This article was downloaded by: [University of Michigan] On: 03 October 2011, At: 14:13 Publisher: Taylor &

Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Journal of Engineering Design

Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/cjen20

Incorporating user shape preference in engineering design optimisation

Jarod C. Kelly , Pierre Maheut , Jean-Franois Petiot & Panos Y. Papalambros
a a a b b

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

b

Institut de Recherche en Communications et Cyberntique de Nantes, Ecole Centrale de Nantes, 1, rue de la Noe, Nantes, 44321, France Available online: 24 Jun 2011

To cite this article: Jarod C. Kelly, Pierre Maheut, Jean-Franois Petiot & Panos Y. Papalambros (2011): Incorporating user shape preference in engineering design optimisation, Journal of Engineering Design, 22:9, 627-650 To link to this article: http://dx.doi.org/10.1080/09544821003662601

PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-andconditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Journal of Engineering Design Vol. 22, No. 9, September 2011, 627650

Incorporating user shape preference in engineering design optimisation

Jarod C. Kellya * Pierre Maheutb , Jean-Franois Petiotb and Panos Y. Papalambrosa
a Department

Downloaded by [University of Michigan] at 14:13 03 October 2011

of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA; b Institut de Recherche en Communications et Cyberntique de Nantes, Ecole Centrale de Nantes, 1, rue de la Noe, Nantes 44321, France
(Received 16 July 2009; nal version received 26 January 2010 )

Form versus function is a classic design debate. In this article, a practical approach to combine shape preference (form) and engineering performance (function) under a design optimisation paradigm is proposed and implemented. This synthesis allows form and function to be considered in quantitative terms during the design process to identify shapes that can benet overall product design. Two methods of preference modelling, PREFMAP analysis and conjoint analysis, are used to model user preference as a mathematical function of design variables. Physics-based models express engineering performance as functions of the same design variables. The models are combined in an optimisation formulation to capture the design trade-offs involved. A simple illustrative study of bottle design is presented. A divergence is found between the most preferred shape and the technically optimal shape; a Pareto frontier provides insight into the trade-off between these two goals. Keywords: preference modelling; shape preference; decision-making; product design

1.

Introduction

Mathematical design optimisation traditionally deals with design considerations related to product functionality because the availability of physics-based models allows for quantitative expression of product performance as a function of design variables (Papalambros and Wilde 2000). Extending such a quantitative approach to include subjective design considerations makes design optimisation more valuable but also substantially more challenging. Modelling methods from the behavioural sciences offer a foundation for developing quantitative behavioural models, such as user preferences for certain design aspects. Shape is a product aspect that often affects its performance. Shape also affects user preference for the product, often associated with aesthetic preference. Shape preferences may be motivated by non-aesthetic considerations, e.g. ergonomics, and so it is difcult to extract an objective metric for purely aesthetic shape preference. Preference modelling for optimal product design related to shape would be more manageable if the shape preference metric does not attempt to include causality for the preference. This is
*Corresponding author. Email: jckelly@umich.edu

ISSN 0954-4828 print/ISSN 1466-1837 online 2011 Taylor & Francis DOI: 10.1080/09544821003662601 http://www.informaworld.com

628

J.C. Kelly et al.

consistent with modelling approaches in marketing (Tybout and Hauser 1981). Even without explicit understanding of preference causality, a quantitative study of trade-offs relating preferred product shape to functionally optimal product shape, within the connes of shape constraints (e.g. manufacturing limitations, ergonomics), can provide valuable insights to designers, engineers and product planners. In this article, we limit the notion of shape preference and say nothing about the inherent beauty of a product. In the following, shape preference simply means that one product shape is more liked than others in the given context of how the product will be used. Preferences are also limited to the geometric qualities of the product that users are permitted to vary. We cannot extend the ndings or shape preference from the present work to suggest a universal shape preference, because this does not account for many contextual issues. Industrial and architectural design has a rich tradition of studying aesthetics (e.g. Pye 1978, Norman 2002, Lidwell et al. 2003, Park 2004, Park et al. 2005), including quantitative shape metrics such as balance, symmetry, rhythm and proportionality. This tradition suggests that a quantitative, mathematical metric for user shape preference is plausible. We further postulate that one may be able to identify combinations of shape attributes that yield an optimally preferred design for a particular artefact within a particular context, subject to the physical constraints dictated by required engineering performance. Assessing subjective tastes of users and utilising that information in the product design process is critical for success in a competitive marketplace and has received signicant research attention (e.g. MacDonald 2001, Petiot and Chablat 2003, Petiot and Grognet 2006, Orsborn and Cagan 2009, Orsborn et al. 2009). Kansei Engineering, initially developed in the 1970s and often referred to synonymously as Emotional Engineering or Emotional Design, utilises semantic information to match user wants and expectations in product design (Nagamachi 1995, 1997). Liu (2003a, 2003b) has suggested the idea of engineering aesthetics to seek methods that help designers make better decisions regarding the subjective aesthetic qualities of a product. The marketing literature on utilising preference to guide product design is expansive. Combining marketing models with engineering ones in a decision-making framework is a more recent topic in the emerging area of design for market systems. Such a combination of approaches (and models) is necessary to avoid dislocated and even infeasible designs (Michalek et al. 2005). As noted earlier, designers successfully apply rules, or heuristics, in industrial, graphic or architectural design. Application of these heuristics does not inherently dictate a products appeal; heuristics provide designers with a structure around the creative process of design (Tjalve 1979). Liu (2003b) has noted that, while unscientic, these design heuristics offer important insights into aesthetic questions and provide useful perspectives from which we can examine aesthetic concepts. Bauerly and Liu (2006) focused on the graphical layout of displays and web pages, and proposed quantitative methods that matched the perceptual and mental processes of (2D interface) users. That work specically provided a numerical quantication of the effects of symmetry, balance and compositional blocking. Bauerly identied these as the three compositional elements of aesthetic judgment, devised formulas to account for each of these compositional elements for 2D interfaces and validated them through human experimentation. However, preference for compositional characteristics can be context dependent, for example, the context of the objects function. Then, applicability of design rules becomes tenuous. The golden section is the best-known quantication of shape preference, indeed beauty, dened as the ratio of the length of two line segments, a and b, such that the ratio of a to b is equal to the ratio of a + b to a: a+b a 1+ 5 = . a b 2 (1)

Downloaded by [University of Michigan] at 14:13 03 October 2011

Journal of Engineering Design

629

Downloaded by [University of Michigan] at 14:13 03 October 2011

This ratio has been extensively studied and found to be relevant to many mathematical and biological phenomena (Green 1995). The rst psychophysical tests on this ratio (Fechner 1897) have been methodologically challenged (Green 1975), but the golden ratio appeal remains strong and is still used in current products. This paper examines how preference models of shape can be utilised within design optimisation for product development. This includes the examination of methods for understanding shape preference, and a specic case study that incorporates shape preference models within design optimisation. In the following, Section 2 gives some background on PREFMAP and conjoint analysis, the two preference modelling methods used in the subsequent study. Section 3 describes modelling examples to further examine the preference models. Section 4 presents the linking of behavioural (preference) and engineering models in a design optimisation framework for a bottle, and a discussion on the obtained optimisation results. Section 5 offers conclusions and suggestions for future work.

