Concept convergence process: A framework for improving product concepts

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Concept convergence process: A framework for improving product concepts q

Manu Augustine a, Om Prakash Yadav b,*, Rakesh Jain a, Ajay Pal Singh Rathore a

a Mechanical Engineering Department, Malaviya National Institute of Technology, Jaipur, Indiab Department of Industrial and Manufacturing Engineering, North Dakota State University, Fargo, ND 58105, USA

a r t i c l e i n f o

Article history:Received 2 July 2009Received in revised form 22 April 2010Accepted 13 May 2010Available online 16 May 2010

Keywords:Concept selectionConcept convergenceFuzzy logicProduct design and development

a b s t r a c t

Concept selection is one of the most important decisions in product development, since success of thefinal product depends on the selected concept. The exploration and evaluation of alternatives early inthe product development (PD) process reduces the amount and magnitude of changes in later stagesand increases the likelihood of success of new product development (NPD) projects. Though, currentlyavailable methods attempt to select the best concept from the available set of initial concepts, they donot help create an improved concept based on the learning and knowledge generated through the eval-uation of initial concepts. The paper proposes a framework for selecting and/or evolving improved con-cepts through a rigorous concept evaluation and convergence process. The concept convergence processallows bringing together the best (desirable) traits from the initial set of concepts and creates a new set ofhybrid concepts. The framework uses a fuzzy inference process for evaluating each initial concept againstidentified decision criteria, thus generating hybrid concepts to select the best feasible concept undergiven cost and technological constraints. The approach is demonstrated using a steering wheel conceptgeneration example.

Published by Elsevier Ltd.

1. Introduction

Early design decisions during the PD process have become anincreasingly important prerequisite competency to ensure corpo-rate success in today’s global market environment. Decisions madeearly in the PD process significantly influence an organization’scapability to reduce development time and cost, and producehighly reliable products. Moreover, it helps organizations to movetowards First Product Correct—getting it right the first time andevery time—philosophy that is the ability to transition from designconcept to a finished product with absolute certainty of a correctresult (Yadav & Singh, 2008). With this in mind it seems particu-larly imperative to make early design decisions in the most optimalmanner possible.

The PD process is the sequence of steps or activities that anenterprise employs to conceive, design, and commercialize a prod-uct. This process starts with the initial creation of a wide set ofalternative product concepts, followed by the subsequent narrow-ing of alternatives and increasing specifications of a product untilthe product can be reliably and repeatedly produced by the pro-duction system (Ulrich & Eppinger, 2000). In PD process, conceptselection is one of the most important decisions, since success ofthe final product depends on the selected concept. A poor concept

selection can rarely be compensated at later design stages and cangive rise to a great expense of redesign costs (Pahl & Beitz, 1996).Many in the design community accept the notion that more than70% of the final product quality and cost are determined in the con-ceptual design phase (Ishii, 1995; Nepal, Monplaisir, & Singh,2005). Therefore, thorough exploration and evaluation of alterna-tives early in the design process can significantly help reduce thechanges in later stages and increase the likelihood of success ofnew product development (NPD) projects (Chin & Wong, 1999).This paper intends to provide a structured methodology that helpscreate improved concepts based on the learning and knowledgegenerated through the evaluation of an initial set of generatedconcepts.

Concept selection is the process of evaluating concepts with re-spect to customer needs and other relevant criteria, and selectingone or more concepts for further investigation and development.Concept screening and scoring are popular decision matrix basedmethods that are often used to narrow down the number of con-cepts to a select few. Unfortunately, the typical construction ofdecision matrices makes it difficult to ensure that promising con-cepts are not erroneously eliminated (Mullur, Mattson, & Messac,2003). Additionally, detailed and precise information regardingproduct concepts is normally not available at this early stage ofproduct development, and thus decisions are always made usingqualitative information and judgment (Rosenman, 1993). More-over, none of the existing concept selection methods address theissue of concept improvement. Mostly the focus is on elimination

0360-8352/$ - see front matter Published by Elsevier Ltd.doi:10.1016/j.cie.2010.05.009

q This manuscript was processed by Area Editor Satish Bukkapatnam.* Corresponding author. Tel.: +1 701 3231 7285; fax: +1 701 231 9185.

E-mail address: [email protected] (O.P. Yadav).

Computers & Industrial Engineering 59 (2010) 367–377

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of poor design concepts. Moreover, after the stage of concept selec-tion, very little attention is paid to the concepts that are rejected.Nevertheless, there is always some possibility of these rejectedconcepts containing some traits, which if incorporated with the fi-nal concept, might contribute positively to further improve it.Although the existing methods have their own merits, none offersany structured mechanism to capture the knowledge generatedthrough concept evaluation to improve design concepts.

This paper proposes an effective methodology namely conceptconvergence process for selecting and/or evolving improved designconcepts through a rigorous concept evaluation and convergenceprocess. The methodology essentially involves evaluating an initialset of concepts against identified selection criteria and subse-quently generating improved hybrid concepts. This makes the pro-posed approach radically different from the traditional evaluationtechniques. The concept convergence process allows bringing to-gether the best (desirable) traits from the initial set of conceptsand creation of a new set of hybrid concepts. Later, the best feasiblehybrid concept is selected against given cost and technologicalconstraints. In order to deal with uncertainty and fuzziness inthe evaluation process, fuzzy logic approach is used to aggregatethe ratings given to concept alternatives against selection criteria.

The rest of the paper is organized as follows: Section 2 providesa brief review of the existing literature on concept selection. Sec-tion 3 presents the proposed methodology for improving productconcepts through the concept convergence process. Finally, Section4 presents some concluding remarks.

