Computer Innovation

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OGICAL FORECASTING AND SOCIAL CHANGE 33, 267-278 (1988)

MODIS and A. DEBECKER

A learning-curve approach has been employed to study inventiveness in the computer industry. Theof new computer manufacturers have been followingc S-c urves over the last 26 years of compu ter history. Innovation seem s to come in S-waves, andmany of todays major manufacturers are close to exhausting their maximum innovation potential

its maturity phase. Remarkably invariant over the 26 years considered , and throughfor every five new computer models appearing on

IntroductionA learning process, like any other growing process, typically follows an S-curveh time. T hat is, it starts slowly, then prog ressively increases in rapiditygrowth. Later on, the rate slows down to asymptoticallyvalue. The constraining maximum carries the hallmark of capacity

soon impossible, while learning to better play chess can go for a longso because of the learnersusting the niche of his intellectual capacity-rather than the num ber ofIn either case, however, it will happen

We propose here to look at innovation in the computer industry as a learning process.

on the analogy of the chess game, the number of new

THEO DOR E MODIS is an experimental high energy physicist who has carried out research experimentsofbia and Geneva Universities. ALAIN D EBECKER is a mathematician and has been teaching in variousl sc hools in France and Switzerland since 1982.Address reprint requests to Mr. Theodore Modis, Digital Equipment Corporation, Mgt. Science Dept.,

, chemin deEtang, 1219 Chatelaine, Geneva, Sw itzerland.

1988 by Elsevier Science Publishing Co ., Inc. 0040-1625/88/$3.50


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T. MODIS AN D A . DEBECKER

been all trained in a particularIn either case, at any given time some niche will be in the processThe usefulness of the approach is in forecasting the remaining of a w ell establishedce the filling up of a niche has followed a logistic path for the historical rangeing becomes po ssible for the remaining of the curve. Under-performingunnatural-no niche was ever left partially filled in nature for natural reasons. O ver-

If one considers that in the computer industry, the historical periods treated here25 years, the forecasting horizon is a rather long-term one, reaching2000. We gained confidence in our endeavor to describe innovation in com-

5itself, be used as a forecasting tool-a ratio between new

The historical data we used were drawn from the International Data Corporation1985 Processor Data Book covering the period from the beginning of 1958 up to

IV because we felt that they were probably belongingniche distinctly different from other computers. App earance date for a g iven model

. The ModelThe idea to study markets with growth curves is not new [1-31. The diffusio n off has b een described by growth curves in several publications [4,5].nattempts to further develop the use of growth curves. To just give[6 ] allows for aand M eades adaptive radiation [7] parametrises market developm entns rather than time. In s pite of the fact that these approaches

orks, we decided to use the sim plest possible logistic version.ound out that the simpler a law, the more fun damental itt covers. But most im portant, being simp leestablished between successful entrepreneurship and the use of elaborate formulations

The logistic form we are employing is the same as that of Fisher and Pry [4] andfilled (or emptied) is proportional to the rem aining section of the original niche.mathematical terms, if P is the population at time t :


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269

= ( M a x - P )dPP dr- _

P = a ( t - r o )

a, nd to are constants.The solution of the differential equation (1 ) is an S-curve, while t k ogarithmiction of the ra tio Actual/Remaining is a straight line.Equation ( 2 ) is emplo yed in a three-parameter fit via an x2 minimization techniquea, nd to. If we suspect that data are missing in the early part of the

C is introduced, and equation ( 2 ) becomes

I n ( - ) = a ( r - t o )Max - P-C) (3 )he x2 minimization process has now to provide determinations for the four parameters

a, o, and C.Deviations from the logistic path are expected at the low-end, i.e., when P is onlyare not yet naturally established.A weakness of the model is that fits, based on data limited to the range where P

50% of Max yet, carry a large uncertainty in the determination of Max,a simple exponential. F urthermore,which are often the case in industrial reporting, will introduce additionalIt is for that reason that we undertook an extensive simulation study to be published

ve determination of the expected e rrors on Max as a function of data errors and rangebe

20% with 90% confidence level [8].Finally, the niche definition is of crucial importance. If the members considered dosame nic he, their collective population will not follow a logistic patternaccording to computer families, e. g., VA Xes,

a and +or a larger niche being made up of several smaller niches-are

Case StudiesNine m ajor comp uter manufacturers are analyzed in detail. T hey are all well described80% of the computer industry. Results

of Figures 1 and 2 and Table 1 on five of those cases, whichinteresting aspects of the logistic pattern. For one case , that of company B , the


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T. MODIS AND A . DEBECKER

6.0

4.0

3.6

Fig. l(a). Data points and logistic fit for the company described in Case Studies (company E).d of 1979. A 4-parameter fit revealed 14 models missing from the

f the historical period.

