(1) A Model for the Measurement of Creativity. Part I - Relating Expertise, Quality and Creative Effort
C
Redelinghuys
Department of Mechanical Engineering, University of Cape Town,
Cape Town, South Africa
As a first step towards a methodology for the measurement of creativity, quantified definitions of product design quality, designer expertise and creative effort are introduced in such a way that their interrelationship can be portrayed as a set of hyperbolic curves, the cEQeX-diagram. Product quality is mathematically related to the product characteristics. Designer expertise is defined to include all the invested tertiary education and relevant experience contained in the design team, as well as investment in design software and laboratory facilities. Designer creativity is defined to be proportional to (a function of) product quality obtained and inversely proportional to the product of (a function of) initial expertise and creative effort expended. Guidelines for the construction of the cEQeX-diagram are given. The cEQeX-technique holds potential for the measurement of creativity and is useful as a guide for curriculum development.
"To be creative" is deemed to be an important quality in probably every field of human endeavour. The topic has been researched by academics from many different fields such as psychology, education, philosophy, architecture and engineering and much effort has been devoted, on the one hand, to the identification of the special human characteristics which lead to creativity, and to the ways that creative people perform their creative deeds. On the other hand, it appears that there does not exist an accepted method for the measurement of creativity in individuals or in a group of persons working collectively on a creative project.
Based mainly on insights gained as a practising systems engineer for the design of complex engineering systems, the author proposes a guiding model for the measurement of creativity below. The model relates product quality, designer expertise and designer creative effort in such a way that creativity can be calculated as a function of time as the creative process proceeds. The model shows what demands are placed on the designer to ensure quality designs and as such hints at engineering curriculum and syllabus design.
The model approaches creativity from the outside looking in, ie, it evaluates creativity by looking at the quality of the product (the consumer's view) which is being formed; duly considering a) the effort which has been spent on the process (the investor's view) and b) the level of appropriate education of the creator (the educational establishment's view). It is neither concerned with any other characteristics of the creator nor with the details of the process which is followed, quantities which would be important if creativity were analyzed from the inside looking outward.
A schematic presentation of the present model is shown in fig. 1. As shown, the designer "absorbed" prior education and experience from the outside world, which also supports him financially, and for which he develops a product of a certain quality. Any other creative characteristic, eg. attitude, judgement and motivation [1] is included in the shaded segment as it influences the present definition of creativity only indirectly. For the same reason details of the creative process which is followed [2-7] are contained in a shaded segment. It is assumed that favourable creative characteristics and processes would imply a reduced required creative effort to develop a product of a certain quality. The reduction in creative effort would imply a measurement of increased creativity.
The paper begins with some relevant comments on the creative process as used in systems design. In preparation for a more rigorous subsequent treatment, a superficial introduction to the creative effort-quality-expertise (CEQEX)-diagram is given in the following section. This is followed by discussions on topics such as product design characteristics, quality, designer expertise and creativity; each being carefully defined such that they can be mathematically interrelated. In Part II it is shown how the cEQeX-diagram can be used as a nomogram for the graphic portrayal of creative processes and how the present model may be used for the measurement of creativity by means of a case study.
Creativity is a popular topic for discussion in the literature. The Oxford dictionary defines being creative as:
To form out of nothing,
a definition which covers most others put forward in other sources. As the present study examines creativity from the outside looking in it is not essential to consider the exact form of the creative process that the designer follows. It will suffice to consider a single (but crucial) facet of the creative process, that of hypothesis generation and testing as depicted by fig. 2. This model closely resembles the basic design cycle proposed by Roozenburg and Eekels [8] and the TOTE cycle (test-operation-test-exit) as a formal description of trial-and-error procedures in human problem solving, of Miller et. al. [9]. Step 1, the search for promising concepts, relies heavily upon human creativity. What needs to be emphasised, though, is that the search for and evaluation and acceptance of viable concepts depends largely on the product-related knowledge or expertise of the designer. No matter how creative a group of poets might be, working together on the design of a high performance gearbox, it is unlikely that a useful solution will emerge. Vice versa, assigning an engineering student to compose a violin concerto would rarely produce a presentable result. In both cases the hampering factor is a lack of expertise, rather than creativity. Especially steps 1 and 3 are most efficiently executed when the designer combines original thinking with his comprehensive product-related knowledge. Put differently, the more expertise there is available, the less creative effort should be required.