2. Literature review

Product concept selection is a very unique multi-criteria deci-sion making problem where decisions are usually made based onhighly imprecise knowledge regarding the decision criteria. Vari-ous researchers have attempted to address this unique problemof concept selection through the use of various multi-criteria deci-sion making approaches, such as Quality Function Deployment(QFD) (Hauser & Clausing, 1988), Analytic Hierarchy Process(AHP) (Saaty, 1981), Pugh Matrix (Pugh, 1991), multi-criteria opti-mization (Ip, Yung, & Wang, 2004; Ebadian, Rabbani, Jolai, Torabi,& Moghaddam, 2008) and fuzzy logic (Zadeh, 1965).

The most widely used methods in industry involve decisionmatrices (Pahl & Beitz, 1984). Decision matrix based methods gen-erally involve assigning weights to each selection criteria; ratingeach product concept based on its estimated ability to satisfy eachof those criteria; and summing up to achieve an overall score foreach concept. These methods are highly suitable especially in thosescenarios where decision making is mostly dominated by qualita-tive criteria. Among the matrix-based concept selection methodol-ogies (CSMs) available in literature, the methodology given byPugh (1991) is perhaps the most basic popular approach for con-cept selection. It has been employed for initial concept screeningto eliminate highly infeasible concepts, when the number of initialconcepts is very high. The Pugh’s method does not assign weightsto the selection criteria (they all have equal weights) and each con-cept is rated as ‘‘better than,” ‘‘equal to,” or ‘‘worse than” a refer-ence concept. Ulrich and Eppinger (2000) propose an extensionto Pugh’s method to make a final selection from the concepts thathave passed the Pugh’s screening process. In this case, weights areassigned to the selection criteria and concepts are given ratingsfrom a rating scale. Takai and Ishii (2004) propose modificationsto the Pugh’s methodology by introducing the concept of probabil-ity. Their approach involves evaluating the concept alternatives onthe basis of their probability of achieving certain set targets.

King and Sivaloganathan (1999) opine that one of the major short-comings of matrix-based CSMs centered on the Pugh’s method is their

inability to deal with coupled decisions. QFD based CSMs appear to bea good solution to this problem. The interaction chart of the QFD ma-trix helps indicate those product concepts that can exist together andtherefore reinforce each other. It also shows which concepts arehighly incompatible with each other. King and Sivaloganathan(1999) propose the Flexible Design CSM, with emphasis on the impor-tance of coupled decisions. This methodology follows a QFD like pat-tern, but with a significant difference that the interaction chart isreplaced with a compatibility chart in the decision matrix.

Although decision matrices provide a simple and systematicapproach to the problem of concept selection, they fail in emphasiz-ing on the relative importance of concept evaluation criteria. Theevolution of AHP-based CSMs can be mostly attributed to the needto overcome this shortcoming (Okudan & Shirwaiker, 2006). TheAHP, which was originally proposed by Saaty (1981), has been exten-sively used both in academic research as well as in industrial practiceto solve multiple-criteria decision-making problems. It basically in-volves a systematic decomposition of a given problem into a hierar-chical form to perform simple pair-wise comparisons and rankingsfor synthesizing importance weights at different levels of the hierar-chy (Augustine, Jain, & Yadav, 2010). One of the notable AHP-basedCSMs specifically aimed at design decision making was developedby Marsh, Moran, Nakui, and Hoffherr (1991). Mullens and Armacost(1995) propose a two-stage CSM wherein the Pugh’s method is usedin the first stage for initial concept screening, and in the second stage,AHP is used for final quantitative evaluation of the concepts. Ayagand Ozdemir (2006) propose the use of Analytic Network Process(ANP) in concept selection, to accommodate for the variety of inter-actions, dependencies and feedback between higher and lower levelelements of a hierarchy in a better way.

AHP-based approaches have been the mainstay in multi-criteriadecision making in the past few decades. However when it comesto handling uncertainties involved in weighting and scoring vari-ous criteria and alternatives, crisp numerical values do not suffice.The use of fuzzy logic (Zadeh, 1965) in conjunction with AHP hasemerged as a solution to this problem. As an example of incorpo-rating fuzzy logic in AHP, Ayag (2005) gives a fuzzy-AHP-basedCSM for use in an NPD environment. There are many more inter-esting applications of fuzzy logic in the development of CSMs thatcan be observed in the literature. For instance Thurston and Carna-han (1992) propose the application of fuzzy set theory to a multi-ple-attribute engineering design evaluation process. Wang (2002)extends Pugh’s method with fuzzy set theory to measure the qual-ity of a chosen concept. Jiao and Tseng (1998) propose a fuzzyranking methodology for conceptual design evaluation in the con-text of mass customization. Wang (2001) provides fuzzy outran-king models, where linguistic terms (fuzzy numbers) are set bythe designer and used to compare various design concepts. Con-cepts that are outranked (dominated) are removed, leaving onlythose that merit further development.

Another popular concept selection approach found in the litera-ture is based on utility theory (Thurston, 1990). Utility theory is amulti-attribute decision making approach which in general involvesthe association of utility functions with decision criteria, and theevaluation of alternatives on their overall utility across the criteria.Pahl and Beitz (1984) were among the first to include utility theoryinto a systematic design method. Using utility theory in conceptselection Thurston and Locascio (1994) attempt to build on theshortcoming of existing approaches in not being able to guide thedecision-maker towards appropriate trade-offs. Although utilitytheory based CSMs have proved to overcome most of the limitationsof CSMs based on other approaches, its acceptance in the engineer-ing design community has not been very encouraging (Okudan &Shirwaiker, 2006).