---

1.22./ * = I

1 . . 1 . . . . . . . . . . . . . . . . . . . . . . . . I .60 64 68 72 76 80 84Fig. l(b). Life-cycle plot showing yearly rates of new models (dark circles) and 5-year averagesis the derivative of the S-curve of Figure l(a).


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27 1TABLE 1Fit Parameters for the Five Comoanies

1985 1985 Yearly Max. YearlyMax. No. Position Growth Appearance Rate at Dateof Models (% of Max.) Rate 1st Model (% of Max.)7 6 * 8 39 (51%) 3.4 1211959 3.4 (4.4%) 1984

2 1.5 25 (93%) 0. 6 1011964 1.5 (5.4% ) 1975'' 1.5 9 (70%) 1.4 511978 1.5(11 .6%) 198487 ? 18 25 (29%) 3.6 1111966 4.3 (4.9% ) 19892 45 62 (27%) 3. 8 81I960 4.8 (2.1%) 19964 2 88 (87%) I .5 101 960 3.6 (3.5% ) 1973

E, 14 units have been added, which were missing from the early part (see Figure 1) .

k-up tables in our simulation study mentioned above ,one assumes a conservative 5% error per historical data point and asks for a confide nceacturer with substantial market share and long tradition in the industry. The logisticC was allowed to

of 103 models withf 1.5 new m odels per year. The peak of innovation was back in 1973of this wave's maximum potential.In order to test the forecasting power of the logistic description, we tried to pro--curve superimp osed to the data is determinedf 1979. The parameters determine d in this

inor other time-seriesard trend, much less the exact turnover point.

5 years at a time, the thin histogram line already shows a better agreementThe precision of the determination of the turning point, how ever,

In this light, the forecasts made are expected to agree well with the long-termaround the predicted rate, as large as the ones shown on Figure l(b ),

For each case study, a logistic graph is given in the logarithmic representationsuitability of the model ca n be qualitatively judged by the quality of thethe actual population, P(t) . As mentioned earlier, dev iations

All graphs depict the innovationof time.


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2 T.MODIS AND A . DEBECKER

20

950 1

90805 0

20

60 62 64 66 60 70 72 74 76 78 00 02 84Fig. 2(a)-to 2(d). Logistic patterns for companies A, B, C, and D, respectively, in the logarithmic

of new models expressed in percentage of maximum.B has been split in the two families of products that it produces (see text). Straight lines have

---

of growth. The date of the first model in the S-wave ishis is the installation date of the first model as reported by IDC. The com panyFor company A , in Figure 2(a), two clusters of innovative activities around 1972-and 1976-1977 could be analyzed in terms of shorter logistic curves, the cas e of

or otherD as shown in Figure 2(d), the straight-line logistic de-of the data points is excellent for the historical period starting in January 1966

52

Company B

5 -2 -

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0 -1 . l l l l I l l l l l l l l l l l l I I I I I I l l _

-0 -

I I I I I I I I I I I I I I I I I I I I I I I I _

Fig. 2(b)


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ON IN THE COMPUTER INDUSTRY

9095900050

20105

21 3

% _ ( l l l l l , , l l l l l l l l , , I I I I , I ~- -r --- -- -

L j-: i82 - 0l _ ~ I I I I l I I I I I I I I I I I I I r I I I I.

