A prognosis of patent activity development

World Parenr In/orrnot~~n. Printed in Great Britain.

Vol. 8. So. 2. pp. 122-142,

A Prognosis

1986

017~-2190/8663.00+.0. Pergamon InfoLme Inc.

of Patent Activity Development

Jan KrejZ and DuZan KendereTki, Chirana Research Institute of Medical Engineering, Brno, c. S. S. R.

Summary

Nomenclature

The paper the rate of activity in a criterion

A,B,C,D...

symbols

for marking

D

constant

(used in diffusion

F

transformation which changes time size by the calculations

F-’

inverse transformation to F which changes the time size used by calculations to the time used in data input

i

index i = 1,2,.

k

constant

provides a statistical theory for estimating development of a technical field. The patent the technical field is determined and used as of development in this field.

The paper comprises

three sections:

1. Formation of basic statistical ideas about the creation and materialization of an invention. Finding an appropriate mathematical expression of these ideas.

single problems model) the

$ mim,ion 2. Derivation of numerical methods enabling the solution of the statistical problem stipulated in the first section. 3. Testing of the created theory through examples of a patent activity in the world.

k =

dimension of the vector space V(T) (dim I’(T) = .\I)

several

In the first section it is shown that it is possible to find an analogy between the methods of statistical mechanics and the methods describing the process of inventing. The theory is created using these analogybased axioms and enables the creation of a great numer of models by which the process of inventing can be controlled. In the third section the theory is tested through the example of the patent activity in the technical field chamber X-ray apparatus supplied by a current of frequency considerably higher than from the mains in the F.R.G., U.S.A and U.S.S.R.

N=ti(r. T)

number field

of inventions

in the technical

N(r)

number of inventions invented the origin of search to ttme I in the studied technical field (diifusion model)

h' 0

maximum number of inventtons which could be invented in a giLen field

kax

maximal rate of increment determining the number of patent applications

n

the analyzed applications

from

set of patent

index for which hold i > n (to) = r, > rO residual sum of square see (14), (16) flow of the number the space I’(T)

The simplest model already provides a very good agreement between the number of patent applications actually deposited and the theoretical results and enables the prognosis of the patent activity and in this way also the estimation of the future development in a technical field. On the other hand the sensitivity of the method upon the correct selection of patent applications into the fields is shown. The theory may be used as an effective help in deciding about licence investments, in regulation of research works, for production of technical field development prognosis and in many problems relating to economics in which a knowledge of supposed development of the technical field is important. 122

of derivations.

of in\ entions in

T

time vector the magnitude of which indicates a time period necessary for solving a single problem and direction of which characterizes the degree of exploitation of the given time period for creation of the invention

ITI, T

size of the time vector

T4.I

projection T* into the time required for the creation of the inventton axis

1, ts

time period

to

time of beginning the given field

of a rewarch

in

Prognosis

of Patent

data of finishing the development of the invention to the state when a patent applications is or may be deposited

123

Activity

Basic Statistical Representation Invention Creation

scalar field associated with ‘psychological inertia’

General

vector space created vector T

At first there are compared basic axioms the validity of which enables an application of a method of statistical mechanics. These axioms (1) are presented in reference (2) and are expressed as follows: A 1. There exist a great number of systems. (1) A 2. The systems are identical. A 3. Interaction between the systems is negligible.

by time

level of the economical efficiency. If .V(r) ,V,,, < (Ythen the development of the technical fields is Ineffective from economical reasons

considerations,

of an

premises

constant constant constant characterising the shortest time for the creation of invention (diffusion model) upper index, marks the systems in question partial

derivation

operator

by time

nabla causing

VT =

in V(T)

>

where T‘/ are jh invention associated axes exponential natural

function

logarithm,

e’= exp (x) In=logp

symbol of sum points numbered by I,2 ,..... n limit for f goes to I, from left

.

d = _ total derivation dr

base of the natural

by time

logarithm

Introduction The paper provides a statistical theory for estimating the rate of technical development of a defined technical field or materialization of a general principle. The number of inventions being produced during a given time period, in the investigated problem area is employed as a measure of the development. The article comprises three main sections as detailed above. In the following pages the first section presenting the principle derivation and the third one giving an idea of how far the theory agrees with an actual development will be accentuated.

As regards a limit of activity this question requires a more detailed analysis and therefore it is assumed that there exist such a great number of systems that this number can be substituted with sufficient accuracy by an infinite number. The term ‘system’ used in the axioms X 1-A 3 presented above comprises an inventor or a group of inventors and all technical, technological and perhaps even psychological problems which an inventor has to solve before he is able to deposit a patent application. The compliance of the axioms (1) with such a defined system is apparent from the following comparison: A 1. There exist a great number of systems. Indeed the majority of problems in the present time are solved in many workplaces. It results quite unambiguously from the existing level of development of science. A 2. During a period of investigation of a given problem some ideal image of the goal. though undefined at the beginning, is formed (e.g. a car). Thus during the investigation a set of problems which are to be solved to attain the goal is established (in the said example these are motor, wheels, seats, gear box, etc.); this set of problems is identical or nearly identical for all the systems defined above. The systems differ from one another only in the personalities of the inventors. When taking only average capable inventors into account, the assumption of identity of systems gives a good approximation of the practice. Therefore omitting systems where an inventor possesses outstanding abilities to create an invention opening new ways for further progress, the axiom A2 allows for suitable approximity of the actualsituation. From the consideration presented above the following presumption can be formulated: P 1. The statistical theory of a technical development cannot cover extraordinary original new solutions. It can only express the evolution of the technical field within standard conditions.

(2)

A 3. An interaction between the systems is negligible. In fact the majority of inventors, in order to maintain the priority, economic profits and even because of their

124

J. KrejE and D. Kendere?ki

character (e.g. egoism, vanity) try to prevent information about their activity from searching the public since this could facilitate work for other technicians. Such a practice thus supports the axiom A3.

A 1. There exist a great number of inventors, research departments etc. attempting to solve technical problems. A 2. Single problems any inventor has to solve are identical for all of them. Personal abilities of inventors do not differ substantially.

The other way round there is a steady increase in an interchange of scientific-technical information and in collaboration and cooperation. This results in a very important effect which, using the terminology of the said theory, can be described as a movement increasing an interaction between the systems. Therefore another presumption can be formulated: P 2. The statistical theory of a technical development is applicable only providing there is no significant cooperation between inventors or technicians investigating the problem in question. Assuming

A 3. Inventors another.