Another category of CSMs supports the notion of rigorous numer-ical and optimization techniques. Optimization-based approaches

368 M. Augustine et al. / Computers & Industrial Engineering 59 (2010) 367–377


are primarily used during the detailed phase of the design process.Relatively few optimization-based approaches for concept selectionhave been proposed till date. Notable among these few include theCSM using s-pareto frontiers as given by Mattson and Messac(2002); using hypothetical equivalents and inequivalents as givenby See and Lewis (2002); using genetic algorithm and combinatorialoptimization as given by Crossley, Martin, and Fanjoy (2001); andusing linear physical programming as given by Mullur et al. (2003).

To summarize the discussion on existing CSMs, it can be saidthat although powerful in many cases, methods based on decisionmatrices may fail to aid designers in selecting potential conceptalternatives. This is simply because decision matrices are basedon an inadequate mathematical construct and it is possible to mis-interpret the results of the concept selection process, as theweights may not be a true reflection of the decision-maker’s pref-erences (Mullur et al., 2003). Further, the existing methods do nothave any mechanism to capture the knowledge and learning gen-erated during concept evaluation process and to utilize it for fur-ther improvement of concepts. Although some variants of thePugh’s methodology (e.g. Ulrich & Eppinger, 2000) have attemptedconcept improvement by combining individual concepts in theconcept selection phase of the PD process, these are not genericallyapplicable and failed in detailing out a structured procedure forimprovement. On the other hand, multi-objective optimizationmethods can bring additional rigor to the concept selection pro-cess, but these methods are primarily used during the detailedphase of the design process.

The research work presented in this paper derives motivationfrom the belief that rather than selecting the better among avail-able alternatives, the progression towards better solutions by com-bining strengths of all available concepts within given constraintsis a more robust approach for concept improvement. The proposedmethodology is built on the existing decision matrix models butpresents a different approach by assigning expectation levels toselection criteria instead of weights. Further it provides a mecha-nism to screen concept traits instead of whole concepts using thecriteria expectation levels in order to identify superior traits orcharacteristics from each concept.

3. Proposed approach

The proposed methodology suggests a new approach for bring-ing out the preferences of decision-makers for each decision crite-ria. In the proposed approach, the criteria are treated like sieves,and the importance of each criterion is reflected in its sieve poresize. In a way, the sieve pore size of a criterion represents its expec-tation level regarding the set of concept alternatives. Higher theexpectation level of a given criterion, smaller will the pore sizebe, and hence finer (better) a given concept has to be to passthrough that criterion sieve.

Another unique feature of the proposed methodology is in theway ratings are assigned to individual concepts with respect to theselection criteria. Each criterion is decomposed into its sub-criteriaand is represented as a tree structure. The concepts are rated with re-spect to the lower level sub-criteria because it is fairly easy to makemore accurate comparison and judgment at lowest level. These rat-ings are then aggregated towards the top of the tree to assign a finalrating to the given main criterion. In the final stages of the method-ology, the concept traits that have passed through sieves success-fully are used to generate hybrid concepts. These new conceptsgenerated out of the initial set of concepts will almost certainly ex-ceed the expectations of the decision-maker in all performanceaspects.

Fig. 1 illustrates the overall concept convergence and selectionmethodology, and the following sections delineate the proposed meth-

odology in a step-wise manner along with a suitable example involvinga firm that is developing a steering wheel for a luxury class car.

3.1. Step-I: establish a cost ceiling for concepts screening

Concept generation and selection without giving any due con-sideration to cost is a futile exercise. A concept may be very goodas far as the performance is concerned; it is not a very promisingconcept if the customer rejects the product due to its high cost.Therefore, cost consideration must be incorporated in any conceptgeneration and selection methodology. Although, there may be in-stances when cost is not at all an important factor compared tohigh performance demand. In such cases, the stage of the method-ology where treatment of the cost factor is carried out may be by-passed. It is therefore better to keep a provision for costconsideration in a methodology to generalize it.

In the first step, it is proposed to establish a cost ceiling forscreening the initial set of concepts as well as the final set of hybridconcepts. This helps us to screen those concepts whose estimatedcost value lies below the pre-determined cost ceiling and takethem to the next step. Market potential and competition analysisare useful techniques that the team could use to arrive at a suitablecost ceiling for their product. This involves clearly identifying themarket segment to be targeted. The identified segment of the mar-ket is then placed on an economic scale to find out the payingpower of the customers. To do this, a market survey may be con-ducted to find the average income of the target market. This setof information along with the price range of competing productscan be taken as the basis for a rough estimate of the cost ceiling va-lue. The detailed discussion on estimation of cost ceiling is beyondthe scope of this paper.

To demonstrate the applicability of the proposed framework,we consider an example of a steering wheel concept selection pro-cess for a luxury car. Based on market potential and competitionanalysis, the team has decided on a cost ceiling value that has al-lowed four concepts from the initial set of concepts generated bythe design team to pass through. Fig. 2 and Table 1 provide detailedinformation on the four steering wheel concepts.

