If you don't read past this first paragraph, remember just two things: You almost never move up a learning curve, only down. And the steeper the curve, the easier the learning.

Learning curves were first used by the aircraft industry in the 1930s. The Boeing Co. pioneered the discipline when it discovered that the cost to build new airplanes was highly predictable.

For example, it might cost $100 million to build the first copy of a new airplane, $80 million to build the second, $64 million to make the fourth, $51 million for the eighth and so on, with the unit cost falling 20% at every doubling of volume before reaching a plateau, say $15 million. The planes get cheaper to build as the company learns how to do it more efficiently. Workers work faster, make fewer mistakes and waste less material.

Plotting these production costs against units of production along a graph yields a learning curve that slopes from the upper left to the lower right. The steeper it is, the faster the person, project team or company is learning to produce that item or service.

When Down Is Up

Moving up the curve would represent negative learning, or forgetting, and wouldn't normally occur except perhaps in a company with an accelerating rate of employee turnover.

People often get the learning curve nomenclature backwards. For example, securities firm U.S. Bancorp Piper Jaffray Inc. in Minneapolis has a booklet on the Web titled, "Helping Investors Climb the E-Learning Curve." But it should be about descending the learning curve, not climbing it.

Even Boeing has gotten it wrong. In 1998, the Seattle-based firm delivered the aft fuselage of its third F-22 Raptor fighter three weeks ahead of schedule. But in the press release touting the achievement, the F-22 program manager quipped, "We're climbing the learning curve at a good rate."

Mankind has known that performance improves with practice since cave men made the second wheel. But what's surprising is how accurately performance can be predicted given early production data.

This can be crucial for a company like Boeing. It knows it can't price its new airplane at $100 million or even $50 million. But can it make a profit by pricing them at $25 million each? When will the company reach a break-even level of production, how much will it have lost up to that point, and how much profit will it make on planes built after that? Learning curves can help answer those kinds of questions.

Today, Boeing uses learning curves for capacity analysis, resource requirements planning, cost-reduction proposals and estimations of production-line performance, says Dwight Miller, director of industrial engineering for Boeing's commercial airplanes group. "We benefit daily from this concept."

Indeed, the equations underlying learning curves can be an essential part of cost estimating, pricing and staff planning. "The potential applications of learning curves far outstrip their current usage," says Charles Bailey, an accounting professor at the University of Central Florida in Orlando.

Tools of the Trade

Bailey offers freeware for performing learning curve calculations at www.bus.ucf.edu/bailey. NASA also has a tool (www.jsc.nasa.gov/bu2/learn.html) that allows anyone to perform simple learning curve calculations online. More powerful software is available in commercial packages such as Curv1 from Production Technology in Tampa, Fla.

"There is a new recognition that learning curves can create incentives for aggressive pricing in the early phases of a product life cycle," says Michael Riordan, a professor of economics and business at Columbia University in New York.

For example, a semiconductor manufacturer might use a learning curve to price a new chip far below its initial manufacturing cost to discourage competition from an imitator. That low price then stimulates demand, which "moves the company quickly down its learning curve," Riordan says.

Practice Makes Perfect If it costs a company $100 million to make its first airplane, and if learning enables it to work 20% more efficiently at every doubling of volume, production costs will follow this learning curve:

Curve Calculations Charles Bailey, a learning curve expert at the University of Central Florida, says learning curve calculations can answer questions such as these: A new bank clerk needed an hour to encode his first 500 checks, 50 minutes for the second 500 and 45 for the third 500. When will he be able to work at the standard rate of 1,000 checks per hour? An electrical contracting firm wired two identical homes in two hours each. The same team took 90 minutes to wire a third home. How long will it take it to wire the 10th? A fast-food trainee takes an hour to prepare his first 20 sandwiches, 45 minutes for the second 20 and 36 minutes for the third 20. What will his production rate be after 24 hours of experience? A custom boat builder has built a prototype of a new sailboat. From past experience, he knows the learning curve rate for similar boats. What are the labor requirements for the second and third boats?

- Gary H. Anthes