In order to be able to design any product, the designer needs a certain level of expertise, ie, product related knowledge. As the product design progresses, its performance and effectiveness are constantly measured leading to a gradual growth in quality, as seen by the potential client. In most cases the design process is guided by a development specification in which the minimum acceptable product performance criteria are spelt out. The designer (designer A, say), which in general may imply an individual, a company or a group of companies, continues spending creative effort on the project until the requirements of the specification are met. Assuming it is possible to measure this designer's expertise, EXA, and his total creative effort until design completion, CEA, the state of affairs may be summarized on a graph as shown on fig. 3. On the vertical axis the initial expertise is shown, where it is appreciated that this quantity will increase during the execution of the design. Also shown on the figure is the performance of designer B, who has a lower initial expertise and hence usually would require more creative effort to completion. The curved locus of such coordinates of required CE vs EX is shown as a solid line which could resemble a hyperbola. The infinite number of different designs represented by this locus have one thing in common, ie, they all conform to the development specification. From the client's perspective, therefore, quality (Q) = 1 for these designs. The hyperbola implies that, on the one hand, with little EX a lot of CE is required for an acceptable design and, on the other, a lot of EX requires little CE.
Assuming that premature termination of the design process results in an unfinished product with measurable quality Q, where Q < 1, graphs of required CE vs initial EX for various Q-values are shown in fig. 4 - henceforth referred to as the CEQEX-diagram.
During and after the first appearance of a new class of engineering product (eg, first aircraft, automobile or personal computer), expertise related to such a product evolves and becomes entrenched in growing amounts. The Wright brothers did not possess a comprehensive understanding of wing aerodynamics but by WWII volumes of design data on the aerodynamics of wing sections had appeared. Seen from a historical perspective then, design of a product range of fixed quality would chronologically proceed as shown by the arrow in fig. 5. Region P, Pioneering Design, represents break-through, first-time designs where the designer initially hadn't possessed much expertise but had to invest a large quantity of creative effort for success. This is the world of the great minds such as James Watt and Thomas Edison. Due to the high associated development risks, designers are seldom contracted to work in this area. Region V, Verified Design, is the region where the technical feasibility of a product-type has been demonstrated beyond doubt but design remains risky, expensive and of a highly specialized nature. Typical designs, which are normally led by highly qualified engineering personnel, are new high technology engineering products such as nuclear power stations and commuter aircraft. The remaining region, region R, Routine Design, represents cases where so much empirical design data has emerged that design procedure almost becomes routine, such as designing a shaft and bearing support system for an ordinary power transmission application. Designing a standard air-conditioning system for a standard building would also fall in this category.
To show how the CEQEX-diagram can actually be constructed and used in real-world situations, parameters such as quality, expertise and creativity are carefully defined and quantified in the next two sections.
The quality of a product is of vital importance to the client or consumer. Hence designers must be highly conscious of the quality of their designs and must have means to define and measure it. Definition of quality is by no means trivial, as Pirsig [10] points out in his delightful book but, fortunately, seeing engineering products mainly as those having to fulfil functions and with measurable performance, it can be attempted.
The engineering literature contains lots of definitions for and discussions of quality. According to ISO 9000:
Quality is the totality of the characteristics or performance that can be used to determine whether or not a product or service fulfils its intended application.
For the present it is important to distinguish between quality of design and quality of conformance [11]. In the following, quality will be restricted to quality of design.
For a physical product a useful categorization of quality factors can be obtained by forming two groups of properties: 11 classes of externally visible properties plus the (invisible) internal ones [12]:
- Functions, effects
- Functionally determined properties
- Operational properties
- Manufacturing properties
- Distribution properties
- Delivery and planning properties
- Liquidation and environment properties
- Ergonomic properties
- Aesthetic properties
- Law and societal conformance properties
- Economic properties
- Design properties
For the present, quality of design relates to all those properties listed above which are under the direct control of the designer.
For a particular product, the major performance and effectiveness parameters, of which each one influences the product quality, can be identified. For a Formula 1 racing car, for example, some of these parameters would be:
- Maximum speed,
- Maximum acceleration (longitudinal and lateral),
- Specific fuel consumption and
- Reliability.
For each parameter (say parameter i) let its measurable size be given by Ci, where i = 1, N, and N is the number of parameters. In the product development specification, desired values for each of these will be stipulated as CSi, say. Of relevance is the fact that many parameters have limits on their most-extreme size, the latter quantity being determined by our current understanding of science, engineering and economics. Denoting these limits by Cbi, some examples are:
- Carnot efficiency,
- Speed of light,
- Zero absolute temperature and
- Zero production cost.