3.2. Step-II: identify evaluation criteria

To effectively evaluate concepts, identification of appropriateevaluation criteria is an essential and key step in concept selectionprocess. Generally, these criteria should manifest customer, corpo-rate, and regulatory requirements as well as manufacturing con-straints and limitations. At this stage, the design team mustmake sure that the criteria that are decided upon are as generalizedas possible. For example, suppose one of the criteria decided uponby the team is ease of steering, and another is ease of access to fea-tures, then instead of taking these two criteria separately, the teamshould find a more general way of expression, let us say ease of use.This will encompass both the above-mentioned separate criteria aswell as many more of their sort. In short, the team should makesure that none of the identified selection criteria are in any waya part of any other criterion that has already been included inthe list. Henceforth the criteria identified in this step will be ad-dressed to as ‘main criteria’. The design team has decided to in-clude the following four main criteria for evaluation purpose:aesthetics, convenience of usage, durability, and safety (see Fig. 3).

3.3. Step-III: decompose each main criterion into sub-criteria

In the decomposition process, each main criterion is broken intosub-criteria, which may further be decomposed to lower level sub-criteria. This decomposition process continues until a set of sub-cri-teria that could be easily rated based on available information is

M. Augustine et al. / Computers & Industrial Engineering 59 (2010) 367–377 369


achieved. Therefore, while decomposing these criteria into sub-cri-teria, the team must make sure that each main criterion is brokendown to a level where adequate information necessary to rate the

concept is available and the team can make fairly accurate judgment.Fig. 3 demonstrates the hierarchical decomposition of all the fourmain criteria, into their respective lower level sub-criteria.

Depressible portion with switch for A.C./heater underneath

Soft, smooth, ultra high quality urethane cover over center

Soft, smooth, ultra high quality urethane cover on spokes

Soft, smooth, ultra high quality urethane rim cover

Switch for rim heater

Power switch for stereo/radio

Switch for A.C/heater blower

Light switch

Metallic color coated plastic cover

Button for changing channels

Granulated thick plastic rim cover

Visual display screen on upper half of fixed center

Urethane cover over lower half of fixed center

Polished teak-wood cover over spokes

Urethane cover over rim

Power switch for stereo/radio

Teak wood rim cover

Soft leather cover

Light switch

Button for changing channels

Urethane covering

(a) Steering wheel concept-I (b) Steering wheel concept-II

(c) Steering wheel concept-III Steering wheel concept-IV

Fig. 2. CAD drawing of four concepts.

Decompose each main criterion into sub-criteria (sieves)

Establish a ‘sieve pore size’ for each criterion (Xj)

Rate concepts with respect to each sub-criterion

Aggregate the ratings of each concept with respect to the sub-criteria to get its main

ratings. (Zij)

For all i & a given j,

is Zij > Xj?

Retain Zij

Take Zij to form Concept roots Form the set of all theoretically

possible Hybrid roots

YES

NO

Customer viewpoint

Company viewpoint

Benchmarking viewpoint

Establish cost ceiling and screen generated concepts

with the ceiling

Identify selection criteria

Extract the set of technically feasible hybrids

Extract the set of hybrids whose rough cost estimate falls below the cost ceiling.

This final set of hybrids can be taken up for further development by the team

Fig. 1. Flow-chart for the proposed methodology.



3.4. Step-IV: allocate a ‘‘sieve pore size” to each main criterion

From this step onwards, each main criterion is treated as asieve. These sieves act as gates to screen out the concept traits,which do not meet the expectation levels of the design team. Itis therefore important to establish expectation levels for each cri-terion of the product concept. Higher the importance of a given cri-terion, higher will be the expectation level for that criterion. Eachcriterion (or sieve) is assigned a ‘sieve pore size’ on a scale of 0–10. A high score indicates a finer (or smaller) sieve pore size. Thefiner sieve pore size for any given criterion means higher expecta-tion levels and therefore, these finer sieves will stop concepts frompassing through if their rated scores do not meet expectation lev-els. On the contrary, a low score indicates a liberal sieve, which willallow most of the concepts to pass through.

The problem of establishing an expectation level (sieve poresize) for each main criterion should encompass different perspec-tives. In this study, we suggest to include three main perspectivesnamely: customer’s perspective – how important that criterion isfrom customer’s point of view; company’s perspective – capabilityof the manufacturing firm in achieving the given criterion and itsmatch with the company’s overall market strategy; and bench-marking perspective – the current rating of the product amongexisting competitor’s products and future target for a given crite-rion. The outcome of this step will be a sieve pore size for eachmain criterion considered in the concept selection problem. Inthe example of steering wheel concept selection, the design teamfirst assigned expectation levels to each main criterion, keepingin mind these three different perspectives and thus arrived at threedifferent ratings for each criterion. The overall expectation level

Table 1Detailed description of four steering wheel concepts.

Concept 1Spokes Two in numbers, rectangular section, urethane coveringRim Hollow tubular, teak wood covering, urethane cover at intersection with spokesMain features Horn at center, air bag within center with soft leather cover

Accessoryfeatures

Light switch (press button type) on right spoke, power switch for stereo/radio near center on left spoke, single button for changing channels on rightspoke near center

Concept-IISpokes Three in number, rectangular section, soft plastic cover (metallic color coating)Rim Hollow tubular, soft, thick plastic covering with granulated surfaceMain features Fixed center; air bag within center with soft plastic cover (metallic color); horn in center

Accessoryfeatures

Light switch on extreme right of fixed center; switch for stereo/radio at center of left spoke; channel change button in the middle of right spoke;embedded rim heater beneath plastic cover, switch for rim heater on extreme top of the fixed center; switch for AC/heater blower on extreme top ofthe fixed center

Concept-IIISpokes Three in number, rectangular section, soft smooth, ultra high quality urethane coveringRim Hollow tubular; soft, smooth, ultra high quality urethane coveringMain features Air bag beneath center with soft, smooth, and ultra high quality urethane cover over center; horn on each spoke beneath cover

