FUNDAMENTALS

The phrase “learning curve” has cometo mean almost any situation in whichsomeone accumulates more knowl-

edge of a business or process. However, fewpeople except specialized cost analysts haveformally used the learning curve model.

Developed by Dr. T.P. Wright in 1936,learning curves projected World War II pro-duction capacities. Afterward they becamestandard in the aircraft industry. In defensecontracting, an expected learning rate isoften factored into negotiations. However,learning curves seemingly made little impacton manufacturing progress in aviation orelsewhere. The history of the learning curveillustrates our 20th century mindset in NorthAmerican manufacturing, a mindset whosetime should have gone, but that is too deeplyembedded to easily dislodge.

Manufacturing Progress

The learning curve was one of the ear-liest operations research models to emerge inWorld War II era, and widely used to predictwar production output. Shortly after thistool’s “buzz” peaked in the 1950s, a pair ofexperienced manufacturing researchers, R.W.Conway and Andrew Shultz, critiqued theuse and validity of the learning curve in awell-known article, calling it the “manufac-turing progress function.”1

They saw a number of shortcomings.Because of the “mental box” they were in,they didn’t see others that are more obvioustoday. All models have limitations, and someof their assumptions are easily seen. Othersare too much a part of us to stand out.

Conway and Shultz noted that very fewperformance measures were tracked. A two-dimensional graph can plot only one vari-able against output, it does not suggest thatmanufacturing progress is multi-dimensional.Learning curves relate improvement to onlyone variable, cumulative production. In prac-tice, most companies used the learning curveto predict either unit cost or labor hours perunit. (A brief review of the model is in thebox copy.)

But the biggest problem was lack ofdata, or lack of timely data. In pre-computerdays, summary data from the shop, particu-larly unit cost data, arrived as historicalreports. In practice, most learning curve pro-jections were extensions of cost systems.

In the 1950s cost systems were as cum-bersome as today. Assumptions to assigncosts and spread overhead were necessary,but arbitrary. Few cost systems track data tospecific units produced, so these wereimputed from averages, and analysts oftenhad to “tease out” cost data. Even deciding

Lessons from theLearning CurvePart 2 of Out of the Box: Overcoming Our Mind Set Legacies

Robert W. Hall

8Target Volume 17, Number 4

Pre-Production Factors During-Production Factors

Tooling: Type and degree of Tooling changes during production completion before start of production for increasing capacity

Equipment and tool selection Methods changes and simplification

Product design for manufacturability Design changes: effectiveness of ECOs

Methods: effectiveness of pre-production Improvements in management andpreparation planning methods

State-of-the-art: Ability of the organization Volume changes: changes in rate or into cope with the level of technology anticipated duration of production that

affect other decisions (like investment)

Magnitude of process design effort: Quality improvement: reduction ofattention to specs, test, inspections, etc. rework and repair

Shop organization: material handling, Incentive pay plans: manner in whichtraining, skills, planning, organization, etc. administered and when installed

Operator learning or skill development(considered to be a very minor factor).

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how many units were complete was notclear-cut. Then as now, the devil plaguedthe details.

Production was frequently interrupted.Much of it was batch, not continuous. If thetime between batches was so long that thesame equipment and personnel were notused for subsequent runs, should that inter-ruption be considered normal, or as a newstart?

Summarized from “The Manufacturing Progress Function,” R.W. Conway and Andrew Schultz,Jr., The Journal of Industrial Engineering, Vol. 10, No. 1, Jan.-Feb. 1959, pp. 39-54.

curve. Improvement came in spurts, some-times interrupted by backsliding. Althoughthey were not emphatic about it, Conwayand Shultz saw that cost data, and managingby it, stays remote from reality.

Both of these phenomena are depicted inFigure 2. The erratic data did not surpriseConway and Shultz. They attributed “toe up”to nearing the end of ramp up or of a pro-duction contract, so that resources werediverted to other processes. Also, at somepoint the production process no longerpainted targets of opportunity obvious tomanagerial radar.

“Toe Up” and “Spurts”

At the time, the Conway and Shultzarticle was noted for revealing “toe up.”Using data from several companies, theyshowed that some point learning appearedeither to stop, or to slow considerably.Reality was that manufacturing improvementdid not always progress without end.

Another issue was that analysts usuallyshowed only nice, smooth graphs using costdata or other unit estimates from averages.However, data detailed unit by unit showedthat improvement did not follow a smooth Figure 1. Conway and Shultz’s Learning Curve Improvement Factors (1959).