The outline of a derivation inventions development

of one

qf the number of

In the following paragraphs the process of inventing will be discussed. Assume there is an invention (see Fig-l) which requires the solving of single problemsA, B. C, E to be put into practice. The work on each problem needs a certain time T, (i= A, B, C...) to clear all the questions. All the time devoted to an investigation of the corresponding single problem does not add to the materialization of the invention. The procedure of creation of an invention and its definition is not explicit at the beginning. A part of the time period is lost or brings irrelevant results and only the ‘projection’ of particular time periods on the time axis yields the invention. The projection of a particular time period on the axis demonstrating time necessary for the inventing of an invention may be equal to zero in case where a problem is being solved not relating to the solving of an invention. The time period T, may even be a negative one, when by solving the problem such conditions come into existence which make the solving of other single problems leading to the solving of the invention more difficult in the future and this way the realization of the invention is postponed in time (e.g. the inventor marked 0 in Fig.1 lost a certain time period TA’ by solving a partial problem D and in addition he aggravated his conditions for solving a single problem E at least by a time period

(3)

P2, the axiom A3 holds true.

It can be concluded that both Pl and P2 presumptions allow for analysis of the patent activity by methods of mathematical statistics. It has to be noted that a procedure establishing an applicability of methods of mathematical statistics and statistical mechanics can be held for a not rigorously based extrapolation. It is necessary to follow exactly the logic of particular statements. It is not maintained that the axioms apply for all the systems but it is claimed that on certain conditions (Pl, P2) even such a system like an inventor and a set of problems he has to tackle satisfies the axioms and therefore it is possible to study the system through methods of mathematical statistics. The particular formulation of the axioms Al-A3 applying for the study of a development of a certain technical field reads as follows

,_Te’!

Fig. I. A schematic

try to work independently

(4)

representation

T!,!!

of the inventive

/

process.

Prognosis

of Patent

I’${). Such considerations poses a question of the time vector, the magnitude of which indicates a time period necessary for solving a single problem which is directly connected with the invention itself, while the direction on the vector characterizes the degree of exploitation of the given time period for creation of the invention. The time vector forms a vector space marked V (T). Apart from the time vector having its dimension (time period) a real time as a physical quantity has to be taken into consideration. In such a case the term time will be used. Let us discuss the inventing process presented in Fig. 1. possesses such material The inventor No. conditions, personal qualities and has such ideas about his task that from the very beginning of the work he will need a time period ir<‘) to achieve his aim. For solving the first single problem he nevertheless needs the period ITy)l of which only the time axis component IT’:!,/ brings the inventor near the solution. Further steps requiring the creation of an invention can be described in a similar way. It is obvious that the single problem D caused just a loss of the time and the aggravation of conditions for solving the partial problem E. The total time period t,, which the inventor spent on his task is given by equation (5)

01

t zz ITa”/ = ITf’I = IT-“/ = ITb”l = IT:“I,

(5)

But considering the conditions the inventor had for his work he could under ideal circumstances (can they, however, exist? Can the inventor find the shortest way possible, if he does not know all the problems he will have to solve?) come to the invention in the time period t;=

IT’;,),/ = IT’;,),/ = IT’&l = IT’;,iil = IT’$,I.

125

Activity

general procedure of inventing. On the other hand it can be seen that the time vector corresponds to the space coordinate radius vector in the classic statistical mechanics. When realizing that a solution ofany single problem does not add only to the appropriate invention but also to the solution of a great number of technical problems through the particular time vector component in an it4-dimensional space (with !M- “) the axes of which are axes of time periods required creation of single inventions, then the analogy with a coordinate in the statistical mechanics is quite perfect. To be accurate it is nevertheless necessary to illustrate this space as a factor space, in a mathematical sense so called ‘modulo thesaurus’. the methods of statistical mechanics”’ Adapting concerning a transfer of a system from a place with the coordinate q. to a place with the coordinate q,, the Einstein-Fokker-Planck equation can be deduced and the Markov strings can be done. It suffices only to substitute the radius vector by the time vector. The equation then reads as follows z

= I* V, ((VT U(T)) N + 0 VrN)

(7)

where N represents the number of inventions in a given field as a function N = N(t,T); U is a scalar field (its interpretation is discussed later);p$ are constants. This equation was deduced only on the basis of the analogy with statistical mechanics, not by esact means. The most simple case of equation (7) is a diffusion process. Let us see how the inventing process will be carried out in such a case (Fig. 2).

(6)

In a manner analogous to the one given above the inventing process of the second inventor can be described. From the moment he started his work on the subject he had to cover a time period r*‘. He had to work under such conditions that the solving of the single problem A took him much longer than in the case of the first inventor but the majority of the time was spent directly on the creation of the invention. Solving the single problems B, C the inventor 2 was ‘a little bit at a loss’ but the single problem E he solved spending all the time only on the solution leading to the invention. The third inventor was at the beginning devoting his working time to problems having no relation to the invention in question and thus he was just losing time and he created such conditions which worsened for him its realization later but when solving the single problem F he became aware of his mistakes and very effectively arrived at his aim. It is worth noticing that the sequence solving the single problems need not be explicitly expressed. The inventor @ solved them in sequence B, A, C, E,

At the same moment a great number of inventorsstart working on the same problem requiring a time period

0

It is obvious

that the presented

model fitsvery well toa

Fig. 2. Diffusion

model of the inventing

process.

126

J. KrejEi and D. KendereSki

I to be solved. Let us assume that ~!“i.milo” =IT ,fliyni,,,n ev’er\ inv.entor creates one invention. Such an assumption is not a limiting factor as these inventors who create more inventions can be included into the model several times but each time only for one invention. This leads to the question: how many in\.entors will reach beyond the boundary set b!, a circle with a radius T,~,~~,!,,~ depending upon the time? This dependence determines the development of the number of inventions in time and therefore the development of the technical field. This diffusion problem hasalready been solved”‘. The solution can be expressed as follows: N(f) = N,.exp - ( 4 r&y;O))

(8)

where N(r) is the number of inventions created from the origin of search to time I; NO is the maximum number of inventions which could be created in a given it field; r,,,znrronis a magnitude of the time vector T,,,Pen,,o,,; is the time period required for creation of an invention (see Fig. 2). It holds: T,$?~,,~~ = r,“i.e”iiO”~ T/“Lc”m= ~,“irnrron; 1, is a beginning of a research in the given field; D is a constant characterising the influence of the society upon the inventor. The importance when substituting This substitution

$

D is more apparent D = p 0, U= 0 into the equation (7).

of the constant yields

= - DV,.S

S=-V,N

(9)

where S is a flow of the number of inventions in the vector space V(T). It can be also said that S represents the number of inventions being created under ideal conditions when the inventor reached his aim directly per time unit.