2.

Preference modelling with PREFMAP and conjoint analysis

A brief review of PREFMAP analysis and conjoint analysis provides some necessary background directly related to the studies in Section 3. 2.1. PREFMAP PREFMAP analysis is a tool that relates preference data to a stimuli space in order to generate an external mapping of preference (Chang and Carroll 1972). In an external mapping of preference, the stimuli space is based on data obtained independently to the preference assessment (Chang and Carroll 1972, Coxon et al. 1982). For instance, if several examples of light were shown to participants and the participants rated their preference for each sample, then we could determine brightness preference by mapping the light samples preference onto a stimulus space of lumens as the external map. A designed object examined in PREFMAP is composed of design attributes that are continuous, but bounded. Specic designs from within this bounded design space can then be used to query users and develop a preference model. So, in a PREFMAP survey, a respondent would be shown several different designs dened by variations in the design variables. The respondent would then assign a numeric value, associated with their preference, to each design that they observe. This provides response data that can then be used in a mathematical regression. The governing equation for the PREFMAP model is
2 2 Pmodel (x1 , x2 ) = b0 x1 + b1 x2 + b2 x1 + b3 x2 + b4 x1 x2 + b5 ,

(2)

where Pmodel (x1 , x2 ) is the model of preference, x1 and x2 are design variables and B = {b0 , b1 , . . . , b5 } are constants. The principle of PREFMAP is to model the preference by a quadratic form. Equation (2) gives the denition of this form in the case of two design variables, x1 and x2 . According to the complexity of the model, four types of models, called phases, are dened (Figure 1). Phase I is the most general model; all of the coefcients must be estimated in this phase. It corresponds to an elliptical paraboloid that can be rotated within the plane. The different phases of the model are dened according to the nullity of certain coefcients, which are presented in Figure 1. The model ts user response data, individually or in the aggregate, to the paraboloid dened in Equation (2). The constants, B = {b0 , b1 , . . . , b5 }, are determined by minimising the Euclidean

630

J.C. Kelly et al.

Phase I x2

Phase II x2 x1 Phase 1V b2 = b3 = b4 = 0 x2 x2 x1 x1 b4 = 0

x1 Phase III b4 = 0 b2 = b3

Figure 1. The different phases of PREFMAP are suited to different situations.

Downloaded by [University of Michigan] at 14:13 03 October 2011

distance between observed user response data, Pobs (x1 , x2 ), and Pmodel (x1 , x2 ). This can be done using the following optimisation formulation: min F (B) =
i j

(Pmodel (i, j ) Pobs (i, j ))2 ,

(3)

which is simply the criterion for least-squares linear regression. The external stimuli space is simply the two design variables weighted on a linear basis. The model is described by six parameters, B = {b0 , b1 , . . . , b5 }. Phase II is like Phase I, except that the paraboloid is not rotated (thus the variables are decoupled). Phase III is simpler yet, as the paraboloid is circular. Phase IV is a vector model where the vector can be thought of as pointing in a direction of ever increasing preference for the given design attributes associated with the stimuli space. For Phase IV, one can imagine that the ideal point predicted in Phase III is very far away from the actual stimuli tested; thus iso-preference curves of the circular map are nearly parallel and suggest a gradient of ascent towards the ideal point. Figure 1 visually shows the difference between the four phases. Rotated ellipses indicate a coupled relationship between design variables while a non-rotated ellipse indicates that one variable has a greater impact on preference than the other. A circular shape indicates an equal inuence of each variable on the resulting preference. A linear model only indicates the direction of increasing preference. The Phase II portion of the PREFMAP model is obtained by removing the interaction term, b4 x1 x2 , from Equation (2). However, in either case, Phase I or II, the possibility of a saddle point exists. Saddle points occur when the determinant of the Hessian matrix is negative. 2 Pmodel 2 x1 2 Pmodel 2 x2 2 Pmodel x1 x2
2

< 0.

(4)

The basic idea behind PREFMAP is that each individual has an ideal point of maximum preference and is capable of ranking different stimuli in such a way that the ideal point is revealed (Coxon et al. 1982). The ideal point assumption appears to be axiomatic. As an example related to vehicle preference, consider a person that likes large vehicles with high amounts of power. The preference space (Pmodel in Equation (2)) would be dened by two design variables, vehicle size and vehicle power (x1 and x2 in Equation (2), respectively). The model of preference would describe a paraboloid whose function value was maximal at a design point of large size and high power, perhaps corresponding to a sport utility vehicle.

Journal of Engineering Design

631

2.2. Conjoint analysis Conjoint analysis is a method for modelling preference that has been used extensively within the social science (Ryan and Farrar 2000, Green et al. 2001) and marketing communities. The goal of conjoint analysis is to determine the ideal combination of feature attributes based on the preference responses of a participant or group. It is frequently used in industry to determine information related to product design, concept evaluation, product positioning and market segmentation (Green and Srinivasan 1990). The method is based on the principles of utility, and the notion that consumers attempt to maximise product utility when they make choices. In order to collect data for a conjoint analysis, respondents are shown several descriptions or images of potential products. Each product is of a similar nature, but the product is decomposed into characteristic attributes (variables). These attributes are further decomposed into levels. The attribute may be size and the levels may be as large as a marble, as large as an orange or as large as a grapefruit. Or, the attribute-level can be more technical, as in 060 mph acceleration time, with levels of 10, 12 and 15 s. Respondents are then asked to evaluate the products in some fashion; a popular form of evaluation is through selection of one product among a set. This type of conjoint analysis is known as discrete choice analysis. Michalek presented a review of the foundations of discrete choice analysis, primarily with reference to the use of the logit model (Louviere et al. 2000, Michalek 2004). When using discrete choice analysis for the assessment of utility functions, it is assumed that utility, uiq , is composed of a deterministic term, viq , and an error term, iq , where i and q are the product offering and individual, respectively. A no-choice alternative is included in the product offerings. uiq = viq +
iq .