Accessoryfeatures

AC/heater blower ON/OFF with depressible center

Concept-IVSpokes Two in numbers; rectangular section; polished teak wood coveringRim Hollow tubular; urethane covering except at intersection with spokes; intersections having teak wood covering; soft leather strip wound over the

rimMain features Fixed center (divided into two halve); air bag beneath the lower half having urethane covering horn on both spokes beneath the cover; horn in center

Accessoryfeatures

Visual display screen on upper half of the center showing the rear side view while in reverse gear

Orientation beautyof spokes

Sophisticated look

Aesthetics

Gloss

Ergonomic advantage gained by accessory

features

Accessibility of features

Convenience of use

Grip

Accessibility of main features

Accessibility of accessory features

Durability of rim cover

Reliability of features

Durability

Durability of surface finish

Reliability of mainfeatures

Reliability of accessory features

Risk from protrusions

Risk from rim cover material

Safety

Reliability of air bag module

Fig. 3. Hierarchical decomposition of main criteria.



can be achieved by combining these three ratings. Presently, theteam arrived at final expectation levels for each criterion by solic-iting the responses from three experts each representing the differ-ent perspective and assigning equal weights to each perspective. Itis important to mention here that the weight assigned to each per-spective could vary, depending on the competitive strategy of thecompany. Moreover, there are different well established methodsthat can be used to combine different ratings and arrive at finalexpectation level. Fuzzy logic (Zadeh, 1965) and AHP (Saaty,1981) are well tested methods to arrive at sieve pore sizes basedon the given criteria and perspectives. The final expectation levelsfor aesthetics, convenience of usage, durability, and safety respec-tively are given below in matrix form:

Xj ¼

6:006:507:508:00

8>>><>>>:

9>>>=>>>;

where Xj represents expectation level (sieve pore size) for jth maincriterion.

3.5. Step-V: rate all concepts with respect to each sieve

The purpose of this step is to rate each concept against eachlower level sub-criterion and then to aggregate these sub-criteriaratings to arrive at main criteria rating scores. Interestingly, atearly stage of PD processes, no quantitative information is avail-able for objective rating of concepts. We, therefore, propose touse a suitably defined rating scale of 0–10 to solicit expert’s opin-ion to rate each concept against identified sub-criteria. Neverthe-less, this rating process relies more on subjective assessment,which could be imprecise seeing that it is almost impossible tohave complete knowledge about concept characteristics. Thismotivates us to seek the help of fuzzy logic to account for, to someextent, the fuzzy nature of the human decision making process inrating the concepts, and in combining these ratings to arrive atmain criteria ratings.

We, therefore, propose to use fuzzy logic system to deal withqualitative or imprecise concept rating scores and combine themto achieve main criteria rating scores. Fig. 4 provides the structureof a Mamdani type fuzzy logic system (FLS) which is the most com-monly used fuzzy inference methodology. For detailed discussionand understanding of fuzzy logic systems, readers are advised torefer Yadav, Singh, Chinnam, and Goel (2003) and Chen, Lin, andHuang (2006). Since the process involves aggregating multiple in-puts into a single output (i.e. the main criterion rating score), weare therefore dealing with the MISO (multiple input–single output)topology of fuzzy systems. Each input (i.e. each lower-level sub-criterion rating score) as well as the output of the FLS is consideredas a fuzzy linguistic variable. A linguistic variable takes values froma set of fuzzy sets which are labeled with linguistic terms like ‘‘verylow”, ‘‘low”, ‘‘medium”, ‘‘high”, etc.

These linguistic variables are defined on a base variable thatspecifies the universe of discourse (rating scale 0–10) in both inputand output spaces. Triangular membership functions have beenconsidered to define linguistic variables (see Fig. 5). Triangularmembership functions have the advantage of simplicity, and arealso the most widely and frequently used (Yadav et al., 2003; Bow-les & Pelaez, 1995). The set of all linguistic variables associatedwith the inputs constitute the input space of the FLS. The outputspace of the FLS is defined by a single linguistic variable associatedwith the main criterion. Carefully chosen membership functions,associated fuzzy sets, and fuzzy rules can efficiently tackle theproblem of prioritizing the inputs as desired by the team.

Tables 2 and 3 describe in an increasing order, the fuzzy setsand their associated linguistic labels that were used for the inputand output variables respectively for the main criterion: ‘Aesthetics’(refer Fig. 6).

The fuzzy IF-THEN rules provide a natural framework forexpressing human knowledge and dealing with imprecise informa-tion. Experts often find fuzzy rules to be a convenient way to ex-

Fuzzification Fuzzy inference process

Defuzzification

Crisp inputs Crisp output

Fuzzy rule baseDecision maker’s knowledge

& expertise

Fig. 4. Structure of Mamdani type fuzzy logic system.

0 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 8.8 10

1

Mem

bers

hip

Very low Low Medium High Very high

Fig. 5. Fuzzy variables in an input or output space.

Table 2Linguistic terms and fuzzy sets used in the three inputs of the FLS for ‘Aesthetics’.

Linguisticterm

L LM M MH H

Fuzzy set (0, 0, 2.5) (0, 2.5, 5) (2.5, 5, 7.5) (5, 7.5, 10) (7.5, 10, 10)

Table 3Linguistic terms and fuzzy sets used in the output of the FLS for ‘Aesthetics’.