Vr S is a flow of inventions originating in ideal conditions within the space of time (T,T+ dT) in the time unit. According to the equation (9) the constant D determines how many times is the real speed of the invention creation (i.e. depending on physical time) slower than its speed under ideal conditions. If a number of inventions is characterising the development of the technical field, then the constant D indicates how much slower is the development of the technical field under given conditions than it would be under the ideal ones. (Here the constant D should be understood a little bit different than usually in physics but such an approach is perhaps more illustrating.) In the equation (8) the constants T,,,,~,~~ and D are presented in a quotient and therefore they cannot be determined by studying the development of patent

activity in a single field. The development of the given field can, of course, be studied in different countries or companies. It is evident that it is not the time period necessary for creation of an invention which depends upon the society but the constant D characterizing the speed with which the invention is created under ideal circumstances and under the conditions of the particular society. This fact offers therefore an objective method for an evaluation of the relation of the technical field development and the influence of the society. By means of statistical methods there has been found the general formula of the dependence ofdevelopment of a number of inventions upon time in the case of the simplest method. (When constructing the model according to Fig. 2 it is possible to calculate explicitly some integrals included in the solution which therefore becomes significantly simpler. It is possible to set LIP different models based on equation (7) but because of the simple form of equation (8) the model according to Fig. 2 was preferred.) There has even been found a suitable interpretation of single parameters comprised in the equation (8). Before proceeding to the second chapter in which a method for defining the constants will be derived, the interpretation of the quantity U of the equation (7) shall be noticed. Vr U is very obviously closely connected with the vector of the psychological inertia. The connection can be intuitively made clear by means of Fig. 3. Solving the single problems the inventor tries to come closer to the invention. But habits, conventional opinions and mistrust of the society surrounding him present steady obstacles for the inventor. All the influences can be included into a single effect expressed by the quantity c’.

Numerical Modified method

Solution of the smallest

squares

for

the

functiorl

At first let us transfer

equation

N(t) = N,e- k

(8) as follows

(10)

where

(11) To verify theoretically established results it is necessary to set up a method to define the constantsfl;, k and 1, on the basis ofdata about the patent activity. It turned out that the most advantageous procedure is

Prognosis

.

I

Time

0

of Patent

I

of the inventing process -

the modified nonlinear method of the smallest squares. The equation (10) can be presented as follows (In N(t) - lnNJ*(t-t,)+k

= 0 for t > to,

and to define the equation

for t < f0

N(t) = 0

for t < lo.

(12)

(13)

The unknown constants shall be determined through the minimalization of the following expression ,i, [(ln N(tJ -InN,,)(t,-r,,) with respect mathematical

k=

(nS,-S,S,)

(nS,-S,S,)-(nS,-S:)

No = exp (nS,-S,S2)2 (nS,-.Sj)

where

- (n.S,-Sf)

- (nS,-Sf)

S, = ,i, t,

,I,In N(h)

S, = ,p, f, In N(t,)

(14)

Further

I

the interpretation

T’21 of the psychological

All three expressions (15) present the constants k, N,,r, in such a way that the residual sum total is minimal for in the interval (--, m). Its the function No e -i(‘C’-‘~,l branch for negative times gives incorrect results as for lim e-~/(r-r,,l_ 00. It is therefore necessary to find the &%stants k, to, No meeting the conditions of the equation (13), hence it is necessary to minimalize the residual sum

R: (No, to, k) =,=~~,“~[hrcl,)-N,.e-~~2 ”

+‘V~‘;‘?P(tJ (16)

where n,(t,) is the index for which it applies i 2 n,(t,) and therefore t, > 1,. On the right side of equation (16) the first sum can be minimalized. It is sufficient to use formulae (15) in which the one in the lower limit of sum index i is changed for value n,(t,). The value of the second member on the right side (16) can be calculated directly. It holds true

“‘yN,(t,) =+[n,(t,) I=1

lrlN0

inertia.

-11 n,(t,) [2n,(t,)

n%ro) + l] > 12

(nS,-SJ,)

(nS,-.I?:)

(nS,-SJ,)-(nS,-S,Sd

(nS,-S,S2)2

S2=

f,, k.

(S, lnN, + &.1,-S,)-&.

n

to = -

+ k12 = R2 (N,,, t,, k)

to the constants N,, arrangements yield

- l

, T”’

T’S1

Fig. 3. Chart representation

127

Activity

for n,(t,) > 1 (n&-SJ,)

Ss= ii, ln2N (L)

The value of the second number on the right side (16) increases faster than no3(1,)/12. The minimum of expression (16) will exist for small values n,(t,) and it is possible to determine it easily by sequential calculation R,2(No,to,k) for n,(t,) = 1,2,3... until the value R,*(N,,t,,k) increases.

S, = ,I, t, ln*N (t,)

Reliabilily

(nS,-S:) s, =

i tz I=,

(15)

S, = ,i, t, In2 fV(f,)

and t, are dates finishing the development of the invention to the state when a patent application is or may be deposited, N(f,) total number of developed and finished inventions before the date t, and n is the extent of the investigated set of inventions.

intervals

The theory the basic ideas of which have been briefly presented in the first chapter statistically describes the development of the number of patents depending upon the time. As it is statistical theory in question it is necessary to know the probability of the validity of the result. That is to say it is necessary to determine an interval or region of reliability within which, with a given probability, occurs a real cumulative curve of a

128

J. KrejEi and D. KendereSki

patent activity i.e. a curve showing the cumulative of patent applications as time increases.

total

The function (8) describing a development of patent activity in th2 above presented simplest model is nevertheless too complicated to allow us simply to find an expression for reliability intervals. However the following estimation can be applied

lnN(t)=

lnN,-&

(17)

0

k f=fo-lnN(f)-

InN,’

These expressions are identical with the equation (10). But the expressions (17) can also be understood as two straight lines ,; = a, + b,x, (j= 1,2) from which in the first one it holds x, = l/(t-to) and y, = In N(t) and the coefficients are determined a, = In No and b, = -k. In the second on2 is x2 = l/( lnN(t)-lnN,) and y,= t and the coefficients are determined a, = to and b,= -k. In each of these straight lines the reliability region may be easily determined. A good estimation for the reliability region is then given by a total sum of reliability regions of both ‘lines’ lines’ expressions are (17), while these ‘straight transferred to the form of the equation (10). The foregoing formulation only suggests the way of estimation for the reliability regions. The who12 procedure when carried out in detail provides such an expression for the estimation of the reliability region which, when recorded in basic symbols without

auxiliary substitutions, comprises 1250 symbols for variables and relations between them. Such relations are of importance only when stored in a computer memory as they are obviously rather difficult to understand intuitively Implementation

on the HP 982.7 A calculator

This section presents a numerical solution executed by means of the calculator HP 9825 A. Figure 4 presents the flowchart of the calculation. Tab12 1 exhibits input values illustrating the results, Table 2 illustrates a computer output, Table 3 presents the prognosis and the Figs 5-10 show the graphic output for the Table 1 file. A detailed description ofall curves is demonstrated in Figs 5 and 6. The meaning of the single curves as described in Figs 5 and 6 will be maintained in all other figures. In the case of about 50 patent applications the calculation takes less than 5 min which is a sufficient speed to operate the program effectively.