Downloaded by [University of Michigan] at 14:13 03 October 2011

(5)

The logit model assumes that the unobserved error term is randomly distributed and has a double exponential probability distribution (Gumbel distribution) (Guadagni and Little 1983, Louviere et al. 2000). This assumption, while not being based on theoretical grounds, has been shown in studies to agree well with the results of a normally distributed probability function, which has more theoretical validity (Michalek 2004). f ( ) = exp exp . (6)

Here is a location parameter, and is a scale parameter. Presuming that the deterministic component of utility can be predicted through regression of observed choice data to mathematical models of utility yields the mathematically tractable multinomial logit (MNL) model. The mathematical formulation of viq can be broken down, such that each i consists of an attribute term, m, each having n-levels. In our case, we consider n to be the same for all m, but in general the number of levels, n, do not have to be equal for each attribute, m. Further, it is assumed that all individuals act in a consistent and similar manner, thus treating a group as a single individual and negating the need for the q term. Therefore, the new model becomes Pi =
M

e vi
J vj j =1 e N

(7)

vj =
m=1 n=1

mn j mn .

(8)

Here mn represents the part-worth of level n for attribute m. While j mn represents a dummy variable that is equal to unity if the level of attribute m in product j is n. Otherwise j mn is zero.

632

J.C. Kelly et al.

The above formulation only considers that main effects impact utility. Each attribute is considered independent of the other attributes in affecting utility. However, it is quite possible that variations in one attribute will impact the other attributes contribution to utility. This can be modelled using a form that takes into account second-order effects between the attributes. Here, a model is again presented that consists of m-attributes and n-levels: vj =
m n

mn j mn +
o p

mnop j mnop .

(9)

Downloaded by [University of Michigan] at 14:13 03 October 2011

Now, j mnop = 1 when alternative j possesses attributes m and o at levels n and p, respectively. Note that the attributes comprising set o are exactly the same attributes as those comprising set m, and that the levels in p are exactly the same as the similarly associated levels in n. The inclusion of interaction terms in an analysis is warranted in situations, such as shape preference, where it is likely that the utility of an offering is not composed of independent attributes. This discrete model of preference can then be made continuous by tting a cubic spline through the design points (Michalek et al. 2005). Doing this allows us to model the design space with a continuous mathematical model that can yield gradient information. This assumes that preference is continuous in relation to continuous variables across the entire design domain. While this makes axiomatic sense to the authors, it is possible that discontinuities exist. The number of parameters to estimate in this model depends on the number of attributes and levels examined. In utility, only the difference between levels matter; thus it is necessary to normalise the values, and this is often done such that the sum of each mn , or mnop , is equal to zero. The model must also contain a term for the no-choice option. The model without interaction terms consists of (m (n 1) + 1) terms, while the model with interaction consists of (m (n 1) + p (p 1) + 1) terms. So, for a two-attribute ve-level model, a total of nine parameters are needed not accounting for interaction, and 29 are needed to account for interaction effects. However, in this paper, when reporting values we will include the redundant terms, thereby yielding a total of 11 (or 36) terms depending on the model type. It can be difcult to conduct conjoint analysis studies as the number of attributes and their associated levels increase because the number of responses required of a participant becomes very high. Conjoint analysis is often conducted on groups in order to obtain generalised information regarding preference for various attribute levels for use in designing products.

3.

Preference tool examination

To illustrate some differences between the PREFMAP analysis and MNL conjoint analysis modelling techniques, and to further explain PREFMAP analysis and conjoint analysis to the reader, we used a test function representing real, or goal preference. The two analysis models were then tested in their ability to reproduce this function using only information requested by the querying tool of each technique and subject to that models own constraints. This is not a comparison of PREFMAP analysis against conjoint analysis; it is an illustration of these two different modelling tools and the preference models that result from their application. Evaluating the merit of one model explicitly against the other is not realistic in this study because the necessary input data for each model is very different. PREFMAP is based upon continuous variable values, while conjoint analysis is applied to discrete variables. In these experiments, both PREFMAP and discrete choice analysis were used to develop a mathematical representation of both a predened unimodal and bimodal mathematical function. A unimodal mathematical function has a single global maximum, while a bimodal mathematical function has two local maxima. We explore both unimodal and bimodal mathematical goal functions because they represent different levels of

Journal of Engineering Design

633

modelling complexity, with the bimodal being more complex. The goal is to show that these two techniques yield different results and must be applied judiciously to design problems. 3.1. Unimodal examination We dened an example unimodal goal preference function as f (x1 , x2 ) = [(x1 2.5)(x1 + 3)(x1 + 2)]2 + [(x2 2.5)(x2 + 3)(x2 + 2)]2 . (10)

Downloaded by [University of Michigan] at 14:13 03 October 2011

This polynomial surface (see also Figure 2) has ridges and a single maximum (x1 , x2 ) = (0.86, 0.86) within the intervals [2, 2] for x1 and [2, 2] for x2 . The surface could represent the preference that an individual has for the location of a clock on a wall with relation to the centre of the wall. The design variables, x1 and x2 , could be vertical and horizontal location, respectively. We are interested in observing how well the two preference modelling techniques represent this goal preference model. To provide preference information, the design space was discretised into a 5-by-5 grid of equally spaced design points (uniform design). This discretisation was chosen because it is a logical way of discretising the space. A design point is simply one instance of the design dened by the combinations of the design variables. So, design point (1,1) would be the design associated with (x1 , x2 ) = (1, 1). We used this model and the discretised decision space as a way to inform both the PREFMAP and discrete choice query tools. 3.1.1. PREFMAP For the PREFMAP query, we rated the 25 design points by scaling the function values at the discrete points to be integers between 1 and 9, as shown in Table 1. This scale is typical of actual PREFMAP surveys, where 1 corresponds to least liked and 9 to most liked. This information was then used in Equation (3) to create a predicted model of preference. This information was then regressed to the characteristic PREFMAP equation. This table is associated only with PREFMAP evaluations because it is a rating of the various designs. The conjoint analysis MNL input data are based on discrete choice selections, not on ratings.

Figure 2.

Contour plot of model for unimodal comparison of preference tools. Contour separation = 100.

634

J.C. Kelly et al. Table 1. Values used to answer unimodal PREFMAP survey. x2 x1 2 1 0 1 2 2 1 2 4 5 2 1 2 2 4 6 3 0 4 4 7 8 5 1 5 6 8 9 6 2 2 3 5 6 3

Downloaded by [University of Michigan] at 14:13 03 October 2011

Figure 3.

PREFMAP interpretation of proposed unimodal preference model. Contour separation = 0.2.

Table 2. b0 0.54

PREFMAP solution b-values. b1 0.54 b2 0.59 b3 0.59 b4 0.01 b5 6.82

PREFMAP yielded an elliptical paraboloid centred at (x1 , x2 ) = (0.46, 0.46), Figure 3. The b-values associated with Equation (2) are shown in Table 2. The R 2 value for this model is 0.68 (68% of preference variance is explained by the model). Clearly, it would be impossible for a paraboloid model to identify the ridges associated with Equation (10). However, we do notice that these results provide a solution that identies the appropriate quadrant of the design map for further investigation and it identies the general trends well. Using the results of this PREFMAP study could allow a producer to properly identify an area of interest in the design space. Its optimal point indicates that it would provide the producer with a design point that closely matches the actual optimal design point. This shows us that the generality of this model to certain unimodal design situations may yield results that are desirable by the market of interest. It can be used to determine some valuable information about the market data, but it should be noted that identifying which variables to examine is a difcult issue in a real design problem.