Some analysts plotted the learningagainst time, assuming that production wasnearly linear with time. Conway and Shultzsuggested that unit-specific data directly fromthe process source gave better results. Costaverages were too remote, hiding too manydetails, and creating artificially smoothcurves.

Despite its many problems, Conway andShultz’s data showed that manufacturingprogress according to learning curvesappeared real. It wasn’t mostly the spreadingof fixed cost over more units as productionaccumulated, as alleged by a few critics.They assured managers that during ramp up,manufacturing inexorably continued toimprove as more units were produced.

Conway and Shultz had no suggestionson how to make learning go faster. Figure 1is a summary of learning rate factors as theysaw them.

10Target Volume 17, Number 4

time were not popular measures, but nottotally unknown. As evidence, Figure 3 is areplica of a detailed learning curve of cycletime to assemble center wings of B-24bombers at Willow Run. It shows the cycletime for each job from early 1942 to May1943. (They also kept a learning curve onman-hours per unit.) The cycle time curvewas discontinued on Job 600, when it hit 44hours. After about 7800 more bombers werebuilt, cycle time was down to 9 hours, so“learning” continued long after data collec-tion for the curve ceased. However, by Job600, it became obvious that capacity wouldbe sufficient to meet the goal of a bomber anhour.

Keeping Learning in a Box

Looking back on it, toe up indicated thatprocess improvement was in a mental boxconstructed of managerial thinking.2 At thetime, few people had any cohesive concept ofoverall process improvement. It was thedomain of engineers and managers, soimprovement was largely “engineered,” asrevealed in Figure 1. Unless it was glaringlybad, improving workflow received littleattention.

Leadtime, throughput time, or cycle

Figure 2.

A learning curveaccording to the log-log model.

A log-log learningcurve showing“toe up”

A log-log learningcurve showing theerratic nature ofunsmoothed data

The literature of the time shows that themanagerial mind set using learning curveslimited its use mostly to ramp up. When pro-duction hit a budget goal or a capacity goal,improvement effort cut back substantially.At that point, the process was ready for“normal operation,” or “turning over to pro-duction.”

The behavioral side of this mind set isperfectly captured in the first sentence ofanother old article describing cost reductionmethods: “Enactment of cost reduction pro-grams is a management prerogative.”3

No blather about worker participation.No drivel about teamwork. Managementtakes responsibility, getting all the credit, andsometimes the blame.

Anyone seriously pursuing lean manu-facturing, much less other excellence goals,knows that this mind set is a serious block-age to progress, and one difficult to escape.In effect, we consider process improvementto be a program. When the chosen improve-ment initiatives are in place and the teamsare functioning, we consider lean to be“operational.” Usually many other issuesthen consume leadership attention. Mindsets have expanded one stage beyond rampup, but learning is still closed in by a mentalbox as shown in Figure 4.

Toe Up and Erratic Improvement Compared with a Smooth Learning Curve

11Fourth Quarter 2001

The Traditional Learning Curve ModelThe Traditional Learning Curve Model

A learning curve is a graph showing that performance using some criterion changes by X percent each time production volumedoubles. Since labor hours or unit cost have been by far the most popular performance criteria used, a learning curve is typicallydescribed as a percentage. For example, if unit cost decreases by 20 percent each time cumulative production doubles, it’s calledan 80 percent progress function. The steeper the learning curve, the faster the learning.

In this case, “learning” refers to process improvement – results, not mere insight. Since improvement is marked each time pro -duction doubles, this is a non-linear curve. A typical shape is shown below on a linear scale graph.

Improvement appears very steep at first. For example, consider reduction in unit cost by a 70 percent curve. The second unit’scost is 70 percent of the first; the fourth, 70 percent of the second, and so on. By the time production cumulates to around 100,000units, one must make another 100,000 units to see another 70 percent reduction. The logic of this model makes “learning” appearto tail off.

The learning curve formula is:

yx = y 1 (x-b), where y 1 is the unit cost (or labor hours) for the first unit built.

However, a learning curve is usually shown in logarithmic form:

(log y x) = (log y 1) – b(log x)

On a log-log scale the “curves” appear as straight lines, a phenomenon more familiar to those old enough to have used slide rules,whose scales were based on logarithms.

Besides tracking the current unit cost, the curve has been used to track cumulative cost, that is, how much has been spent for allproduction up through the “xth” unit. Dividing by the number of units thus far produced yields the cumulative average cost perunit. If you have taken on a fixed cost contract, that’s a matter of considerable interest.

To the profit-minded, the difference in progress between a 70 percent curve and a 90 percent curve is the difference between makinga bundle and losing your shirt. Over the past half-century, the learning curve has been used when bidding on contract produc -tion, especially in the defense business. If a bid assumed a 70 percent learning rate, but the process only improved at a 90 percentrate, disaster was likely. Even a two percent gap between an estimate and the actual is troublesome.

