*Copyright 1995, Mustafa Uzumeri and David Nembhard*

This study examined a large volume of electronically collected data
on worker performance. This data was gathered for workers engaged in manual
assembly operations in a large manufacturing firm. The raw data consists
of records of work performance taken at frequent intervals during designated
*learning episodes. *These episodes occur when workers are first hired
or when they are reassigned to a new job. As workers tried to master the
task, bar-code scanners recorded their output on a regular basis. From
the analog perspective, each measurement of a worker's output is a "signal"
of that person's mastery of the task. To describe this signal, we fit a
3-parameter model of individual learning. This function (shown in Figure
2) was chose because it was malleable, easy to apply, and is believed to
reflect the way in which individuals improve both conceptual and motor
skills.

**Figure 2** - Fitting an Analog
Curve to Individual XYZ's Productivity History

Since the function is non-linear, non-linear regression software was
used to find the values of *k, p* and *r* that best fit the underlying
data. Both the data and the fitted equation rise smoothly over the relevant
range. Hence curve-fitting is straightforward and full convergence occurred
in all but a small number (0.6%) of the episodes. Although equations with
more than 3 parameters will mold more closely to subtle changes in the
data, the goal was to create a picture of organizational learning that
could be visually depicted in simple graphs. With only three parameters,
it is possible to create diagrams that fully describe the signal shapes
for an entire *population* of workers. Figure 3 shows an example of
this for a subgroup of workers that are learning the same task. In this
graph, each point summarizes an individual's entire improvement history
and the learning behavior of the entire group is evident in the shape of
the well-defined 'cloud' of points.

In the study of learning, more than 60,000 measurements were converted
to the values of *k, p *and *r *that defined the shapes of 3,800
individual learning curves. Very little information was lost in the process
and most of that was unexplainable variance or "noise". As a
result, diagrams like Figure 3 have the potential to serve as very efficient
"maps" to the distribution of learning behavior across entire
groups of workers.

Other simple graphs can be created that compare learning behavior across different populations of workers and identify shifts in the distribution of learning behavior over time. Eventually, the data in graphs like these may also provide the basis for more effective simulations of learning in dynamic environments, where strategic business decisions frequently concern entire groups and populations (e.g., of employees, departments, products, machines, customers, and investments).

Finally, each point in Figure 3 represents a mathematical equation that can be manipulated both symbolically and numerically. One can, for example, find the derivative of the best fit equation and solve it to estimate the rate of learning for any level of accumulated experience. Alternatively, one can integrate the curve and use the result to calculate the average workforce productivity for any amount of experience. Calculations like these could help manufacturers to more accurately estimate manufacturing costs when product changes force employees to learn new jobs.

For a working paper on this topic (in zipped Word for Windows 6.0 format) click here.

*This research is being conducted jointly with David Nembhard, a colleague
at Auburn's College of Business.*