Journal of Engineering Design

635

3.1.2.

Conjoint analysis

Downloaded by [University of Michigan] at 14:13 03 October 2011

The discrete choice analysis query was formed using Sawtooth Softwares Choice-Based Conjoint module (Orme 1999). Forty participants, modelled by computer agents, were used to answer the survey with their preferences dened by the function in Equation (10). Each unique survey consisted of 16 questions; each question had ve options: four were designs selected from the discrete set of equi-spaced designs consisting of two attributes and ve levels, and one was a no-choice option. So, for the MNL model, 40 16, 640 choices from a set of, 40 16 5, 3200 were needed in modelling. In the PREFMAP model, only 25 data points were collected, with integer ratings between 1 and 9. To highlight one assumption of the MNL model, we used Equation (10) to answer these questions in two different ways. First, the agents answered each question using Equation (10), such that the option presented in the set with the greatest functional value was chosen from the set. Second, each question was answered using Equation (10) along with an error term having a double exponential distribution. This random double exponential distribution term, characterised by = 0 and = 200, was added to the value derived in Equation (10), causing some improper choice selections. These data were then analysed with Sawtooths SMRT (Sawtooths Marketing Research Tool) module, and the resulting part-worths for each attribute level were analysed in an MNL model, thus creating an interpretation of the full-factorial marketplace (MacDonald et al. 2007). This describes how each design option is preferred relative to every other option. We then t natural cubic splines to this data to obtain a continuous and differentiable model of preference. The natural cubic splines t to the data were used in order to reconcile the discrete nature of the conjoint analysis survey with the continuous nature of the design variables. This use of conjoint analysis is not typical, but is also not unprecedented (Michalek et al. 2005, MacDonald et al. 2007). The premise is to determine spline-interpolated part-worths for the continuous set of design options. The cubic splines t to the data were specied to be natural cubic splines and the second derivate of the spline end conditions were set to zero. It was then possible to use these cubic splines to determine the probability of selection of any design within the design space. The MNL model derived from the rst set of answers mentioned earlier is shown in Figure 4, with part-worth values given in Table 3. These values are used in Equation (8); however, a

Figure 4. MNL model interpretation of proposed unimodal preference model without error distribution term. Contour separation = 0.1.

636 Table 3. 0 36.05

J.C. Kelly et al. MNL model part-worths for data without error distribution term. 11 45.75 12 28.31 13 25.52 14 60.04 15 11.50 21 45.50 22 28.50 23 25.63 24 59.90 25 11.53

Downloaded by [University of Michigan] at 14:13 03 October 2011

part-worth must also be included for the no-choice option, 0 . The model is polarised at an optimal value of (x1 , x2 ) = (1.06, 1.06) and appears relatively insensitive to the ridges of Equation (10). The optimal point is located near the discrete choice (x1 , x2 ) = (1, 1) available in the survey. Logistic regression models do not have an equivalent R 2 analysis to describe their goodnessof-t. But, a pseudo-R 2 value can be calculated; however, it should not be considered as directly equivalent to the R 2 that are reported in most regression situations. The pseudo-R 2 used in this 2 article is the Cox and Snell R 2 , which will be termed Rcox (Allison 1999). The model described 2 by Table 3 has an Rcox = 0.95. Figure 5 presents the MNL model results using the second set of answers, which included the random error term, with part-worth values presented in Table 4. This model, while not fully able to recreate the original model, is much more successful than that shown without the error distribution accounted for. The ideal point coincides with the ideal design option available in the discrete set. However, the contours are less polarised towards that point and more gradient 2 information is available to understand the preference space. This model has an Rcox = 0.82. Indeed, the error term is an important assumption of discrete choice analysis. Using perfect preference data without an error term, the MNL model quickly identies the most preferred option and denes the design space so that the most preferred option takes outstanding preference over all other options. At the extreme, using survey information from a large number of respondents answering perfectly according to a specied preference model, the MNL model would specify

Figure 5. MNL model interpretation of proposed unimodal preference model with error distribution term. Contour separation = 0.05. Table 4. 0 17.14 MNL model part-worths for data with error distribution term. 11 1.59 12 0.82 13 0.85 14 1.86 15 0.31 21 1.32 22 1.04 23 0.90 24 1.82 25 0.36

Journal of Engineering Design

637

precisely the most preferred option, but would obscure the slopes and curvatures of the surrounding design space. Thus, if the most preferred design was technically infeasible, which might occur in a marketing survey, then identifying acceptable alternative designs would be very difcult. A marketing survey will never have perfect data, it will always contain human error and individual differences in preference. This is accounted for in the mathematical model with the inclusion of simulated error. 3.2. Bimodal examination To further explore PREFMAP and MNL models, we dened an example bimodal goalpreference function as

Downloaded by [University of Michigan] at 14:13 03 October 2011

f (x1 , x2 ) =

1 e((x1 1)2 +(x2 1.2)2 )

1 e((x1 +1.3)2 +(x2 +1.2)2 )

(11)

This mathematical model has two points that represent locations of highest preference, one at (x1 , x2 ) = (1, 1.2) and the other at (x1 , x2 ) = (1.3, 1.2). These two points have the same function value; thus neither dominates the other. We would therefore hope that a model of preference would be capable of understanding such a bimodal response of users to such an incident, and further, be able to accurately identify those two optimal locations. The goal model, shown in Figure 6, was examined within the intervals [2, 2] for x1 and [2, 2] for x2 . The design space was again discretised into a 5-by-5 grid of equally spaced points, as was done in the unimodal case. We used this model and the discretised decision space as a way to inform both the PREFMAP and discrete choice query tools. 3.2.1. PREFMAP For the PREFMAP query, we ranked the 25 design points by scaling the function values at the discrete points to be integers between 1 and 9, as shown in Table 5. This information was then used in Equation (3) to create a predicted model of preference.

Figure 6. Mathematical model used to inform bimodal conjoint analysis and PREFMAP queries. Contour separation = 0.1.

638

J.C. Kelly et al. Table 5. Values used to answer bimodal PREFMAP survey. x2 x1 2 1 0 1 2 2 4 6 2 1 1 1 5 8 3 1 1 0 2 3 2 4 3 1 1 1 3 9 5 2 1 1 2 4 3

Downloaded by [University of Michigan] at 14:13 03 October 2011

Figure 7.

PREFMAP interpretation of proposed bimodal preference model. Contour separation = 0.2.