Cumulative Production in Units (x)

Logarithm of Cumulative Units Completed

Unit CostOrUnit laborHours (y)

Logarithm ofUnit Cost, orLogarithm ofUnit LaborHours (y)

90%

80%

70%

12Target Volume 17, Number 4

Figure 4.

Note the normal curve outside the learning curve box. It denotes thata process has now reached a goal, so that variations thereafter aremore like deviations from an ongoing, stable process. By the logicof the normal curve, the objective becomes control, holding theprocess within its design limits, with minimal attention to furtherimprovement.

Other Applications of the Power Law

The learning curve is but one exampleof a power law relationship. Almost anyfunction that plots as a straight line on log-log paper follows a power law. Many basicphenomena have been plotted as a powerlaw, for example the frequency of word usagein a language. That relationship, called Zipf’sLaw, is shown in Figure 5.

Word count frequency is used to evalu-ate whether two different pieces of writingare from the same author. If the word fre-quency of an unknown writing is similarenough to that of an authentic work, thechances are high that the same person wroteboth. Many authors have “signature” wordfrequencies just as by ear a characteristicstyle of music is considered likely to have

Figure 3. This curve is graphed on a linear scale, and is typical of other detailed curves. From the collections of the Research Center, Henry Ford Museumand Greenfield Village, Accession. 435, Box 40, Willow Run.

Cycle Time Learning Curve for B-24 Center Wings

The mental box limiting learning

ProcessImprovementProgram

NormalOperation

13Fourth Quarter 2001

Figure 5. Illustration of Power Law: “Zipf’s Law” of frequency ofword usage in the English Language. FromWould-Be Worlds, JohnL. Casti, Santa Fe Institute, Santa Fe, NM, published by John Wiley,New York, 1997. Figure 3.14, p. 126.

been written by a familiar composer.

A better-known power law example isMoore’s Law for computing. Manufacturinghas many familiar examples of power lawrelationships: The utilization of equipmentin a job shop. The frequency of part usage ina part number database. The volume of salesof a series of models in a product line.

The power law expresses the “80-20rule.” Applied to quality defects, it is oftenasserted that 80 percent of the defects comefrom 20 percent of the known causes. Ofcourse, 80-20 is not a precise ratio, but a wayto indicate that defects follow a power lawrelationship. Eliminating a few major cul-prits eliminates a high percentage of defects.A Pareto chart roughly classifies observeddata by a power law.

14Target Volume 17, Number 4

Perhaps Normality is an Illusion

For teaching the concept of emergence,a favorite power law example is avalanches.Huge, destructive avalanches commandattention, but small avalanches occur withmuch greater frequency. Unless an observeris watching carefully, a lot of snow goesdownhill unnoticed. Avalanche sizes andfrequencies have been found to follow apower law.

Each avalanche occurs because amyriad of local conditions releases snowfrom its angle of repose. No two individualavalanches are exactly the same. One cancollect approximate data and calculate theaverage frequency and average size of ava-lanches. However, reality is that no ava-lanche event is average.

A more obvious example is trying to cal-culate the average size branch on a tree. Ifone cut it up and measured weights ofbranches, the weight versus number wouldbe a power law, but that’s arbitrary. Wheredoes one branch end and another begin?What of the little nubbins that have not yetclearly formed a branch?

Calculating the average branch diameteris even sillier. Each branch starts fat and disappears to nothing, or into other branches,and nowhere along the length is a branch’sdiameter uniform. Any average and standarddeviation of tree branches is meaningless.

However, because most manufacturedparts are expected to be nearly uniform –conform to a spec –-- seeing that each one,and the exact circumstances of its making, isunlike every other is much less obvious. Ver-ifying such a thing would be a precisionmeasurement project no one is likely to payfor, so we don’t think about it. Historically,after design and ramp up, we only checkedwhether parts met spec. Quality muchimproved by thinking outside that box tocompress process variance as much aspossible – thinking “power law,” not deviation

As with Zipf’s Law, a power law rela-tionship is thought to signify a system encod-ing complex information. A wide range ofword frequencies make language inter-pretable by enabling complex, unique pat-terns. If every word were used with equalfrequency, the message would be more likerandom noise than information. That is, apower law relationship suggests a system formeaningful information, but the relationshipitself communicates no specific message, justas Zipf’s Law describes no specific messagein English. (All languages can be describedby a power law.)