Verification of the Theory by Examples of Patent Activity The theory derived in the first section of this paper explains the dependence of the numbrr of inventions invented in the technical field in question on time period. The actual number of inventions, however, cannot be found out objectively. Only the dependence of the number determining the patent applications on time can be found. When a large set of patent applications is studied it can be supposed that the

Transformation Fof the file: before starting the calculation it is necessan/ to transform the file so as not to have an excesswe

Search for constants characterizing the

The analysis comprises even an economic side of tne ~nvenrlon. It IS discussed in the conclusion and the second part of the paper.

.

Inverse

transformation

Fig. 4. Flmvchart

F '

of the parent

activlt!

analysis

program

Prognosis

of Patent

Table 1. Data of the F.R.G., U.S.A. and U.S.S.R. patent applications in the field of chamber X-ray apparatuses. Number

I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 46 47 48

Priority date F.R.G. 30. 4.1962 27. 4.1966 30. 7.1966 2. 2.1967 26. 5.1967 2. 5.1969 18. 6.1969 2. 9.1969 2. 1.1970 5. 3.1970 7. 3.1970 18. 5.1970 17. 8.1970 9.12.1970 18.12.1970 15. 1.1971 21. 1.1971 3. 2.1971 9. 6.197 I 14. 7.197 I 10.10.1971 3.11.1971 20.12.1971 12. 5.1972 6.10.1972 17.10.1972 22. 2.1973 7. 3.1973 22. 3.1973 9. 4.1973 25. 5.1973 28. 6.1973 28. 6.1973 12. 9.1973 21. 9.1973 5.IO. 1973 8. 1.1974 19. 2.1974 22. 3.1974 10. 5.1974 21. 5.1974 24. 6.1974 2.10.1974

U.S.A. 11.10.1964 13. 5.1965 18. 8.1966 24. I I. 1967 23. 1.1968 28. 1.1968 28. 2.1968 4. 3.1968 16. 7.1968 11. 9.1969 30.11.1969 25. 2.1970 30.11.1970 28. 6.1971 9. 7.1971 1.11.1971 24. 4.1972 IS. 5.1972 7. 3.1973 10. 5.1973 30. 6.1973 20. IO. 1975 12.11.1975

U.S.S.R. 20.10.1969 30. 7.1970 9.11.1971 4. 5.1975 9. 9.1975 29. 9.1975

1I. 10.1974 2. 5.1975 2. 5.1975 2. 5.1975 20. 8.1975 20. IO. 1975

number of patent applications deposited in the technical field in question is proportional to the number of really created inventions in this technical field. This premise may easily fail e.g. by a suitable time regime of depositing the patent applications for inventions invented but not patent applications applied for, inclusions of all patent applications relating to a single invention into the analysed set etc. A premise P3 has to be formulated which makes possible the use of the theory derived earlier for analysis of patent activity. P3. The number of inventions invented in the technical field in question in dependence on time is proportional to the number of patent applications deposited in this technical field in dependence on time.

Activity

129

Supposing the premise P3 is fulfilled, the theory derived previously may be used for the analysis of patent activity. To illustrate the applicability of the above introduced theory this section presents an analysis of the patent activity in the F.R.G., U.S.A. and U.S.S.R. in the field of chamber X-ray apparatus supplied by a current of a frequency considerably higher than from the mains, the apparatus meeting the following technical conditions: (a) Design of the chamber from the standpoint of minimal demands on a high voltage isolation. (b) Design of the chamber from the standpoint of simple and fast exchange of the X-ray tube. (c) Setting of current and voltage of the X-ray tube. (d) Optimalization of current voltage and time period for examination (organ selection). (e) Exposition control from the standpoint of optimal exploitation of X-ray tube parameters. (f) Application of microprocessors for optimal examination. (g) Incorporating of elements of feedback control for exposition control (photodetectors, ionization chambers). For this purpose our institute elaborated a patent analysis comprising a search as to prior art in the above mentioned field within the time period 1970-1982. On the evidence of this study the said field was characterized by solution of the following subfields: (1) chamber X-ray apparatus, (2) a.c.1d.c. converter, (3) exposition control, SCR control - rectifier control - diode control - thyristor control, (4) X-ray tube overloading protection, (5) exposition control-exposure automatic, (6) exposition control, (7) exposition control by ionization chambers, (8) exposition control through photodetection, (9) programmer, (10) organ selection, (11) X-ray film identification, (12) automatic insertion and removal of films, film cartridge, (13) laser switch. The analysis procedure comprises data from the beginning of the development until the year 1975. All the patent applications after the year 1975 were not included but were used to check the prognosis. Table 1 contains input data, i.e. patent application priority dates for the F.R.G., U.S.A. and U.S.S.R. in the selected field. Priority dates have been chosen because the condition P3 will be fulfilled best for the set including only original patent applications. In Table 2 there are the analysis results produced on the 95%

130

J. KrejEi and D. KendereSki

Table 2. Analysis results of the development U.S..& and U.S.S.R.

in the field of chamber

X-ra!

.tpparatuses

in the F.R.G..

F.R.G.

U.S.A.

U.S.S.R.

Xiasimal number of inventions 177 Reliability interval of the maximal number of the Inventions (147-213) Starting point of research in the investigated area Year 1965 hlonth 5 Da\ 10 Reliability interval of the starting point of research in the investigated area (1964.5-1966.2)+ Constant characterising speed of the development in the investigated area Year 13 hlonth 8 29 Da> Reliability interval of the constant characterising speed of the development in the investigated area (12.42- 14.90) ,411 reliability intervals or hypothesis are evaluated with the probability 95% SIaximum development expansion is in years ( l969- 1983) In years of maximum development expansion is 80 inventions The development in the investigated area will be terminated in year 1999 for reasons of economical ineffectivity on the level 20% Correlation coefficient 0.9937 Average quadratic derivation 0.2450 Sum of quadrats of derivations 129.6321

klaulmal number of inventions 62 Reliability interbal of the maximal number of the inventions (51-75) Starrmg point of research in the investigated area Year 1961 Month IO Day 23 Reliability interval of the starting point of research in the investigated area (1961.2-1962.4) Constant characterking speed of the development in the investigated area Year I3 Month II I2 Day Reliability interval of the constant characterising speed of the development in the investigated area (12.76-14.97) All reliability intervals or hypotheses are evaluated with the probability 95% Maximum development expansion is in the years ( 1965- 1980) In years of maximum development expansion is 28 inventions The development in the investigated area will be terminated in year 1996 for reasons of economical ineffectivity on the level 20% Correlation coefficient 0.9889 Average quadratic derivation 0.2248 Sum of quadrats of derivations 23.2436