Linguistic term L L + 1 L + 2 L + 3Fuzzy set (0, 0, 1) (0, 1, 2) (0.5, 1.5, 2.5) (1, 2, 3)

Linguistic term M � 4 M � 3 M � 2 M � 1Fuzzy set (1.5, 2.5, 3.5) (2, 3, 4) (2.5, 3.5, 4.5) (3.5, 4.5, 5.5)

Linguistic term M + 1 M + 2 M + 3 M + 4Fuzzy set (4.5, 5.5, 6.5) (5.5, 6.5, 7.5) (6, 7, 8) (6.5, 7.5, 8.5)

Linguistic term H � 3 H � 2 H � 1 HFuzzy set (7, 8, 9) (7.5, 8.5, 9.5) (8, 9, 10) (9, 10, 10)



press their knowledge about the relationship between input andoutput variables. Therefore, fuzzy IF-THEN rules are developed tocombine imprecise ratings of lower level sub-criteria to achievemain criteria ratings. Few sample rules are given below:

Rule 1: IF ‘Gloss’ is L, AND ‘Sophisticated look’ is L, AND ‘Beautyof orientation of spokes’ is L, THEN ‘Aesthetics’ is L.Rule 2: IF ‘Gloss’ is L, AND ‘Sophisticated look’ is L, AND ‘Beautyof orientation of spokes’ is LM, THEN ‘Aesthetics’ is L + 2.

However, in the case of MISO topology of fuzzy systems, therehas to be an appropriate mechanism to capture the relative impor-tance of the inputs if a priority structure exists among them. Toincorporate the priority structure existing among the inputs inthe respective fuzzy rule bases, we devised an ‘incremental pullmethod’. In this method, the inputs are assigned pulling powersdepending on their relative weights or priorities. The higher prior-ity input gets more pulling power. The rules are then formulated insuch a way that an increment in the antecedent for a relativelyimportant input across the rules would pull the consequent (out-put of fuzzy rule) towards the higher or lower side in the outputspace. The direction of pull depends on whether the increment ispositive or negative, and magnitude of pull is always proportionalto the pulling power of the corresponding input.

To further explain the incremental pull method; let us considerthe priority structure of lower level sub-criteria for the main crite-rion ‘Aesthetics’. Suppose the sub-criterion ‘sophisticated look’ isthe most important one, and the sub-criterion ‘gloss’ is the leastimportant. The final priority structure is given as ‘sophisticatedlook’ > ‘beauty of orientation of spokes’ > ‘gloss’. Keeping in mindthe priority structure, we assign pulling powers 3:2:1 to ‘sophisti-cated look’, ‘beauty of orientation of spokes’, and ‘gloss’ respec-tively. Now consider the two sample rules (rule 1 and rule 2)presented earlier. In rule 1, the antecedent of the input variable‘beauty of orientation of spokes’ is the fuzzy set ‘L’. However in rule2, the antecedent of the same is the fuzzy set ‘LM’. Note that theantecedent part related with the rest of the two variables is thesame for both the rules. This is considered as an increment ofone fuzzy set in the antecedent of the rule related with the inputvariable ‘beauty of orientation of spokes’; since ‘LM’ is the fuzzyset next to ‘L’ in the increasing order of fuzzy sets of that input var-iable in the FLS for ‘Aesthetics’ (refer Table 2). Now observe that theconsequent of rule 1 is the fuzzy set ‘L’ while that of rule 2 is thefuzzy set ‘L + 2’, which is an increment of two fuzzy sets (referTable 3). Hence, an increment of one fuzzy set in the antecedentpart related with the given input variable while keeping the samefor the other two variables constant causes a shift or increment oftwo fuzzy sets in the consequent across the two fuzzy rules. The

Table 4Input and output values for each main criterion.

Input rating scores Output

Grip Accessibility of features Ergonomic advantage Aggregated score for ‘convenience of use’

Main features Accessory features

a. Input and output data for ‘convenience of use’Concept-I 6 6 8 8 4.73Concept-ll 8 6 7.5 9 6.65Concept-Ill 8 8.5 7.5 6 6.55Concept-IV 9 8.5 9.5 9 6.8


Reliability of air bag module Hazardous effects of rim cover material Risk from protruding features Aggregated score for ‘safety’

b. Input and output data for ’safety’Concept-I 9 6 7 7.53Concept-ll 9 8 8 7.84Concept-Ill 9 9.5 9.5 8.34Concept-IV 9 8 8 7.84


Durability of surface finish Durability of rim cover Durability of features Aggregated score for ’durability’

Main features Accessory features

c. Input and output data ‘durability’Concept-I 6 8 8.5 9 7.00Concept-ll 7 9 8.5 8.5 7.48Concept-Ill 8 9 8.5 8 7.99Concept-IV 7.5 9 8.5 7 7.91

8.8 9.5 9.99 5

Sophisticated look

8 9 9 9

Orientation beauty of spokes

8.5 8 9.5 7

Gloss

FLS

6.35 7.85 8.66 6.35

AestheticsOutput

Inputs

Fig. 6. Aggregate ratings against ‘Aesthetics’ for four concepts.



reason for this is that the pulling power allocated to the input var-iable ‘beauty of orientation of spokes’ is 2. Had the pulling power ofthis input variable been 3, the consequent of the second rule wouldhave been ‘L + 3’. The incremental pull method thus offers a conve-nient solution to the problem of incorporating any priority struc-ture that may exist among the inputs of an FLS with a MISOtopology in the conventional combinatorial rule base generationprocedure.