Now, after measuring each characteristic parameter for a product (which might still be under development) and having defined the set of parameters such that not one is redundant, the system characteristic vector can be defined as an N-dimensional Euclidian vector:
(1)
| where | ei | is a unit vector along axis i and | ||
| wi | is a weighting value such
that: |
The Euclidian assumption requires all the vector components to be independent which is not true for the system characteristic vector when viewing it from the inside of the design process. For the client, who generally is not concerned with engineering, and who is viewing the product from the outside, this interdependence is irrelevant and he has the "right" to use the definition as given by eq. (1). The fact that some of the characteristics would be highly stochastic in nature, with large standard deviations, implies that a non-deterministic approach would be more appropriate. This would obscure the essence of the present study and, as is shown in the case study of Part II, would be unnecessary in certain applications.For illustration purposes the associated vector space will be restricted to a plane (N=2). Such an example is shown in fig. 6, on which is also shown the limiting physical boundary as discussed above. For the sake of generality it is assumed that this boundary may be influenced by combinations of parameter values and is hence given by an equation of the type:
B(C1, C2, .... CN) = 0.
On the figure are also shown the region in which the specification is satisfied, the specified characteristic vector, cS (where it follows from eq. (1) and the definition of wi that cS = 1) the actual vector c and the deficit vector, cD.
The Simple Case
Suppose we are dealing with a very simple design requirement which demands the satisfaction of a single specified parameter value, eg, the thermal efficiency, h . From eq. (1) the system characteristic vector becomes a scalar of size
c = h /h S,
where h S = specified thermal efficiency.
A sensible definition for quality would in this case be (setting the Carnot efficiency = hC):
(2)
A graphical portrayal of this "fundamental" relationship between quality and system characteristic is shown in fig. 7. In the following three sections the general case where more than one system characteristic are important, will be considered.
Quality Demands of the Stubborn Client
In this case it is demanded that the design solution shall satisfy each and every specified design characteristic, ie:
ci 3 1, I = 1, N.
A possible case is depicted in fig. 8. For certain characteristics the specification will call for a required nominal value and an allowable tolerance. In such cases a simple algebraic function of the inverse of the tolerance could be used as the characteristic. Despite the fact that the size of the actual characteristic vector, c, exceeds that of the one specified, cS, no credit is given for the overdesigned characteristics. In other words, from the client's perspective, c and ceff are equivalent.
Hence, the equivalent definition of quality could be:
(3)
where cb is defined in the figure.
Quality for the Accommodating Client
Here the client does give credit for characteristic values which exceed those specified (fig. 9), though some might still fall short, and the magnitude of the effective characteristic vector is:
ceff = c.cS/cS.
Hence Q can be calculated by means of eq. (3).
Quality as Assessed by the Thinking Client
During the design of sophisticated technological products it often happens that at an advanced stage it is found that some of the design requirements are met or exceeded whilst others are not. For example, if the product to be designed is a gas turbine engine for a commuter aircraft and it is found that although the engine is heavier than was specified, the specific fuel consumption turns out to be less that the specified requirement. In such cases the client (in this example, the prime contractor) would consider the effect of deviation from specification on a crucial overall system performance parameter, eg, the maximum permissible payload or the projected return on investment in the system development. To be able to do this, knowledge of the following functional relationship is required:
P = P(c1, c2,
....., cN)
= P(c), (4)
where P = appropriate system performance parameter.
By means of eq. (4), surfaces of constant P can now be calculated and portrayed in the characteristic space, fig. 10. In this case, a suitable definition for quality would be:
(5)
where the symbols are defined in fig. 10.
It is interesting to note that this latter definition of quality can be interpreted as being equivalent to the preference parameter of Malen and Hancock [13].
As shown above, it is possible to quantify quality of design. The exact quality-model used in each case would have to be established by means of consultation with the client.
Expertise is a concept which is currently being warmly debated by a number of disciplines such as computer science, engineering, psychology and philosophy. A thought-provoking set of papers by a group of researchers from these various disciplines has recently collectively appeared in a special issue of the International Journal of Expert Systems (Volume 7, number 1, 1994). It is interesting to note that some of these authors treat expertise with a little contempt, eg, experts having obtained epistemic powerful positions [14] in society and often thriving on "persuasive bluff". In the present study the term expertise will strictly relate to a designer's knowledge base which allows him to create a product according to requirements contained in the development specification. The quality of his product is objectively measurable by means of the criteria as discussed in the previous sections ensuring elimination of any form of bluff.