Sequences of codons in DNA follow apower law. Even “junk DNA” sequencesfollow a power law, which suggests that thejunk is not devoid of useful information.However, no one yet knows what it is.

Some applications of the power lawhave made truly cosmic projections. Forexample, Richard Coren used power law rela-tionships to project evolution over millennia,where evolution is ever-increasing “informa-tion content” in the universe, includinghuman activity in our small corner of it.4Coren’s projection is based on the observa-tion that as they age, individual organisms(like people) have a longer time intervalbetween significant learning events.However, a large population of interacting“organisms” consistently decreases the timebetween significant learning events. Wechange more slowly; our environmentchanges more rapidly.

Coren’s lesson for process learning: Itgoes faster with genuine, coordinated, wide-spread human involvement by people whohave the tools to do it.

A power law pattern indicates that amass of detail is present, waiting to be inves-tigated, but action is taken case-by-case. Justas with Zipf’s Law for languages, little islearned staring at the graph. You must learnthe specific language.

15Fourth Quarter 2001

Perhaps that’s the reason most compa-nies pursuing a version of lean manufactur-ing stagnate at C-class as defined in Figure 6.Breaking out of that box is a total business,change – beyond making cultural modifica-tions to improve flow and quality on the shopfloor. By thinking of lean practices, includingthe human side of them, as techniques, acompany can shuffle the organization.However, changing mindsets is a differentgame with a strange deck of cards.

The mind set change is subtle. Consid-er standard work according to the Toyotasystem, which sounds as boringly close toholding a norm as one can get.

Without adhering to method, you don’tknow “where you are” improving it.However, thought of as part of continuousimprovement, or constant learning, standardwork has feedback built into every workcycle: Finish early, why? Take extra time,why? What’s happening outside the workcenter box that could be a cause? But beyondthat, one cycle of standard work is neverexactly like another, and like a power lawlanguage, actual performance reveals cluesto making it “better.” And better may bedefined as handling more task variety withinthe work cycle, not just making sure thateverything is acceptably the same.

Whether working line assembly ordeveloping business unit strategy, themindset to persist in that kind of detailedlearning does not come naturally. A workgroup “really into the process” constantlysees ideas for improvement, noting the littleavalanches, and not just the big ones. Ifimprovement seldom occurs unless man-agement or staff prompts it, the task ofhuman development is not done.

How to organize for this? The typicalorganization chart is – well – a set of boxesthat lend themselves to setting up budgetcontrols. Reorganization usually shufflesboxes or shuffles people among them, aswith a tinkertoy set. Knowing primaryresponsibilities is vital, but for superior per-

from mean or from spec.

The argument has been made that yearsof using the normal distribution for statisticalmeasurement has dulled our insight into thereality it supposedly represents, even inscience. Many phenomena aren’t statisti-cally “normal” at all. We just think they arebecause our thinking follows the measure-ments we use.5

Quality thinking has begun to change“normal distribution” mindsets. We don’tassume that it’s enough to control an opera-tion inside its normal limits. We don’t wait tosee real errors to take corrective action. Insafety we take preventive action based onnear misses. In quality, we do the same, cod-ified in the phrase: “Quality is an attitude.”

Out of the Box Organizational Performance

Considered organization-wide, out-of-the-box performance follows the analogybetween the normal distribution and thepower curve. Our legacy of business andmanagerial customs assumes that there is a“normal state” of operations. Once normal isachieved, “instinct” is for management tomaintain that state. Any significant deviationfrom norm should take management per-mission.

Hiring practices, budgetary controls,supplier contracts, ad infinitum are regardedas control systems by caretaker manage-ments. More aggressive managers setimprovement goals, then control to meetthem. At the company level, woe betides themanagement of a publicly traded firm thatprojects an earnings goal, but fails to meet it.

All these practices lend themselves tocontinue managing “in the box.” Buried inour legacy of business and managerialcustoms is the assumption of “some normalstate to be maintained” or “next normal stateto be achieved.” Just as with the old ramp-uplearning curves, they continue to createmental boxes of our own making.

16Target Volume 17, Number 4

that keeps learning curves going and going.Organizational changes and techniqueimprovements follow naturally in the pursuitof the learning culture.

A Different Kind of Leadership

Leadership to change culture to a learn-ing mindset uses a different language,leading by example and by asking questions,stimulating people to see and to think.Learning people sustain learning processes.As people develop, they begin to improveoperations on a broader and broader scope.Teaching people to see and to think is not theexercise of control in some normal state.There is no such thing.

Without development of people asimprovement agents, tools and organiza-tional changes, while necessary, are oflimited effectiveness. If one changes to a“product line” organization,” for instance,people will just accommodate to new boxesunless they learn to see and work a long way

formance, people in their boxes (or cubicles)see a long way outside them. Otherwise theystrive to improve the performance of onlytheir little box.