After enumerating the complete fuzzy rule base, the fuzzy logictoolbox of MATLAB is used to develop fuzzy logic system for eachmain criterion. Fig. 6 illustrates the process of combining sub-cri-teria ratings into the rating for the main criterion ‘Aesthetics’ forall four concepts. For example, the grey shaded boxes show the fi-nal ratings given to concept-I with respect to the three sub-criteriaand corresponding output in terms of aggregated rating of maincriterion ‘aesthetics’. These final ratings are obtained by takingthe average of multiple assessments (three evaluators) and pre-sented as single input of each characteristic for a concept. The finalratings assigned to concept-I are: 8.5 for ‘gloss’, 8.8 for ‘sophisti-cated look’, and 8 for ‘beauty of orientation of spokes’. The FLS treatsthese ratings as fuzzy inputs and provides the final output ratingfor the given main criterion. However, the final output of the FLSis also a fuzzy set and it needs to be converted into a crisp value.The centroid of area (defuzzification) method is used here to con-vert the fuzzy set output into a crisp value (Yadav et al., 2003). Thefinal aggregated crisp value is 6.35, which represents the overallrating for concept-I against ‘aesthetics’ criterion. The similar ap-proach is used for other main criteria as well. Table 4a–c gives in-put and output values of remaining three main criteria for all fourconcepts.

The output of fuzzy logic system represents concept ratings foreach given criterion and concept. These ratings are called ‘finenessscores’ Zij, where i = 1, 2, . . . , k represents number of initial con-cepts considered in the evaluation process and j = 1, 2, . . . , n repre-sents number of main criteria. For our steering wheel example, wehad considered four concepts and these concepts were evaluatedagainst four main criteria. The fineness scores are arranged in amatrix form to get a ‘fineness score matrix’ as illustrated in Fig. 7.

It may well be noted here that the ratings are done with the po-sitive aspect of a sub-criterion/criterion. A higher criterion ratingmeans a better concept against that particular criterion. For exam-ple, the high rating of 9.5 given to the concept-III with respect tothe sub-criterion ‘risk from protruding features’ (see Table 4b)

means that the risk is very low for the concept-III, and not theother way round.

3.6. Step-VI: screen all concepts through each sieve and record the onesthat pass through

This step involves the comparison of fineness scores of all con-cepts with the expectation level (sieve pore size) for each main cri-terion. The comparison is done by taking each row of the ‘finenessscore matrix’ (one at a time) and checking each element of the rowfor the condition; IsZij P Xj? A concept is said to have passedthrough successfully if the corresponding concept rating in thejth row satisfies the given condition. Passing through successfullymeans the concept has satisfied the minimum level of expectationsfor the jth criterion. This process is analogous to separating fine-grained particles from coarse-grained particles using a suitablesieve. Here the particles are the concept rating scores and the sievepore size represents the expectation level of the main criterion. Thecondition imposed for successful passing ensures that only thoseparticles (concept scores) with grain sizes finer than or equal tothe sieve pore size (expectation level) of the main criterion are al-lowed to pass through. Larger the Zij score of a given concept, finerthe grain size of the particle (concept). Similarly, larger the Xj valueof a given sieve, smaller the sieve pore size of that sieve. It may benoted here that this is in no way a concept screening process.Though a given concept may fail to pass through one sieve; itmay pass successfully through another. Fig. 8 shows the processof screening concept traits by passing concept scores through thesieves and recording successful concept traits.

3.7. Step-VII: form ‘concept roots’

The concept scores (Zij) that have successfully passed throughthe sieves refer to those traits that meet or exceed the minimumexpectation levels of the stakeholders in the PD process. Fig. 9shows the number of traits (rating scores) of each concept meetingminimum level of expectations. These successful traits are now re-ferred to as ‘concept roots’. To form concept roots, all the main cri-teria (sieves) are arranged in descending order of sieve pore sizes(Xj), so that the topmost sieve has the maximum value of (Xj). Thisarrangement ensures that the criterion having higher expectationlevel is listed first and the one having lower most expectation level

6.35 7.85 6.35 8.66

4.73 6.65 6.55 6.80

7.00 7.48 7.99 7.91

7.53 7.84 8.34 7.84

I II III IV

Steering Wheel Concepts

Durability

Convenience of Usage

Aesthetics

Safety

Fig. 7. Fineness score matrix.

6.35 7.85 6.35 8.66

4.73 6.65 6.55 6.80

7.00 7.48 7.99 7.91

7.53 7.84 8.34 7.84

6.00

6.50

7.50

8.00

6.35 7.85 6.35 8.66

6.65 6.55 6.80

7.99 7.91

8.34

‘Fineness Score’ Matrix

‘Sieve pore size’ Matrix

Passed Concept Scores

Fig. 8. Screening of concept traits.

Steering wheel Concepts

I II III IV Safety 8.34

Durability 7.99 7.91

Convenience of usage 6.65 6.55 6.80

Aesthetics 6.35 7.85 6.35 8.66

Fig. 9. Concept roots from the set of initial concepts.



is listed last (see Fig. 9). In our example, main criteria ‘safety’ hasthe highest expectation level (8.00) and ‘aesthetic’ has the lowestexpectation level (6.00). The rating score (Zij) of each successfulconcept is referred as a ‘node’ of the root. Vacant node positionsindicate that these concept traits failed to meet expectation levelsand therefore were not allowed to pass through the sieves. Theidentified concept roots will now be utilized forming the formationof hybrid roots.