Sternberg [15] discusses nine cognitive conceptions of expertise which are reorganized into two groups in the present study. The one group, called invested expertise, is obtained by adding that which could have been accumulated through education, previous design experience and the purchase and development of software and equipment. The second group, called expertise in action includes those aspects of expertise which are used during a creative process to tap the invested expertise in a constructive way. We deliberately want to separate creative and invested mental capabilities such that the latter can be associated with the (measurable) prior education and experience. Therefore, design expertise will henceforth refer only to the invested component.
Expertise also has to be quantified. This task will be dealt with later.
Consider a designer who is the cream of the crop in a certain product range. This designer (henceforth called the reference designer) possesses a substantial amount of expertise when he embarks on a new product development venture, say. In these early stages of the process he does not know what the final solution will look like but if sound systems engineering practice is followed, the current design will evolve, step by step, towards a Q = 1 solution. This systematic evolution for complex systems is usually done by proposing, analyzing, building, testing and modifying suitable models (= prototypes, in layman's language); to sequentially confirm the conceptual, the form, fit and function and the engineering (eg, reliability, maintainability and producibility) characteristics of the system. This sequentiality is not enforced very strictly as financial and time pressures and modern concurrent engineering approaches demand overlap. Some of the common development models encountered are [16]:
Model Purpose XDM: Experimental development model Confirms cardinal system concepts, eg. control laws for a satellite ADM: Advanced development model Confirms form, fit and function of modules and subsystems EDM: Engineering development model Confirms reliability, maintainability etc. PPM: Preproduction model Confirms producibility of design
At any point in time during system design the performance of the current system design solution is the one obtained by the consolidation of the measured performance of all the various development models under test. The current system characteristic vector can hence be constructed based upon only those system characteristics which have been confirmed by measurement. The associated product quality, Q, will therefore normally gradually increase as the system development process absorbs creative effort (CE), the latter parameter implying the measurable number of person-hours which have been spent on the project.
The expected dependence of CE upon Q is as shown in fig. 11. Even for an adaptive redesign, it is possible to express the system's characteristic vector in such a way that Q will start from a zero value (see the case study in Part II). A certain minimum threshold value of CE is required before Q will become measurable. Now, it is fair to assume that as Q increases to values corresponding to the limits of the designer's creative abilities, further increases will require increasing CE, or dCE/dQ increases with Q at high Q, fig. 11. It is also fair to assume that CE will depend on the designer's expertise, EX, hence, the following functional form is proposed:
(6)
where CE(Q) depends only on Q and g(EX)is a function of EX only, which allows for other than hyperbolic relationships between CE and EX for constant Q.
For the present it will be assumed that EX can be calculated independently and, like CE, expressed in the unit of person-year. A creative effort which is given by eq.(6) will be termed a uniform effort and for the moment the study will be restricted to such cases with the further assumption that
(7)
| where | G 0, G 1, G 2, m and n
are constants and 0 < m < 1 and n > 1. |
|||
This particular mathematical form is chosen as it models the trend suggested in fig. 11. These restrictions are only introduced to compactly illustrate the concepts involved and do not imply a fundamental limitation of the techniques to follow.
Let the specific values of expertise and creative effort for the reference designer under consideration be given by EXR and CER, respectively. It follows that eqs.(6) and (7) can be written in the following dimensionless forms:
(8)
(9)
The concept creativity has to be introduced now. Consider a company with initial expertise EX that has spent a total creative effort CE to produce a product of quality Q. It sounds logical that creativity should be defined such that it will be larger for a larger Q and smaller for a larger EX or a larger CE, hence, creativity (cr) is defined as
(10)
(11)
The rationale behind eq. (10) is the Qxford definition of creativity which was given earlier. According to this equation, less EX or less CE would imply a higher creativity (for the same Q), which is in line with the idea of "forming out of nothing (or little)". We now calibrate creativity by assuming that, for the reference designer, cr = 1. Although another designer may possess less (or more) expertise in comparison, it is assumed (for the moment) that he is inherently just as creative. Thus, setting cr = 1 in eq. (10) leaves:
(12)
which is a hyperbolic relationship for a fixed value of Q. Note that for any hyperbola there exists an associated, constant area, which in this case is
(13)
Eq. (13) is used to solve for kQ by setting
(14)
Eq.(12) is in essence the cEQeX-diagram, as was introduced earlier, which can simply be constructed by choosing values for Q and drawing the corresponding hyperbolas. On a log-log scale, constant Q lines will become straight. Application of eq. (10) to establish the creativity of other than reference designers, will be demonstrated in Part II.In summary then, the reference designer is per definition one with creativity and specific expertise of value unity and one who follows a uniform creative effort.