If status systems and rewards promotefragmentation, performance is the sum ofthe boxes. Organizations have tried all kindsof formulas to break this syndrome, butthinking of the problem structurally is stillbeing in a box. Regarded only as the adop-tion of techniques, lean manufacturingremains limited to C-class performance.Improvement is a now and then thing, ofteninitiated by a coordinator, to control whathas been achieved. Managers rewarded forlean projects are likely to do the thinking andpersonally direct them rather spending theirtime stimulating others. Take away thechampion, and lean will collapse.

Sustaining the improvement or goingto B-Class, much less A-Class, is not the addi-tion of more techniques or software. It’s achange to a genuine learning culture, one

Pre-C Experimentation. Try it; you’ll like it. No serious organizational change. Results are fragmented. Little overall benefit.

C-Class A comprehensive effort covering at least one complete operating organization. The focus is on technique adoption and development. Have results to demonstrate, and they may be substantial. Operational links to some customers and suppliers.

Still directing change more than leading it. Sometimes distracted by competing initiatives or techniques. The cultural change is incomplete, so measurements and status systems may conflict with support of process compression. Not yet self-sustaining,so may be quickly blown away.

B-Class The culture is maturing. The total unit organizes to support compression of value-adding processes. Changes are now more ledthan directed. Leaders emphasize vision, mission, goals, and values. Work more by “principles” than by emulation of techniques.Have more and closer linkages to customers and suppliers. Measurements and rewards support the system. Improvement is self-sustaining. Changing this culture would take time, so it’s not easily dispelled.

But if the organization becomes obsessed with process improvement, it may not be as innovative as it could be – lose sight of objectives of processes because of the dedication to their improvement.

A-Class Both innovative and operationally efficient. Extend the “principles” or expand “excellence” across more goals and in newdirections. Able to integrate new technology into the “excellence philosophy.” May no longer be a single, conventional organization, but a flexible coalition of working partners. Experiments with new business models.

The same figure appeared in “The A-B-Cs of Excellence,” Target, Vol. 17, No. 3, p. 12.

Figure 6.

Summary of A-B-C (or C-B-A) Classifications

17Fourth Quarter 2001

outside of them.

From control systems to pay policies,the received tradition of the boxes militatesagainst this. A few examples from Toyotamay help. They do not motivate people pri-marily by money. They don’t emphasizebonuses that reinforce status of the boxes, orof those within them. Despite ingeniousdevising, those are apt to result in unintend-ed dysfunctional behavior, and at worst, setpeople on one another when they should becollaborating. Much the same can be said ofcompany data where it is harbored andguarded by departments. People cannotlearn in a closed information environment.

Toyota emphasizes a goal of vehiclesthat people will love. It stirs concern that acompetitor might find a little edge some-where. It stimulates tribal affiliation withToyota and not for some box within it. AndToyota is far from breaking as many peopleout of their boxes as it would like.

Every aspect of an organization and itsleaders’ behavior affects how every personwithin it can work together to improve per-formance. It’s impossible to “implement” atransition to achieve B-Class in the usualsense. Leaders have to learn to lead out-of-the-box, a radical departure from in-boxlegacies and instincts.

Robert W. Hall is editor-in-chief of Target and a foundingmember of the Association for Manufacturing Excellence.

Footnotes

1. “The Manufacturing Progress Function,” R.W. Conway and Andrew Schultz, Jr.,Journal of Industrial Engineering, Vol. 10, No. 1, Jan.-Feb. 1959, pp. 39-54.

2. For discussion of the limits of models and the phenomena of mind set limitations, see “Out of the Box,” Robert W. Hall, Target, Vol. 17, No. 2, 2001, pp.16-22.

3. “Comparative Review of Cost Reduction Programs in Manufacturing,” Frank T. Lastra, Journal of Industrial Engineering, Vol. 16, No. 5, Sept.-Oct. 1965, pp. 340-345.

4. The Evolutionary Trajectory, Richard L. Coren, Gordon & Breach Science Publishers, 1998.

5. An example of such an argument is “Two Lessons from Fractals and Chaos,” Larry S.Liebovitch and Barbara Scheurle, Com-plexity, Vol. 5, No. 4, March-April, 2000, pp. 34-43. (Published by John Wiley & Sons.) The tree limb example is from that article.

© 2001 AME® For information on reprints, contact:Association for Manufacturing Excellence380 West Palatine RoadWheeling, IL 60090-5863847/520-3282www.ame.org

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