Is ~alld the hypothesis constant characrxwnp speed of the development equal to zero. It II; impossible to e\ aluate the in:srx als of ths rsliabilit> Xlaximal number 3i the invenrlons 6 Starting point of research in the Investigated area Year 1969 hlonth 7 Da> 21 Conhtant charactensing speed of the ds\elopment in the investigated area I.car 0 Xlonth I2 Da> I4 MaGmum development rzpansion is in !ssrs 1970-1971 In qears of maximum development expansion is 3 inventions The ds\slopment’in the investigated area ulll be terminated in year 1972 for reasons of economical ineffectivit! on the level 2OcC correlation coefficient 0.0000 Average quadratic derivation 119.329 I Sum of quadrats of derivations 3.42-19

*The time is expressed 1969).

in the years by a decimal

reliability level, which means that these results should be valid with the 95% probability. These results are discussed in the following pages. In the F.R.G. the field had been brought to such an extent and under such conditions that it can with 95% probability produce 147 up to 213 patent applications for inventions. The average value of the number of patent applications for inventions is 177. A systematic research in the field started with the 95% probability at June 1964 up to February 1966. The middle date of the research origin is May 1965. From the input data it can be seen that the first patent applications for inventions appeared already in the year 1962, i.e. under the lower boundary of the reliability of the field development origin. Taking into account all the assumptions on the basis of which the theory is created it is obvious that this invention is a work of an above-average inventor. This invention was not correctly evaluated, appeared

number

in the reliability

intervals (e.g. 1969.5 means June

at an inappropriate time and therefore it did not cause a development of the field and remained isolated. Additional research revealed that it is a U.S.A. invention the application of ivhich u-as placed in the F.R.G. The constant T’,,,,,1,,,/4D appears \vith 95% probability within an interval (12.42; 14.90) years (the time is expressed in years by a decimal number in reliabilit) inter\,als). Its average value is 13 years 9 months. The development of the field is characterized by the rate of increment determining the number of patent applications. Its process curve has a maximum N,,,,,. The points for which it applies .<‘(t)/iq,,,u, = 0.5 evidently define the maximal development of the field. In F.R.G. it is estimated that happened in the period 1969 up to 1983, during uhich 80 patsnt applications for inventions will appear. After 1983 the field reaches

Prognosis

Table 3 Prognosis

of patent

of Patent

131

Activity

activity U.S.S.R.

F.R.G.

L‘S_&

Prognosis of number of inventions on the reliability level 95% Number Year l-11 1975-1976 : 1976-1977 : I- IO l-10 l977- 1978 : l978- 1979 : 1-9 1979-1980 : O-9 1980-198 I : O-8 1981-1982 : O-7 l982- 1983 : O-7 1983-1984: O-7 1984-1985 : O-6 1985-1986 : O-6 1986-1987 : O-5 1987-1988 : O-5 1988- I989 : O-5 1989-1990: O-4 l990- 199 1 : O-4 1991-1992 : O-4 1992- 1993 : O-4 1993- 1994 : O-4 1994-1995 : O-3 1995-1996 : O-3 1996-1997 : c-3 1997-1998 : O-3 l998- 1999 : O-3 The development in the investigated area will be terminated in year 2000 for reasons of economical ineffectivity on the level 20%

Prognosis of number of inventions on the reliabllity level 95% Year Number l975- 1977 : 3-4 19:7- 1979 : 2-3 1979-1982 : 2-4 19S?- 1985 : 2-3 19YS-1988 : 2-3 19S8- 1992 : 2-3 The development in the investigated area will be terminated in year 1997 for reasons of economical ineffectivity on the Iebel 20%

If there are no patent applications after the y&r 1975, there is no comprehensive development of this art in the U.S.S.R. and all inventions included in this field are probably the analogous inventions applications from other countries. If some new patent applications appear in the investigated field it is necessary to make a new analysis with enlarged field of patent applications

level 95%

80 1 2 70.P ;;i 2 60! E 50J m P s 405 z z

30-

1961

Fig. 5.

1964

1967

1973

1976 Time [yrsl

1979

1982

Cumulative curve of patent activity in the F.R.G. in the field of chamber

1985

X-ray apparatuses.

1988

132

J. KrejEi and D. Kenderezki

\ ,+

Maximum

development

Initial period

Development termination expansion

. Upper limit of the reliability region

Reliability region on the probability level 95% Theoretical

curve

E

a 3.571 G P

6 ;

2.678

z ?- 1.786

Lower limit of the

0.893

0.000

I

L

1961

/I

1964

I

19 67

1970

1973

1976

,

I

1979

I! 62

I

1985

1988

Time 1yrs.j

Fig. 6. Distribution

of the patent

activity

in the F.R.G.

in the field of chamber

X-ray apparatuses.

Time [yrs]

Fig. 7. Cumulative

curve of patent

activity

in the U.S.A. in the field of chamber

its final stage and there exists a great probability of creation of a new field causing a transfer of the patent activity to another question calling for exploitation. From economic considerations there can be derived a date after which the further development is no longer effective and it is stopped though there still exists a possibility of new inventions in the field. In the said field such a situation should occur in the F.R.G. in the year 1999. (The last two notes will be discussed in more detail in the second part of this paper.)

X-ray apparatuses.

The last three results characterize the calculation accuracy: correlation coefficient, average quadratic derivation of the patent application number R(N,,, t,, k)/n/(n-3) and a sum of quadrats of derivations R’ (N,,, t,,, k) for the final approximation. The second column in Table 2 displays results applying to the U.S.A. Instead of discussing them in such detail as above let us compare them with those applying to is nearly the same the F.R.G. The constant ~~,,,o,,,,/40 in both cases (reliability intenals nearly superimpose).

Prognosis

of Patent

Maximum

I

133

Activity

development Development termination expansion

2.60~” $

2.315

In c 2.026 .!! .! 1.736 E 0 E 1.447 0 5 a 1.157 % $

0.868

5 = 0.579 0.289 I

o’ooo1960 Fig. 8. Distribution

1963

of the patent

1969

1966

activity

1972 1975 Time [yrsl

curve of patent

Table 4. Comparison

activity

of the actual

number

1975

1976 1977 1978 1979 1980 198 1

Actual number of patent applications

I-11 I-10 l-10 1-9 o-9 O-8 O-7

2

I

X-ray apparatuses.

and of the prognosis

results

U.S.S.R.

U.S.A. Actual number of patent applications

1987

X-ray apparatuses.

in the field of chamber

of patent applications

Theoretically evaluated number of patent applications - prognosis

J

1

1984

[yrs]

in the U.S.S.R.