It follows from the previous discussions that the invested expertise of a designer will depend on a host of factors such as the number of design team members, the educational and practical background of each, the available computational and experimental facilities and the appropriateness of all these with regard to the type of product to be designed. As was the case with the quantification of quality, a rigid law for the quantification of expertise does not exist but an approach which is compatible with the present considerations will be followed here.
Firstly an estimation of the invested education contained in the design team is to be made. Suppose there are nD different engineering disciplines represented, with a total number of nmi, i=1, nD, team members belonging to each one. Suppose further member number j in group i has had Nedij and Nexpij years of formal tertiary education and practical experience, respectively. The following definition of the invested education vector is now proposed:
(15)
| where | a ij | = | experience amplification factor, | |
| b ij | = | adjustment factor for redundancy or amplification between members and | ||
| ed | = | unit vector depicting collective direction of education vector, ie |
(16)
where
(17)
and ei = base unit vector for discipline i.
It should be noted that Ed represents quantity and not quality. The temptation to adjust b ij according to individual competence should therefore be resisted. Ed is only used to help establish the invested expertise. In the present from the outside view of creativity, it is assumed that increased competence would reduce required creative effort, thus it would indirectly influence creativity. Therefore, quality of the designer influences his required creative effort, as is shown below, and manifests itself on the horizontal axis of the cEQeX-diagram. On the latter, Ed has to be applied in a non-dimensional form with respect to EXR. The non-dimensional forms of eqs. (15), and (17) are obtained by replacing the symbol E and N with their lower case equivalents, e and n.
A conceivable form for a ij could be:
where d and A are empirical parameters.
Only the part of Ed which is appropriate to that required for the design of the specific product under consideration, is relevant. This is achieved by calculating the direction of invested education for the reference designer, edR, by means of eq. (16) and then forming the scalar product:
Edr = Ed.edR . (18)
Lastly, the beneficial effects of available design software and laboratory facilities, henceforth referred as facilities, must be incorporated. This is done by following the following steps:
Calculate the person-year "equivalent" of the facility, CEF, which is obtained by dividing the hiring or purchase cost of the available facility by the engineering person-year rate, assuming cr = 1. The purchase cost of a facility is included in CEF in the event where this facility is acquired solely for the particular project.
As was done in eq. (15), form a multidimensional facility space for both the company under consideration (company A, say) and the reference designer and establish the relevant contribution, CEFr, by a scalar product similar to eq. (18).
For the reference designer, therefore:
(19)
| where | CEFR | = | creative effort required to establish all facilities, | |
| nfk | = | number of facilities per discipline, | ||
| CEFkl | = | Creative effort required to establish facility number kl, |
and
Hence
Determine the total expertise for the reference designer, EXR, by means of the expression (see appendix A):
(A4)
For company A the expertise is given by (appendix A):
(A6)
In this paper definitions for product design quality, designer expertise and creative effort have been introduced in a quantified manner such that they are interrelated and can be graphically depicted as a set of hyperbolic curves, the cEQeX-diagram. Product design quality Q is mathematically related to the product characteristics in such a manner that Q = 0 at design inception, Q = 1 when the requirements of the development specification are met and Q (r)Y when characteristics approach physical boundaries. Designer expertise is expressed in person-years and includes all the invested tertiary education and relevant experience contained in the design team, as well as investment in design software and laboratory facilities.
The notion of a reference designer, whose performance is used for the calibration of the cEQeX-diagram of a product type, is introduced. For a reference designer, the functional relationship between expertise, creative effort (CE) and quality is defined such that creativity is always unity and his effort is always uniform with respect to Q.
In Part II it is shown how the performance of other designers can be traced as CE vs Q data points rendering a creative path. The creativity of such designers can be obtained by calculating the ratio of appropriate areas on the diagram.