Table 6. b0 0.1

PREFMAP solution b-values for bimodal problem. b1 0 b2 0.21 b3 0.14 b4 0.67 b5 3.75

PREFMAP yielded a saddle point model showing greatest preference at (x1 , x2 ) = (2, 2), and a point of second greatest preference at (x1 , x2 ) = (2, 2), Figure 7. The b-values associated with Equation 2 are shown in Table 6. The R 2 value for this model was 0.42. Clearly, it would be impossible for a saddle point model to yield a bimodal solution in an unbounded scenario. Bounded scenarios allow this bimodality to be indicated, but only at the boundaries of the design space, as shown here. This bimodal function examination illustrates the case of saddle points in PREFMAP models. This interesting caveat of the PREFMAP model actually provides valuable insight into understanding the bimodal function. 3.2.2. Conjoint analysis The unimodal formulation of the MNL model only accounted for main effects and not interaction effects. The main effects are inuenced by each attribute independent of each other attribute.

Journal of Engineering Design Table 7. 0 17.38 MNL model part-worths for proposed bimodal model, main effects. 11 0.10 12 0.09 13 0.07 14 0.20 15 0.12 21 0.10 22 0.20 23 0.16 24 0.19

639

25 0.12

Table 8.

MNL model part-worths for proposed bimodal model, interaction terms. mn11 mn12 0.29 1.03 0.06 1.02 0.24 mn13 0.18 0.33 0.07 0.14 0.36 mn14 0.32 1.03 0.28 1.20 0.14 mn15 0.36 0.41 0.13 0.29 0.34

Downloaded by [University of Michigan] at 14:13 03 October 2011

11op 12op 13op 14op 15op

0.21 0.74 0.29 0.34 0.33

Equation (9) accounts for interaction terms, which link one attribute to another. Note that a part-worth value is again included for the no-choice option. Due to the nature of the bimodal design space in our example, it is appropriate to use this formulation of the MNL model because interaction effects should be signicant. Again, as in the unimodal example, the survey questions were answered by using the goal model to inform which discrete choice should be selected. Also the random error term was included. Again, the distribution term was characterised by = 0 and = 200, and was added to the value derived in Equation (11), causing improper choice selections. The main effects coefcients are presented in Table 7 and the interaction effects are shown in Table 8. Using cubic splines to t this data, the resulting model was developed (see Figure 8). In this gure, we see that the model predicts two points of local optimality, as we would expect based upon the example function. The location of these two locally optimal points are (x1 , x2 ) = 2 (1.08, 1.16) and (x1 , x2 ) = (1.02, 1.08). This model has an Rcox = 0.50. These points are in modest agreement with the actual optimal points on the real bimodal surface. This model also provides a great deal of gradient data that can be used in instances where the optimal points are infeasible in a larger design problem.

Figure 8. MNL model interpretation of proposed bimodal preference model with interaction terms. Contour separation = 0.02.

640

J.C. Kelly et al.

In general, it is tempting to conclude that using discrete choice analysis to develop an MNL model will provide us with a better model of the design space. On the surface, such a statement seems true. However, this statement neglects an important issue: data collection. It is worth recalling that the PREFMAP model required 25 integer inputs between 1 and 9, whereas the MNL model required 640 choices to be made from a set of 3200. The unimodal and bimodal results illustrate the capacity of the PREFMAP model and the MNL model to reproduce a predened preference function using each models query tool. In the case of bimodality, the PREFMAP model generates a saddle point surface, while the MNL model generates a bimodal surface. This highlights an inherent limitation of the PREFMAP model.

Downloaded by [University of Michigan] at 14:13 03 October 2011

4.

Linking preference and engineering

Now that we have described some techniques to model preference data, we will use them to explore shape preference for the design of a particular product. Two studies will be described that attempt to understand shape preference as it relates to bottle design. In the rst study, conjoint analysis was used to examine the design trade-offs between shape preference and engineering functionality in the design of cola bottles. In the second study, both conjoint analysis and PREFMAP were used to determine the same design trade-offs in the case of bottled water designs. This second study was done to reduce the impact that currently dominant shapes in the cola bottle sector have on the results. Participants for both studies were university-aged students from the Ecole Centrale de Nantes, in France. However, the participants from the rst study are not the same as those in the second. A Matlab program was developed to collect data from the participants, and the data were analysed using both commercial software (Sawtooth, conjoint analysis MNL) and newly developed software (Matlab program for PREFMAP analysis). 4.1. Cola bottle case study Branding through shape is important to the beverage industry. Much effort is put forth in creating unique and appealing bottle designs (Grimm 2000, Lamons 2001, Vanderbilt 2001). The bottle shape used for this study was dened by a spline t through ve points, and subjected to prescribed end conditions. Two of the ve points were considered variable, points R2 and R4 in Figure 9, and provided sufcient shape differentiation. Values for R2 and R4 were constrained between 25 and 50 mm. The other three points were xed parameters during optimisation. Point R1 was set for a perfectly vertical end condition, while R5 was set with an end condition to create an angle of 20 with the horizontal. In the engineering analysis, the variables were continuous. In the conjoint analysis, we discretised the design space with ve possible values for R2 and R4, spaced at an increment of 6.25 mm, thus creating a design space with 25 different designs. 4.1.1. Preference assessment The conjoint analysis survey was administered to 39 college-age individuals from the Ecole Centrale de Nantes, France. Each respondent answered a survey consisting of 16 questions, and each question offered the respondent four shapes and the no-choice option to choose from, as shown in Figure 10. The design space was discretised into a 5-by-5 grid of equally spaced points, yielding 25 possible designs (uniform design). Each individual received a unique survey, thus creating an efcient survey design. The data were analysed using Sawtooth Software to obtain part-worths for each variable and level of the two design variables.

Journal of Engineering Design

641

R1

R2

Downloaded by [University of Michigan] at 14:13 03 October 2011

R3

R4

R5

Figure 9.

Parametrised bottle shape.

I would choose none of these

Figure 10.

Screenshot of survey tool.

4.1.2.