F.R.G. Year

/

1981

in the U.S.A. in the field of chamber

Time

Fig. 9. Cumulative

19

Theoretically evaluated number of patent applications - prognosis

3-4

2 t 2

1I

2-3

0 0 I

3-4

Actual number of patent applications

Theoretically evaluated number of patent applications - prognosis

The prognosis cannot be evaluated - see Table 3

134

J. KrejEi and D. Kenderejki

3,273

itial perb 6 2.909 -

Aaximum .I

development opment -End

expansion

termination

expansion

of the development

$ z 2.545E .o 5 2.182-E ," 1.818E m g 1.455-

b $

1.091

5 2 0.727

0.000

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

Time [yrs] Fig. 10. Distribution

of the patent

activity

in the U.S.S.R.

It means that from the statistical point of view the development of the field wascarried out in the F.R.G. and U.S.A. under very similar conditions. When comparing the origin of the research, its maximal development and its termination it can be seen that the F.R.G. lags 3 years behind the U.S.A. The situation in the U.S.S.R. is quite different. With 95% probability the constant k = 0, which means that the field there is not at an evaluable stage of development. Therefore it is necessary to repeat the analysis with a larger number of patent applications on the studied period and also after the year 1975. If there are no patent applications after the year 1975, there is no comprehensive development of this art in the U.S.S.R. and the six inventions included are just accidental or more probably analogous invention applications from the U.S.A. and F.R.G. and even from other countries with the maximum development of the field at the top within the years 1969 and 1972. It is also possible that the patent applications in the U.S.S.R. are deposited in such a way that the condition P3 is not fulfilled. The Table 5 presents new input datas with more precision and in enlarged extent for the analysis of the U.S.S.R. patent activity and their evaluation. The results are identical with those obtained previously. With probability 95% it is true that the constant k =O, i.e. there exists no development according to the mechanism of the above presented model in the U.S.S.R. Therefore one of the presumptions deduced from the first analysis applies. To verify them it would be necessary to analyze the subject of the invention applications, their relation to the patent applications in other countries and it would be necessary to know the time regime of depositing patent applications after

in the field of chamber

Table 5. Analysis Expanded file Number

2 3 4 5 6 7 8 9 10 I1 I2 13 14 15 16 17

Priority

X-ray apparatuses

of patent

date

20.10.1969 2. 1.1970 8. 1.1970 30. 7.1970 9.11.1971 4. 5.1975 9. 9.1975 29. 9.1975 30. 6.1976 6. 7. I917 9. 1.1978 24. 2.1978 29. 5.1978 8. 6.1978 19. 6.1978 28. 6.1978 22.12.1978

activity

in the U.S.S.R.

Analysis Is valid the hypothesis constant characterising speed of the de\ elopment equals zero. It is impossible to evaluate the intervals of the reliability. Maximal number of the inventions 13 Starting point of research in the investigated area Year 1970 Month 6 Day 15 Constant characrerising speed of the development in the investigated area Year 0 4 Month ‘7 Day Maximum development expansion is in the years 1971- 1971 In years of maximum development expansion is invented in\ennons 6 The development in the investigated area is terminated in hear 1971 for reasons of economical ineffectivity on the level 202 Correlation coefficient 0.0000 Average quadratic derivation 1900.7155 Sum of quadratic derivations 186.1713

the inventing of an invention in the U.S.S.R. (e.g. patent applications may be deposited after the finishing of the whole development planned etc.).

Prognosis

of Patent

A prognosis of the development relating to patent activity is demonstrated in Table 3, Table 4 shows the comparison of the prognosis determining the number of patent applications deposited in the years 1975 to 1981 with the actual number of patent applications deposited. It manifests very good agreement between the prognosis and the actual number of patent applications placed during the period between 1975 and 1981: In the case of the F.R.G. the interval comprising the prognosis is very wide. It is due to the selection of patent applications and their allocation to the technical field. Consequently the number of patent applications does not always give a true picture of the number of inventions created in the field in question, as mentioned in discussing the condition P3. The following discussion of the graphic results reveals why the reliability area is so wide in the case of the F.R.G. Figure 5 displays the cumulative curve of the F.R.G. patent activity during the investigated time period of the field in question and the reliability region on the 95% level. The curve found for the years 1969-1975 nearly perfectly approximates points determined by the number of patent applications really deposited in a certain time point. However around the year 1967 a couple of patent applications were placed, the number of which does not comply with the theoretical curve and in the year 1973 an expressive break appears on the cumulative curve from which the approximation further on is not quite perfect. This feature reflects the fact the classification of the patent application into particular fields is a subjective process depending upon the knowledge of the expert who is responsible for the classification and upon the relation between the number of inventions and the number of patent

Activity

135

applications. In the case presented in Fig. 5 three fields seem to be combined. (The process of dividing the set in question into the subfield is schematically shown in Fig. 11). Therefore the reliability interval is so broad because it has to cover three fields simultaneously and hence the prognosis accurancy is small. An additional analysis of the patent activity in the F.R.G. revealed that first patent applications (1962 and 1966) are analogue applications to U.S.A. inventions and the field consists of two main subfields: organ selection and exposition control to which belong the majority of the applications. The separate analysis of the subfields is presented in Figs 12-15 and the results in Tables 6-8. In the second part of the paper the question of determinating whether one or more fields are involved through the patent data analysis is discussed, a problem of relations between the system as defined earlier and a supersystem consisting of several systems (e.g. a technical field of chamber X-ray apparatus can be handled as a system or supersystem consisting of two systems: body selection and exposure control (see Fig. 11)). These considerations lead towards narrowing the reliability regions and towards more accurate prognosis. The Fig. 6 shows the distribution of the patent activity in the F.R.G. The studied time period is divided into three parts: 1961-1969, beginning period; 1969-1983, maximum development period; 1983-1991 end of the development.

The beginning period is defined by the time during which a half of the maximum value of the rate of increment determining the number of patent appli-

80

70 First subfield: organ selection 60 -

50 -

40 -

Second subfield exposition

control

30-

20-

lo-

0

Fig. 11. Cumulative

1960

1963

1966

curve of patent activity in the F.R.G.

1969

1972 1975 Time Iyrs]

1978

in the field of chamber X-ray apparatuses-a to subfields.

1981

1984

1987

.

schematic representation of the division

136

J. KrejEi and D. KendereSki

cations of the invention is reached. The period maximum development is characterized by points

and the last conditions

period

comprises

points

of

meeting

maximum width. This is really just logic, as the problem is only little known in this period and a heuristic approach and accidental solutions occur. During the period of maximum development such great deviations are no longer possible, the reliability region becomes narrower, but the average value of invention number and, in this way, also the rate of increment determining the number of patent applications is maximum. It is of interest that statistical analysis may find two peaks in the period of maximum development. This may even happen uhen the period of initial enthusiasm is followed by- a disillusion bringing later new but moderate, though more quiet and stable, start of the second maximum stage of development.

the

where CYis an economic level of the development termination. These three periods manifest themselves by several characteristic features. In the beginning period the reliability region in the given time is of a

4036 -i n 32s ._ Z 2a.o a 0 24E ; 20a ‘i; 16z f

12-

; a40

f;y/,

1965

Fig. 12. Cumulative

1

I

1968

1971

curve of patent

I

1974

1977 1980 Time [yrsl

activity

in the F.R.G.

