The first step in conducting improvement curve analysis is plotting your raw data on a graph. Before running any calculations or selecting a mathematical model, you need to visually inspect your production data to spot trends, outliers, and abnormalities that numbers alone can hide. Defense cost analysis guidelines are explicit on this point: data should always be graphed initially, regardless of the analysis method you plan to use.
Why Graphing Comes Before Everything Else
It might seem like the real work starts with equations, but jumping straight to math is one of the most common mistakes in improvement curve analysis. A graph of your data can reveal problems that even sophisticated software won’t flag: a sudden spike in labor hours caused by a supplier change, a plateau that signals a process bottleneck, or a handful of data points that don’t fit the expected pattern at all. These abnormalities, as the Defense Technical Information Center notes, are “not easily evident from a computer print.”
At this stage, you’re plotting the cost or time required per unit (or per production lot) against the cumulative number of units produced. If you see a generally downward-sloping pattern, that confirms an improvement effect is present and the analysis is worth pursuing. If the data is scattered with no clear trend, you may need to clean your dataset or reconsider whether an improvement curve is the right tool.
Collecting the Right Data
Before you can graph anything, you need the right inputs. Improvement curve analysis typically requires two variables: a measure of effort (labor hours per unit, cost per unit, or time per procedure) and the cumulative quantity produced. In manufacturing and defense contracting, production data often comes bundled in lots rather than individual units. When that’s the case, you need to convert lot-level costs into a per-unit figure. The standard approach is to calculate the lot midpoint, which represents the specific unit number within that lot where average performance falls. That midpoint becomes your reference unit on the horizontal axis.
The choice between measuring labor hours versus cost matters. Labor hours give you a purer picture of worker learning because they strip out material price changes and inflation. Cost-based measures are more useful when you’re forecasting budgets, but they introduce noise from factors that have nothing to do with learning.
Choosing a Curve Model
Once your data is graphed and the improvement trend is confirmed, the next decision is which mathematical model to apply. The two dominant models are the cumulative average model (developed by T.P. Wright) and the unit model (associated with Crawford). Wright’s model assumes the cumulative average cost per unit drops by a fixed percentage each time total production doubles. Crawford’s model applies that same logic to individual unit costs instead of averages.
Both models follow a power law relationship, which means they produce a straight line when plotted on a log-log scale. This is why log transformation is central to the analysis: if you take the logarithm of both your unit costs and your unit numbers, a true improvement curve will appear as a straight line. The slope of that line tells you the rate of learning. Research comparing the two models has found that the cumulative average approach tends to produce more accurate estimates when working with limited production data, but both are widely used depending on the context.
Understanding the Learning Rate
The learning rate, expressed as a percentage, is the core output of the analysis. An 80% learning curve means that every time cumulative production doubles, the cost or time per unit drops to 80% of what it was before. So if the first unit takes 100 hours, the second takes 80, the fourth takes 64, and so on. The “improvement” in the name refers to this consistent, predictable reduction.
Different industries show different typical rates. In aerospace, where the concept originated, learning curves for direct labor on airframe production generally range from 73% to 88%. Steeper curves (lower percentages like 73%) indicate faster learning, while flatter curves (higher percentages like 88%) suggest the work is harder to improve on through repetition alone. When the metric shifts from labor hours to selling price, the curves flatten considerably, typically falling between 88% and 95%, because price includes materials and overhead that don’t improve at the same pace as human performance.
From Graph to Regression
After graphing, selecting a model, and transforming your data logarithmically, the actual curve fitting happens through linear regression. You’re finding the best-fit line through your log-transformed data points. The slope of that line gives you the learning rate exponent, which you can convert back into a percentage. The y-intercept represents the theoretical cost of the very first unit produced.
This is where the lot midpoint calculation becomes critical for lot-based data. Each lot’s total cost gets assigned to its midpoint unit number, creating the data pairs you need for regression. If your lots vary significantly in size, getting the midpoints right has a meaningful effect on the accuracy of your final curve.
Applications Beyond Manufacturing
While improvement curves originated in 1930s aircraft production, the same analytical framework applies wherever humans or organizations get better through repetition. In surgery, researchers use learning curves to evaluate how quickly a surgeon becomes proficient with a new technique, measuring both process factors (operative time, blood loss) and patient outcomes (length of hospital stay, complication rates, survival). The first step remains the same: collect sequential performance data and graph it to see whether improvement is occurring and at what rate.
In project management and defense acquisition, improvement curve analysis drives cost forecasting for multi-year contracts. If a contractor is producing 500 units of a system, the learning rate determines whether the government should expect declining costs per unit and by how much. Getting the initial graphing step right, and catching data anomalies early, directly affects the accuracy of projections worth millions of dollars.