-

Company C

. The Overall Computer MarketThe overall computer market was looked at by considering all new models of all3 incorporates many more manufacturers than the ninen detail-947 models enter in the graph of Figure 3 . In Figure 4 the reasoning

i.e. , since 1958, there have been 185new m anufacturers making2 summarizes the parameters for

It is of interest to point out that the computer mark. !ooked at from this viewpointa rather young market occupying-by the end of 1984-the low er third of its maximu mof


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T. MODIS AND A. DEBECKER

-

New models, all manu facturers, non-PC marketY O 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I98

5 t21

905 1

@/'-- @ #@I 1 I I I I 1 I l l I I I I I I I I I I

50o 1

70' I I I I I I , I I I I I I I I I I I I I I I I I ,98 -95 r90 2

--

ao - -50 - -20 - we** / :#.do* -

#J d O O g10 r

S f2 -.. - ,. 4 *J '1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Fig. 3. Populations of new models expressed in percentage of maximum in the non-PC market.

TABLE 2The Whole Com puter Market (PCs Excluded)1985 Max. YearlyMaximum Position 1985 Yearly Rate at Date

Potential (% of Max .) Growth Rate (% of Max.)2800 2 350 947 (33%) 102 112 (4.0%) 1988 .

696 f 145 185 (27%) 19 26 (3.7%) 19801958.


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TH E COMPUTER INDUSTRY

,1100- , -1600 - ,1500 - /

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I-,

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275

l800

14001300120011001000900000100600500400300200100

0 .

11 1500P

I I I I I I I I I I I I I I I I I I I I I I I 1 I I I $

--

-50% Point-- -- -

-- -- -----

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:64 66 60 I 0 12 74 I 6 10 00 02 04 06 00 90 92 94

L

uL 1000n9z500

0 50 100 150Number of companies

Fig. 5. New models verbus new manufacturers in the non-PC market. Linear scales.

1989, when we will see about 112 new models and 26 newThe remarkably logistic way in which new models and new manufacturers evolved

5 depictse against the other in terms of raw data, with linear scales,New models, the PC market

Fig. 6 . Logistic growth (linear scales) for the appearance of new models in the PC market. The solid


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T. MODIS AND A . DEBECKERN ew m a n u f a c t u r e r s , t h e PC m a r k e t

2 602 4 0

14 012 010 00 0

50% Point

./::I-----/' I I I I l l I I I , I I li. .00 64 66 60 70 1 2 1 4 1 6 1 0 0 0 0 2 04 06 00 90 9 2 94Y e a r

Fig. 7. Logistic growth (linear scales) for the appearance of new PC manufacturers. The line is afit.

fits, and no other manipulations whatsoever. Th e 947 points entering in this graph5.1, which implies that on the avera ge, there will be a new com puter manufactureron the market.This strict correlation makes us believe that there should be no difference in the

2 , the ratio 5.1 seems to be well respected far into the future.The PC MarketPersonal c omputers (PC ) were group ed all together and were treated as one species

As before, PC manufacturers were treated similarly. The results areof the logistic curve. Figures 6 an d 7 show the fits for PCs and PC

TABLE 3The PC Market1987Maximum Position 1987 Yearly 2000 YearlyPotential (% of Max .) Growth Rate Growth Rate

1864 * 90 1377 (74% ) 82 5.6321 i 15 234 (75%) 14 1 .3


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IN THE COMPUTER INDUSTRY 21 1l l l l l l l l l l l 1400

12001

4 8 0 0 1k~ 600= 40 0

c I-

Lc rT I I I I I I I I I I I I I I I I I I I I 120 40 60 80 100 120 140 160 180 200 220Number of new companies

Fig. 8. New models versus new manufacturers in the PC market. Linear scales.

y. Table 3 gives the numerical results. Both curves se em to be about1982-1983, there were 125 distinguishable new PCs per year introduced18 new companies per year. In 1987 these rates have dropped to 82 new modelsnies. By the year 2 000, less than six new models and less than two producers

a straight line emerge with a slope of 5.7.. ConclusionsInnovation in the computer industry has been treated as a logistic growth process,ter manufacturers and their m odels

The case studies presented reflect three different categories of manufacturers. We

are like company E, as they have already achieved almost 90% of their

of company A may be found, which create new models at aThe most spectacular, diametrically opposed cases, however, are those of companyand B, both very successful on the market place. D has by far the highest potential

4.8 models per year tomax. per year. Moreover, in spite of its longest history, D definitely belongs to the

Company B , on the other hand, is opposite to D in every respect-smallest potential,13models in its two lines of products, with the smallest maximum rate of growth


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Computer Innovation

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