Engineering model

From an engineering viewpoint, we desired the bottle shape that used the least amount of material to hold the desired amount of uid and resisted the internal pressure without plastic deformation. The internal gauge pressure for this experiment was chosen to be 300 kPa (60 psi). The

642 Table 9.

J.C. Kelly et al. Material properties of PET cola bottle. Tensile strength 25 MPa Poissons ratio 0.3

Youngs modulus 1.25 GPa

Downloaded by [University of Michigan] at 14:13 03 October 2011

analysis model was built using the nite element package ANSYS (Moaveni 2003). An axisymmetric solid model was created with a spline shape as previously described. This spline shape was given a uniform wall thickness treated as a design variable. The cap section was given a double wall thickness to prevent a high level of stress in that area (McEvoy et al. 1998). The bottles bottom section was designed according to an available patent since this is typically the critically stressed location of bottle designs (Rashid 2001); the wall thickness here was also increased slightly to accommodate increased stress. While this bottom section of the bottle is not at, it is axisymmetric; so it appears at to the user in a side view and is therefore consistent with the gures shown to respondents in the conjoint survey. The maximum von Mises stress within the bottle was calculated to ensure that the bottle would avoid exceeding the materials tensile strength. Cola bottles are typically blow moulded from polyethylene (PET); therefore, PET was selected in this design problem. Its material properties are shown in Table 9. A linear multi-objective formulation converted to a scalar substitution was used to nd the optimal designs using single objective optimisation techniques. min s.t. f (R2, R4) = w1 f1 (R2, R4) + (1 w1 )f2 (R2, R4), g1 (R2, R4) max 0 (12)

Here w1 is an objective weighting, f1 is the shape preference function, f2 is the material volume calculation, g1 is the maximum von Mises stress in the bottle and R2 and R4 are the shape variables. In this problem, wall thickness was xed at 1 mm to simplify the calculation and to make the trade-offs between the two objective functions clearer. The convex hull of the Pareto frontier set was calculated by varying w1 between 0 and 1. The Pareto frontier identies the set of all Pareto optimal points in the design space. A Pareto optimal point represents a single design in R2 and R4 that is non-dominated. As w1 changes, the optimal design point may also change due to different weightings for the two competing objectives. In this work, we use a sequential quadratic programming approach, available through the Matlab optimisation function, fmincon, to solve the optimisation. To develop the convex hull of the Pareto frontier, we solved Equation (12) using different values of w1 between 0 and 1 at intervals of 0.01. 4.1.3. Combining the data The preference model, obtained through survey data, is presented in Figure 11 along with the optimal shape. An MNL model that included interaction effects was used, along with splines t to a discrete set of potential bottle designs, to generate this contour plot. The values of the main effect and interaction effect part-worths are in Tables 10 and 11. Interaction terms were considered signicant according to the 2 log likelihood test and included in the model (Orme 1999). The 2 optimal design was (R2, R4) = (32.2, 31.6). This model has an Rcox = 0.40. The shape is similar to that of cola and other soda bottles in the market. The results of the conjoint study suggest that individuals gravitate towards a shape that they are familiar with. In fact, from the stand point of semantics (i.e. the message conveyed by the shape), the result suggests that participants may prefer this particular shape for a cola bottle specically because they have

Journal of Engineering Design

643

Downloaded by [University of Michigan] at 14:13 03 October 2011

Figure 11. MNL model describing preference for cola bottle shape, and most preferred shape. Contour separation = 0.01. Table 10. 0 0.82 MNL model part-worths for preference survey, main effects. 11 0.15 12 0.47 13 0.44 14 0.04 15 0.73 21 0.11 22 0.51 23 0.28 24 0.14 25 0.76

Table 11.

MNL model part-worths for preference survey, interaction effects. mn11 mn12 0.84 0.44 0.23 0.78 0.74 mn13 0.41 0.15 0.32 0.06 0.82 mn14 0.43 0.34 0.02 0.24 0.54 mn15 1.48 0.19 0.11 0.86 0.91

11op 12op 13op 14op 15op

0.66 0.07 0.43 0.27 0.11

encountered it as a cola bottle shape so often previously: This shape means cola bottle to these respondents. From the engineering perspective, the wall thickness should be as small as possible to reduce material volume, subject to the stress constraint. Further, the values of R2 and R4 will be minimised to further reduce the amount of material used to make the bottle. This is shown in Figure 12, which shows monotonic decrease towards (R2, R4) = (25, 25). Note that this gure is presented with a wall thickness of 1 mm to show the general trend. The optimal bottle design has (R2, R4) = (25, 25), and a wall thickness of 0.98 mm. The maximum von Mises stress for the bottles occurred in roughly the same place on the bottles bottom. More importantly, no bottle design will fail with a wall thickness of 1 mm. Therefore, the constant 1 mm wall thickness assumption made in the broader optimisation is justied. The convex hull of the Pareto solutions are shown in Figure 13 and are also plotted on the individual objective surfaces in Figure 14 to visualise the trade-off between maximising preference and minimising material volume. These two objectives are shown to compete. One may argue that

644

J.C. Kelly et al.

Downloaded by [University of Michigan] at 14:13 03 October 2011

Figure 12.

Monotonic surface representing bottle weight. Contour separation = 5e 6.

Figure 13.

Pareto frontier of solutions in the cola bottle design problem.

constraints restricting the interior volume of acceptable bottle designs may change the optimal design. This is true; however, the simplied model exposes the asserted quantication of design trade-offs between shape preference and engineering functionality. More rened engineering models are certainly possible. 4.2. Bottled water case study In the examination of cola bottles, we encountered issues that confounded our study. Namely, users appeared to have a distinct notion of what cola bottles should look like based upon market

Journal of Engineering Design

645

(a)

(b)

Downloaded by [University of Michigan] at 14:13 03 October 2011

Figure 14.

Pareto optimal solutions of cola bottle design plotted on preference (a) and engineering (b) models.

saturation with cola bottles whose shapes are similar to that of Coca Cola bottles. This result helped us identify that the MNL model can be useful in determining shape expectations of consumers. That is to say, given a specic context, users were quite adept at identifying a preference for a known shape. This was captured by the MNL model and gives us some condence that such a model is valuable for understanding shape preference in other contextual instances. In an attempt to limit a preconceived notion of an appropriate shape, we again conducted a bottle study. However, in this instance, we provided users with a different context for their evaluations. We asked them to express their preference for the shapes of bottled water designs. We believed that such an alteration of the experiment would help identify a different preference space that would not be so predictable. 4.2.1. Preference assessment

For the water bottle study, 40 college age students for Ecole Centrale de Nantes were queried about their preferred shape for a water bottle using both a discrete choice survey and PREFMAP survey. The discrete choice data were analysed, as before, using an MNL model with interaction effects. The design space was partitioned in the same way as in the cola bottle study using a uniform design with 25 designs. The results of this study, indicate that, once again, participants had an afnity for the bottle shape often associated with Coca Cola. This may indicate that, beyond a particular visual attraction, this shape may connotate a level of functionality. For instance, the waist of the bottle may be taken to indicate the proper location to place ones hand. The weight of the top versus the bottom of the bottle may assure users that the bottle will not tip over easily, i.e. its centre of gravity is low. Tables 12 and 13 show the associated beta values and Figure 15 shows 2 how the preference model varies with R2 and R4. This model has an Rcox = 0.62. We also queried users with the PREFMAP evaluation tool. The design space was discretised into a uniform design with 16 separate designs (two attributes, at four levels). Respondents then rated each of these bottle design on a scale from 1 to 9 (least to worst, respectively) based on how
Table 12. 0 0.28 MNL model part-worths for bottle water preference survey, main effects. 11 0.20 12 0.47 13 0.54 14 0.35 15 1.16 21 0.17 22 0.90 23 0.74 24 0.61 25 0.85

646

J.C. Kelly et al. Table 13. MNL model part-worths for bottled water preference survey, interaction effects. mn11 11op 12op 13op 14op 15op 1.36 0.81 0.42 1.56 0.19 mn12 1.31 1.15 0.26 1.04 1.68 mn13 0.02 0.14 0.55 0.20 0.63 mn14 2.07 0.65 0.28 1.53 0.90 mn15 0.62 1.15 0.67 0.87 1.59

Downloaded by [University of Michigan] at 14:13 03 October 2011

Figure 15. MNL model describing preference for bottled water shape, and most preferred shape. Contour separation = 0.02.

