, tooling, and engineering, or they may be composite slopes calculated at the system level, such as aircraft, radar, tank, or missiles.
The first unit cost might be arrived at by analogy, engineering build-up, a cost estimating relationship, fitting the actual data, or another method. In some cases, the first unit cost is not available. Sometimes 41 b = log (slope)/log (2).
work measurement standards might provide the hours for the 5th unit, or a cost estimating relationship might predict the 100th unit cost. This is not a problem as long as the cost estimator understands the point on the learning curve that the unit cost is from and what learning curve slope applies. With this information, the cost estimator can easily solve for the 1st unit cost using the standard learning curve formula Y = AXb.
Because learning can reduce the cost of an item over time, cost estimators should be aware that if multiple units are to be bought from one contractor as part of the program’s acquisition strategy, reduced costs can be anticipated. Thus, knowledge of the acquisition plan is paramount in deciding if learning curve theory can be applied. If so, careful consideration must be given to determining the appropriate learning curve slope for both labor hours and material costs. In addition, learning curves are based on recurring costs, so cost estimators need to separate recurring from nonrecurring costs if the results are not to be skewed. Finally, these circumstances should be satisfied before deciding to use learning curves:42
much manual labor is required to produce the item; ■
the production of items is continuous and, if not, then adjustments are made; ■
the items to be produced require complex processes; ■
technological change is minimal between production lots; ■
the contractor’s business process is being continually improved; and ■
the government program office culture (or environment) is sufficiently known. ■
Particular care should be taken for early contracts, in which the cost estimator may not yet be familiar enough with program office habits to address the risk accurately (for example, high staff turnover, propensity for scope creep, or excessive schedule delays).
p
roduCtionr
Atee
ffeCtsonL
eArningIt is reasonable to expect that unit costs decrease not only as more units are produced but also as the production rate increases. This theory accounts for cost reductions that are achieved through economies of scale. Some examples are quantity discounts and reduced ordering, processing, shipping, receiving, and inspection costs. Conversely, if the number of quantities to be produced decreases, then unit costs can be expected to increase, because certain fixed costs have to be spread over fewer items. At times, an increase in production rate does not result in reduced costs, as when a manufacturer’s nominal capacity is exceeded. In such cases, unit costs increase because of such factors as overtime, capital purchases, hiring actions, and training costs.
Another aspect of improvement is the continuity of the production line. Production breaks may occur because of program delays (budgetary or technical), time lapses between initial and follow-on orders, or labor disputes. They may occur as a result of design changes that may require a production line to shut down so it can be modified with new tools and equipment or a new configuration. Production lines can also shut down for unexpected recalls that require repairs for previously produced items. How much learning is lost depends on how long the production line is shut down.
To determine the effect of a production break on the unit cost two questions need answering: How much learning has been lost (or forgotten) because of the break in production? 1.
How will this loss of learning affect the costs of future production items? 2.
The cost estimator should always consider the effect of a production break on the cost estimate. (See case study 36.)
Case Study 36: Production Rate, from Defense Acquisitions,
GAO-05-183
Costs on the CVN 76 and CVN 77 Nimitz aircraft carriers grew because of additional labor hours required to construct the ships. At delivery, CVN 76 had required 8 million additional labor hours to construct; CVN, 77, 4 million. As the number of hours increased, total labor costs grew because the shipbuilder was paying for additional wages and overhead costs. Increases in labor hours stemmed in part from underestimating the labor hours. The shipbuilder had negotiated CVN 76 for approximately 39 million labor hours—only 2.7 million more labor hours than the previous ship—CVN 75. However, CVN 75 had been constructed more efficiently, because it was the fourth ship of two concurrent ship procurements. CVN 76 and CVN 77, in contrast, were procured as single ships.
Single ship procurements have historically been less efficient than two-ship procurements. The last time the Navy procured a carrier as a single-ship procurement, 7.9 million more hours were required—almost 3 times the number estimated for CVN 76 (2.7 million more hours). In addition, a 4-month strike in 1999, during the construction of CVN 76, had led to employee shortages in key trades and learning losses, because many employees were not returning to the shipyard. According to Navy officials, the shipbuilder was given $51 million to offset the strike’s effect.
GAO, Defense Acquisitions: Improved Management Practices Could Help Minimize Cost Growth in Navy Shipbuilding Programs, GAO-05-183
(Washington, D.C.: Feb. 28, 2005).
p
uLLingthep
ointe
stimAtet
ogetherAfter each WBS element has been estimated with one of the methods discussed in this chapter, the elements should be added together to arrive at the total point estimate. The cost estimator should validate the estimate by looking for errors like double-counting and omitted costs. The cost estimator should also perform, as a best practice, cross-checks on various cost drivers to see if similar results can be produced. This helps validate the estimate. The cost estimator should also compare the estimate to an independent cost estimate. The estimate and the independent cost estimate should also be reconciled at this time. (Chapter 15 discusses validating the estimate.)
DOD’s major defense acquisition programs are required to develop independent cost estimates for major program milestones; other agencies may not require this practice. An independent cost estimate gives an objective measure of whether the point estimate is reasonable. Differences between them should be examined and discussed to achieve understanding of overall program risk and to adjust risk around the point estimate.
Finally, as the program matures through its life cycle, as more data become available, or as changes occur, the cost estimator should update the point estimate. The updated point estimate should be compared against previous estimates, and lessons learned should be documented. (More detail is in chapter 20.)
Best Practices Checklist: Developing a Point Estimate 8.
The cost estimator considered various cost estimating methods:
Analogy, early in the life cycle, when little was known about the system 3
being developed:
Adjustments were based on program information, physical and ù
performance characteristics, contract type.
Expert opinion, very early in the life cycle, if an estimate could be 3
derived no other way.
The build-up method later, in acquisition, when the scope of work was 3
well defined and a complete WBS could be determined.
Parametrics, if a database of sufficient size, quality, and homogeneity 3
was available for developing valid CERs and the data were normalized correctly.
Parametric models were calibrated and validated using historical ù
data.
Extrapolating from actual cost data, at the start of production. 3
Cost estimating relationships were considered:
Statistical techniques were used to develop CERs: 3
Higher R-squared; ù
Statistical significance, for determining the validity of statistical 3
relationships;
Significance levels of F and t statistics. ù
Before using a CER, the cost estimator 3
Examined the underlying data set to understand anomalies; ù
Checked equations to ensure logical relationships; ù
Normalized the data; ù
Ensured that CER inputs were within the valid dataset range; ù
Checked modeling assumptions to ensure they applied to the ù
program.
Learning curve theory was applied if 3
Much manual labor was required for production; ù
Production was continuous or adjustments had to be made; ù
Items to be produced required complex processes; ù
Technological change was minimal between production lots; ù
The contractor’s business process was being continually improved. ù
Production rate and breaks in production were considered.
The point estimate was developed by aggregating the WBS element cost
estimates by one of the cost estimating methods.
Results were checked for accuracy, double-counting, and omissions and 3