; Y

Ir 5.246 - p t

2

4.663-

5 > :

4.080 -

‘4 .t! a 4

2.332 -

5 g

1.740 -

5 g

1.166-

1983

I

I

1986

1989

1992

in the field of an exposition

Development

control.

termination End of the fevelopment

2.914 -

E 2

0.583 -

‘5

1968

Fig. 13. Patent activity

1971

1974

in the F.R.G.

1977 i 980 Time [yrsl

i 983

in the subfield

of an exposition

1986

1989

control.

1992

Prognosis

137

of Patent Activity

262422 Izo.o t 18,; 16z 0 14E 0 12T;j g10?G

8-

;

642-

O

I 1968

1970

Fig. 14. Cumulative

z

,1

4.18S-

*

4 z

3.724 -

;

3.258-

.;

2.793 -

.? 2 ‘B m

1972

curve of patent

Initial period

1974

1976 1978 Time [yrsl

activity

in the F.R.G

Maximum development d - expansion

,

,

4

1980

1984

1982

in the subfield

Development termination expansion

1986

of body organ

I

selection.

End of the development

2.3271.862-

5 g

1.396-

‘ii :

0.931-

I! ;

0.4650.000

I

1968

1970

Fig. 16. Patent activity

1972

1974

in the F.R.G.

In the period of the field development termination the region of reliability becomes even narrower and the speed of production of new inventions at first rapidly, later on slowly decelerates. This reflects the fact that in this period it is reasonable that the majority of basic and principal ideas has been already investigated and it is unlikely that a lot of new inventions will appear and a great number of new patent applications has been deposited. Figure 7 shows a cumulative curve of the patent activity in the U.S.A. The distribution of points round the theoretical curve indicates there is probably one field involved. It explains the difference between the

I

I

1976 1978 Time [yrs]

in the subfield

maximum U.S.A.

I

1980

1 382

/

of body organ

numbers

1

1984

I

1986

selection.

of inventions

in the F.R.G. and the

Figure 8 presents a distribution of the patent activity in the U.S.A. concerning the analysed field. It is obvious that the general features mentioned above hold good even here. Figures 9 and 10 depict results of the U.S.S.R. invention applications analysis. Due to the insufficiency of data and with respect to conclusions we came to when discussing the results presented in Table 2, it is not possible to appraise them in details.

138

J. KrejEi and D. Kendere?ki

Table 6. Input data for patent analysts is the F.R.G. in the subfield of exposition control and body organ selection

Table 7. Computerised F.R.G. in the subfields selection

Exposition

Body organ

I 2 3 1 5 6 7 8 9 10

II I2 13 I4 15 16 17 18 19 20 21 22 23

control 22. 2.1967 2. 5.1969 18. 6.1969 5. 3.1970 7. 3.1970 9.12.1970 18.12.1970 21. 1.1971 I?. 7.197 I 10.10.197 1 3.11.1971 20.12.197 i 6. IO. 1972 22. 3.1973 28. 6.1973 28. 6.1973 22. 3.1974 10. 5.1974 24. 6.1974 2.10.1974 15. 3.1975 2. 5.1975 10.11.1975

Body organ

selection

2 3 4 5 6 7 8 9 0

18.12.1970 9. 2.1971 9. 6.1971 3.11.1973 22. 2.1973 7. 3.1973 22. 3.1973 25. 5.1973 8. 6.1973 21. 9.1973

I

25.10.1973

I

2 3 4 I5 6 7

19. 2.1974 21. 5.1974 20.12.1974 6.10.1975 20.10.1975 17.12.1975

Figure 16 comprises the analysis of an extended file of invention application in the U.S.S.R. (see Table 5). By using the analogical process as in the case of the analysis of the patent activity in the F.R.G. (see Fig. 11) it can be found that there are again two fields involved. The obtained results reflect the method sensitivity upon a correct field selection. In this case the method was utilized incorrectly for an analysis of two subsequent fields which had been developing individually and obviously independently. The analysis comprises only the first maximum of the patent activity. The reliability regions were not defined as it was calculated that k = 0. The patent activity in the field of chamber X-ray apparatuses found from the extended file is in Fig. 17. Figures 18-21 cover the U.S.S.R. patent activity analysis in which the extended file was divided into two subfields which were developing within the periods 1969-1975 and 19751979. The results of the analysis are in Table 9. The approximation accuracy improved considerably especially for the years 1969-1975, but still there is not enough data to carry out the prognosis. (In the second case k = 0.)

Conclusion The paper introduces the principles of the statistical analysis of a scientific or technial field development based on the frequency with which applications of inventions are deposited. The study emphasizes an intuitive understanding of leading ideas, sometimes perhaps to the detriment of strict interpretation. Apart from this fact authors are of the opinion this approach is the most suitable one as it is sufficiently inspirative

results of patent activity analysis in the of exposition control and body organ

selection

Maximal number of inventions 35 Reliability interval of the maximal number of the inventions (28-44) Starting point of research in the investigated area Year 1969 Month 7 22 Day Reliability interval of the starting point of research in the investigated area (1969.0-1970.0)* Constant characterising speed of the development in the investigated area Year 5 Month 3 29 Day Reliability interval of the constant characterising speed of the development in the investigated area (4.64-5.85) All reliability intervals or hypotheses are evaluated with the probability 95% Maximum development expansion is in years 1971-1976 In years of maximum development expansion is invented inventions 16 The development in the investigated area is terminated in the year 1983 for reasons of economical ineffectivity on the level 20% Correlation coefficient 0.9689 Average quadratic derivation 0.3226 Sum of quadrate of derivations 25.3926

Exposition

control

Maximal number of inventions 61 Reliability interval of the maximal number of the inventions (45-82) Starting point of research in the investigated area Year 1966 Month 8 Day 15 Reliability interval of the starting point of research in the investigated area (1966.1-1967.2) Constant characterising speed of the development in the investigated area Year 9 Month 3 23 Day Reliability interval of the constant characterising speed of the development in the investigated area (8.51-9.94) All reliability intervals or hypotheses are evaluated with the probability 95% Maximum development expansion is in years 1969-1976 In years of maximum development expansion is invented inventions 27 The development in the investigated area is terminated in the year 1990 for reasons of economical ineffectivity on the level 20% Correlation coefficient 0.9949 Average quadratic derivation 0.1500 Sum of quadrate of derivations 10.3492

*The time expressed in the years by a decimal number reliability intervals (e.g. 1969.5 means June 1969).