Figure 16. PREFMAP model describing preference for bottled water shape, and most preferred shape. Contour separation = 1.

Journal of Engineering Design Table 14. b0 0.0002 PREFMAP solution b-values for bottled water study. b1 0.015 b2 0.0049 b3 0.0047 b4 0.008 b5 8.08

647

Downloaded by [University of Michigan] at 14:13 03 October 2011

well they liked them for a bottled water design. This PREFMAP information was averaged over the entire population of respondents. Using this data, we can see how the two models, PREFMAP and MNL, relate to each other in regards to this bottle design. The PREFMAP space of shape preference is shown in Figure 16 and the b-values are shown in Table 14. The R 2 value for this model was 0.72. Notice that the PREFMAP solution is at the boundary, (R2, R4) = (25, 25), indicating that it will have a colocation with the engineering optimal solution. It is interesting to note that both the MNL and PREFMAP models suggest a rotated preference space; thus an inherent interaction between the R2 and R4 variables is found. Whats more, this trend indicates, in both cases, that there is a nearly 1:1 ratio of preference between R2 and R4. Thus, people appear to prefer R2 and R4 that are of equal proportions. 4.2.2. Combining the data

The engineering analysis for this bottle is exactly the same as the cola bottle design. Thus, we are not surprised to notice that the Pareto curve developed by combining the MNL shape preference results and the engineering objective provides information that is quite similar to that of the cola bottle (Figure 17). We notice that there is not a colocation of the optimally preferred and engineering optimal design and we can tell by looking at the preference space, and engineering space, gures that distinctly different shapes will be produced by the two differing objectives. In Figure 18, we present the MNL determined preference space, and engineering space with Pareto optimal design points shown on them to understand how varying R2 and R4 will affect the design. In the PREFMAP scenario, the optimal engineering design is colocated with the preferred shape design. Therefore, there is no Pareto frontier developed from the combined optimisation, only an optimal point for all weightings.

Figure 17.

Pareto frontier of solutions in the bottled water design problem using MNL for preference.

648

J.C. Kelly et al.

(a)

(b)

Downloaded by [University of Michigan] at 14:13 03 October 2011

Figure 18. models.

Pareto optimal solutions of bottle water design, using MNL, plotted on preference (a) and engineering (b)

4.3. Discussion This study indicates that users may have a particular preference for the shape of bottles based on an association with historically well-marketed bottle shapes. Further, the shape may actually provide an affordance for the user, or a suggestion of how to use the object. We also note that this study limited users to a selection between two variables, R2 and R4. If the bottle were parametrised in a different manner, then it is likely that different results would be found. This study can only speak to the impact of these two variables on shape preference, subject to the constraints imposed by the bottles architecture as explained previously. However, this study does indicate that we can discover distinct relationships between the variables R2 and R4, and how they are related to shape preference by using both PREFMAP and discrete choice analysis. Further, we can use that information along with an engineering model to learn about the trade-offs between the goals of minimising material used, and maximising shape preference. Finalising the form of a product occurs in the detailed design phase of the design process. Prior to that, several concepts are devised and evaluated until one design concept is agreed upon. Information regarding shape preference could be effectively utilised during this detailed design phase. Designers and engineers currently make informed decisions regarding product form. This information can come from marketing demands, engineering specications and designer interpretation of user wants. With a quantitative model of shape preference, this information can be mathematically incorporated into the design optimisation process during the nal stages of design. Meaningful quantication of a products shape preference is possible using standard methods from psychology and marketing. The methods have limitations, and experiments to elicit preference must be conducted carefully. In the presented study, we used two variables (or attributes) to dene the variations in a particular product offering. Doing so allowed a relatively easy generation and interpretation of results. A more complex design model may describe the product with more variables. In this case, the amount of data needed for statistical validity of the MNL model would increase signicantly. To properly create the proposed surveys, the denition of the survey must be made by applying design of experiments techniques, in order to limit the size of the survey and also to improve the condence of the estimates. Two factorial designs must be proposed: one to dene the designs (congurations), and one to dene which congurations will be integrated in the choice-set proposed to each user. The rst factorial design must be generally balanced and orthogonal (or D-optimal), and many papers in discrete choice analysis deal with the denition of the second factorial design (Huber and Zwerina 1996). Several tens of variables can be considered in discrete

Journal of Engineering Design

649

Downloaded by [University of Michigan] at 14:13 03 October 2011

choice analysis. An example with 14 variables, concerning vehicle headlight form preference, is, for example, proposed in (Swamy et al. 2007). The survey had in this case 64 designs, involved in a choice set of 72 questions, asked to 18 users. The respondent fatigue is of course the main limitation to the size of the problem considered. With the PREFMAP model, the increase in the number of variables leads to an increase in the number of coefcients to estimate in the model. To reduce the number of coefcients, a classical way is to carry out a principal component analysis on the design variables and to regress preference on the two or three rst principal components (McEwan 1996). In the same way, partial least-square regression (PLS) can be used with several tens of variables. The experimental design is optimised according to the form of the model, the D-optimality being generally used (Mitchell 1974). A quantication of shape preference allows it to be included along with engineering attributes to explore products that are optimal in a multidisciplinary design sense, specically exploring tradeoffs between form and function. In the study presented, form and function have distinct trade-offs that meaningfully affect each other. Balancing these trade-offs is still a decision that the designer must ultimately make, presumably of quality higher than without the trade-offs quantication.

5.

Conclusions

We proposed and implemented a procedure to collect information regarding shape preference, organise it into a model and incorporate it within a physics-based design optimisation formalism. In the example of bottle design, our ndings showed that there is a dislocation between what is most appealing to users and what is most sound technically. Intuition of industrial designers need not be the only informative evidence to support a particular stylistic desire, and strictly meeting a particular shape preference can have a detrimental effect on product performance. We examined PREFMAP and MNL as the preference modelling techniques. Both techniques are capable of providing insights into shape preference through their mathematical models, which in turn can be incorporated within a mathematical optimisation framework. Other methods may be also studied for improved efciency and accuracy. However, some important product design considerations remain unexamined in this work. A primary one is devising appropriate ways to identify the right attributes of a design and their associated design variables, based on which the models will be built. Ensuring that the proper design variables are identied will increase the effectiveness of determining shape preference. Acknowledgements
The authors are grateful to the US National Science Foundation Graduate Student Research Fellowship.

References
Allison, P., 1999. Logistic regression using SAS : theory and application. Cary, NC: SAS Publishing. Bauerly, M. and Liu,Y., 2006. Computational modeling and experimental investigation of effects of compositional elements on interface and design aesthetics. International Journal of HumanComputer Studies, 64 (8), 670682. Chang, J.J. and Carroll, J.D., 1972. How to use PREFMAP and PREFMAP-2: programs which relate preference data to multidimensional scaling solutions. Unpublished manuscript. Murray Hill, NJ: Bell Telephone Labs. Coxon, A.P.M., et al., 1982. The users guide to multidimensional scaling. London: Heinemann. Fechner, G.T., 1897. Vorschule der Aesthetik. Leipzig, Germany: Breitkopf & Hrtel. Green, C.D., 1995. All that glitters: a review of psychological research on the aesthetics of the golden section. Perception, 24 (8), 937968. Green, P.E. and Srinivasan, V., 1990. Conjoint analysis in marketing: new developments with implications for research and practice. Journal of Marketing, 54 (4), 319.

650

J.C. Kelly et al.

Green, P., Krieger, A., and Wind, Y., 2001. Thirty years of conjoint analysis: reections and prospects. Interfaces, 31 (3), 5673. Grimm, M., 2000. Drink me. Coca Cola. American Demographics, 22 (2), 6263. Guadagni, P.M. and Little, J.D.C., 1983. A logit model of brand choice calibrated on scanner data. Marketing Science, 2 (3), 203238. Huber, J. and Zwerina, K., 1996. The importance of utility balance in efcient choice designs. Journal of Marketing Research, 33 (3), 307317. Lamons, B., 2001. Absolut fortune: one liquors success story. Marketing News, 35 (4), 8. Lidwell, W., Holden, K., and Butler, J., 2003. Universal principles of design. Gloucester, MA: Rockport Publishers. Liu, Y., 2003a. The aesthetic and the ethic dimensions of human factors and design. Ergonomics, 46 (1314), 12931305. Liu, Y., 2003b. Engineering aesthetics and aesthetic ergonomics: theoretical foundations and a dual-process research methodology. Ergonomics, 46 (13-14), 12731292. Louviere, J.J., Hensher, D.A., and Swait, J.D., 2000. Stated choice methods: analysis and applications. Cambridge, UK: Cambridge University Press. MacDonald, A.S., 2001. Aesthetic intelligence: optimizing user-centred design. Journal of Engineering Design, 12 (1), 3745. MacDonald, E.F., Gonzalez, R., and Papalambros, P., 2007. The construction of preferences for crux and sentinel product attributes. Journal of Engineering Design, 20 (6), 609626. McEvoy, J.P., Armstrong, C.G., and Crawford, R.J., 1998. Simulation of the stretch blow molding process of PET bottles. Advances in Polymer Technology, 17 (4), 339352. McEwan, J., 1996. Preference mapping for product optimization. Data Handling in Science and Technology, 16, 71102. Michalek, J., 2004. Demand modeling using discrete choice analysis Part 1 and Part 2. Michalek, J.J., Feinberg, F.M., and Papalambros, P.Y., 2005. Linking marketing and engineering product design decisions via analytical target cascading*. Journal of Product Innovation Management, 22 (1), 4262. Mitchell, T., 1974. Computer construction of D-optimal rst-order designs. Technometrics, 211220. Moaveni, S., 2003. Finite element analysis: theory and application with ANSYS. Upper Saddle River, NJ: Prentice Hall. Nagamachi, M., 1995. Kansei engineering: a new ergonomic consumer-oriented technology for product development. International Journal of Industrial Ergonomics, 15 (1), 311. Nagamachi, M., 1997. Kansei engineering and comfort. International Journal of Industrial Ergonomics, 19 (2), 7980. Norman, D.A., 2002. The design of everyday things. New York: Basic Books. Orme, B., 1999. CBC user manual, version 2. 0 [online]. Sawtooth Software, Inc., Sequim, WA. Available from: http://www.sawtoothsoftware.com [Accessed 12 November 2008]. Orsborn, S. and Cagan, J., 2009. Multiagent shape grammar implementation: automatically generating form concepts according to a preference function. Journal of Mechanical Design, 131 (12), 121007-1121007-10. Orsborn, S., Cagan, J., and Boatwright, P., 2009. Quantifying aesthetic form preference in a utility function. Journal of Mechanical Design, 131 (6), 061001-1061001-10. Papalambros, P. and Wilde, D., 2000. Principles of optimal design: modeling and computation. 2nd ed. New York: Cambridge University Press. Park, H., 2004. A quantication of proportionality aesthetics in morphological design. Thesis (PhD). Taubman College of Architecture and Urban Planning, University of Michigan, Ann Arbor. Park, H.J., Economou, A., and Papalambros, P.Y., 2005. Hermes: a computational tool for proportionality studies in design. In: B. Martens and A. Brown, eds. A learning from the past a foundation for the future (Special publication of papers presented at the CAAD futures 2005 conference), 2022 June, Vienna, Austria. Vienna: IRIS-ISIS Publications, 99108. Petiot, J.F. and Chablat, D., 2003. Subjective evaluation of forms in an immersive environment. In: Proceedings of Virtual Concept 2003, 57 November, 2003, Biarritz, France. Biarritz, France: ESTIA. Petiot, J.F. and Grognet, S., 2006. Product design: a vectors eld-based approach for preference modelling. Journal of engineering design, 17 (3), 217233. Pye, D., 1978. The nature and aesthetics of design. New York: Herbert. Rashid, A., 2001. Plastic container having base with annular wall and method of making the same. US Patent 6,176,382. Ryan, M. and Farrar, S., 2000. Using conjoint analysis to elicit preferences for health care. British Medical Journal, 320 (7248), 15301533. Swamy, S., Orsborn, S., Michalek, J., and Cagan, J., 2007. Measurement of headlight form preference using choice based conjoint analysis. In: Proceedings of the ASME 2007 international design engineering technical conferences & computers and information in engineering conference, Las Vegas, NV, United States. New York: American Society of Mechanical Engineers, Vol. 6, 197206. Tjalve, E., 1979. A short course in industrial design. Boston: Newnes-Butterworths. Tybout, A.M. and Hauser, J.R., 1981. A marketing audit using a conceptual model of consumer behavior: application and evaluation. The Journal of Marketing, 45 (3), 82101. Vanderbilt, T., 2001. Bottled up. International Design, 48 (3), 4449.

Downloaded by [University of Michigan] at 14:13 03 October 2011