in the

and provides a brief representation of fundamental principles. It is apparent that already the simplest model (at the time I, inventors the number of which is N,, begin a development in a new field having no preliminary knowledge) produces very good results in the prognosis of invention number development and the period of development as well. On the other hand it turns out the method is sensitive to a definition of the studied field and to criteria on the basis of which inventions are included into the studied field. This question will be investigated in the second paper together with other problems, model additivity, economic limitations, input data and mistake analysis. Some of the results were already implicitly used as they were indispensable for analysis carried out in this paper. Summarizing it can be said the proposed method may become an effective help in deciding about licence investments, in regulation of research

Prognosis

of Patent

Table 8. A comparison of prognosis and actual number subfields exposition control and body organ selection Exposition control Prognosis of number of inventions on the reliability level 95% Number Year

Actual number of patent applications

o-5 l975- 1976 : 1976-1977: O-4 1977-197s : o-4 1978- 1979 : O-3 1979-1980 : O-3 1980-1981 : O-3 1981-1982 : O-3 1982-1983 : O-2 1983-1981 : O-2 1984-1985 : O-2 o-2 1985-1986 : 1986-1987 : O-2 O-2 1987- 1985 : O-1 1988-1989: The development in the investigated area is terminated in the year 1990 for reasons of the economical ineffectivity on the level 20%

0.

Fig. 16. Cumulative

1968

curve of patent

I

1972

activity

/

1974

of patent

applications

in the F.R.G.

Body organ selection Prognosis of number of inventions on the reliability level 95% Year Number

in the

Actual number of patent applications

l975- 1977 : 3-5 1977- 1979 : 2-3 1979-1982 : 2-3 The development in the investigated area is terminated in year 1983 for reasons of economica1 ineffectivity on the level 20%

2 2 3 4 2

1970

139

Activity

I

1

1976 1978 Time[yrs]

in the U.S.S.R.

I

1980

I

2 3

1982

in the field of chamber

,

1984

I

1986

X-ray apparatuses.

I

The expanded

file.

J. KrejEi and D. Kendere’ski

140

-Maximum

development

+-Development +End

,;

14.147

6 ._ G .g

11.789

2 m E U zP

7.073

z Li

4.716

expansion

termination

expansion

of the development

9.431

f

;

2.358 I0.000

I

I

1968

0

1972

1974

1976

I

1978

/

1980

J

/

1982

1984

1986

Time [yrsl

Fig. 17. Patent activity

in the U.S.S.R.

in the field of chamber

X-ray apparatuses.

Time [yrs]

Fig. 18. Cumulative

curve of patent

activity

in the U.S.S.R.

in a subfield

being developed

throughout

the years 196g-1975.

Expanded

file

Prognosis

of Patent

141

Activity

Initial I”la*llll”III

6.670 T

2

5.929-

% :

5.188-

r” ;

4.447-

“~r~l”~lll~llr~*~~IIJI”,,

+

Development

e

End of the development

termination

expansion

? .: 3.706 J ‘g 2.964m i: 01 2.223 ;;i P 2

1.482 -

2 ;

0.7410.000

I

1961

Fig. 19. Patent activity in the

70

1972

1974

1976 1978 Time [yrsj

1980

0

1982

I

I

1984

1986

U.S.S.R. in a subfield being developed throughout the years 1969- 1975. Expanded file.

10 9F

-i ‘;; 8: ._ z 7,” ;

6-

& z 5P z 4& : ;

32+

1 0’

t

, 1974

I

1975

/I

1976

1977

I

1978 1979 Time [yrl

I

I

1980

Fig. 20. Cumulative curve of patent activity in the U.S.S.R. in a subfield being developed

I

1981

I

I

1982

throughout

1983

the years 1975- 1979. Expanded file.

142

J. KrejE and D. Kendere’Ski

: .;

26.773-

c” ,s 22.310.-: 2 t7.848m E ;;; 13.386 a z 8.924 G :

4.462 -

Time (vrl Fig. 21. Patent activity

in the U.S.S.R.

in a subfield

being developed

Table 9. Analysis results of patent applications inthe U.S.S.R. in the subfield developed in the years 1969 - 1975 and 1975 - 1979. Expanded file 1969-1975

1975- 1979

Maximal number of inventions 7 Reliability interval of maximal number of the inventions (S-9) Starting point of research in the investigated area Year 1969 Month 6 30 Day Reliability interval of the starting point of research in the investigation (1969. I- 1969.8)* Constant characterising speed of the development in the investigated area Year 0 7 Month I3 Day Reliability interval of the constant characterising speed of the development in the investigated area (0.43-0.64) All relrability intervals or hypotheses are evaluated with the probability 95q Maximum development expansion is in years 1970- 1970 In years of maximum development expansion is 3 invented inventions investigated area IS terminated in year 1971 for reasons of economical ineffectivity on the level 20% Correlation coefficient 0.9841 Average quadratrc derivation 0.1763 Sum of quadrats of derivations 0.5595 *The

time

reliability

Da!,

(3) (4) (5) (6)

(7) (8)

reasons of economical ineffectivity on the ZOCC level Correlation coefficient

of 28.6822

number

in the

Expanded

file.

works and for production of technical field development prognosis. Last but not least it is also important to compare the constants lvith respect to different development conditions and their relation to the environment and the society in which the inventor lives and works.

21

0.9841 2.1705 Sum of quadrats derivations

the years 1975-1979.

References (1) Terleckij Statisticeskaja (2) D. Ruelle, Sraristical

Maximum development expansion is m years 1978-1978 In years of maximum expansion is invented invention 5 The development in the investigated area is terminated in kear 1978 for

in the years by a decimal (e.g. 1969.5 means June 1969).

is expressed

intervals

Is valid the hypothesis constant characterising speed of the development equal zero. It is impossible to evaluate the interval of the reltability hlaximal number of the II inventions Starting point of research in the investigated area 1977 Year 12 Month 17 Da! Constant characterising speed of the development in the investigated area 0 Year 2 hlonth

throughout

Benjamin, J. Crank,

fyzika.

lzd. Mir.

Mechanics,

Rigorous

Results.

New York, 1969. The .tfarhemarics of Difjlrrion O,xford

W.

A.

University Press, London. R. Balescu, Equilrbriwn and.~onequi/ibrirrni Srarical .\lechanics John Wiley, New York, 1975. V. Dostal, Algoritmus ieSeni v-yn$lezeck$chtiloh. Podnikorrj automarizece 1. 2. 3; 1982. D. Kendere?ki. L. rMat:jka and R. Hack. A thesaurus to supplement the international patent classification in the field of biomedical engineering. World Pafenr Information 2, 10 I- 109; 1983. V. Pitra, Vynilezectvi a zlepjovatelstvi (slovnik pojmu) &ad pro vynalezy a objevy; 1976. Patentova analcza k’omorov~ xfric: Chirana VUZT, 1983.