3.8. Step-VIII: form ‘hybrid roots’ by ‘root node grafting’

In this step, we generate new (hybrid) concepts from the con-cept roots identified in the previous step. This is done by graftingthe nodes of concept roots corresponding to each criterion ontoempty root templates (see Fig. 10) to form what we now refer toas ‘Hybrid roots’. These hybrid roots, if technically feasible, wouldbe new concepts generated by bringing together desirable traitsfrom the initially generated concepts. The new hybrid conceptsthus formed would exceed, or at least meet, all expectation levelsof the stakeholders that were set in the form of sieve pore sizes.Fig. 10 illustrates the process of hybrid roots formation from an ini-tial set of concept roots. The aim of this process is to develop supe-rior concepts by selecting feasible combinations of desirable traits.Owing to the fact that the initial concept traits are used to con-verge upon new (and better) concepts, we call this whole processas ‘concept convergence process.’ Since there are many conceptroot nodes available, theoretically one can explore a large numberof combinations that will result in the formation of several hybridconcepts.

The overall performance measure called ‘hybrid rating’ (HR) ofthe hybrids thus formed is given by following equation:

ðHRÞi ¼Xn

j¼1

Zij � Xj ð1Þ

Here, n is number of sieves, Zij is the grafted ‘fineness score’ ofthe ith concept corresponding to the jth sieve (criterion), and Xj

is the ‘sieve pore size’ of the jth sieve. In Eq. (1) the multiplicationof Zij and Xj can be considered akin to weighting of rating scores inconventional approaches. The only difference is that the weightingparameter Xj takes values from the interval [0, 10] instead of thetraditionally used interval [0, 1]. The team should form all the pos-sible hybrid roots and arrange them in descending order of hybridratings. This is purely a theoretical step and involves only simpleoperations of choosing and placing the available concept rootnodes onto the root templates (i.e. making all possible combina-tions from among the available root nodes), and is not at all timeconsuming if a simple algorithm is developed for doing the job.The outcome of this step is the set of all theoretically possible hy-brid concepts that can be generated from hybrid roots. As shown inFig. 9, only one concept rating score meets the expectation level of

the main criteria ‘safety’, two concepts meet ‘durability’ criteria,three concepts exceed the expectation level of ‘convenience ofuse’, and all four concept scores meet the expectation level of ‘aes-thetics’ criteria. Therefore, theoretically 1 � 2 � 3 � 4 = 24 combi-nations of hybrid roots are possible. The hybrid rating iscalculated using Eq. (1). A sample calculation of hybrid rating forone of the hybrid concepts (‘T-hybrid-1’) is shown below:

ðHRÞT-hybrid-1 ¼ ½ð8:34� 8:00Þ þ ð7:99� 7:50Þ þ ð6:80� 6:50Þþ ð8:66� 6:00Þ� ¼ 222:805

3.9. Step-IX: check the ‘hybrid roots’ for technical feasibility andagainst the cost ceiling

It is not necessary that simply by grafting together variousnodes, a feasible concept will be generated. By grafting the nodesfrom different concept roots onto a hybrid, we are essentially try-ing to generate a new concept by combining different concepttraits that are considered to be better and meeting expectation lev-els. However, it is not always true that these nodes taken from dif-ferent concepts will be technically compatible with each other. Ifthe nodes are found to be mutually compatible, i.e. the hybrid isfound to be technically feasible, then the next step is to make a fairestimate of its expected cost. On the other hand, if the hybrid is notfound to be technically feasible, then the next best hybrid ischecked for its feasibility. This process is repeated until a feasiblehybrid concept is found. If the estimated cost of a technically fea-

Hybrid root

8.34

7.99

6.80

8.66 6.35

6.65

7.85

8.34

7.99

6.55

6.35

7.91

6.80

8.66

Root-3 Root-2 Root-1 Root-4

Concept roots

j = 1

j = 2

j = 3

j = 4

Empty root template

Fig. 10. Hybrid root formation.

k = 1 to M; k = 1

T-Hybrid-k

Is technically feasible?

Is cost below cost ceiling?

Select for further development

k = (k + 1)

k = M?

Start

Stop

No

Yes

No

YesYes

No

Fig. 11. Screening the hybrids with technical feasibility and cost ceiling constraints.



sible hybrid concept is found to be lower than the pre-determinedcost ceiling (established in the first step of the methodology), thenthis hybrid concept is selected for further development. If the esti-mated cost is above the ceiling, then the next best feasible hybrid isselected and this process is repeated until the required numbers offeasible hybrid concepts are selected for further development. Theoverall process involved in this step can be presented as a heuris-tic/algorithm (see Fig. 11):

1. Generate the set of all theoretically possible hybrid roots(hybrid concepts) from the available concept root nodes.

2. Send (forward) this set of hybrid roots to the design team (thatwas involved in generating the initial set of concepts) alongwith the description of the concept trait combinations for eachhybrid. The design team is supposed to revert back with a set ofhybrid solutions that are technically feasible; these may beslightly different from the actual theoretical hybrids, since thedesign team may have considered some minor trade-offs tomake a theoretical hybrid technically feasible which otherwisewas not so in its actual form.

3. The set of technically feasible hybrids is then analyzed to makea rough cost estimate for each technically feasible hybrid.

4. These hybrids are then screened with the cost ceiling, so thatthe team is finally left with a set of technically feasible hybridsolutions that have cost estimates below the pre-determinedcost ceiling. These hybrid concepts may be taken for furtherdevelopment by the team.

5. If the final set of hybrid concepts is a null set, then the initialconcepts are again taken into consideration by changing expec-tation levels and repeat the whole process.

Based on the design team’s analysis, ‘T-hybrid-1’ was found tobe technically feasible by the design team after making some min-or trade-offs. The final description of ‘T-hybrid-1’ as sent back to theselection team is given in Table 5. This hybrid solution was foundto be having a cost estimate below the pre-determined cost ceiling,and hence was selected for further development. Although therewere three more hybrid concepts, which satisfied both technicaland economical constraints, the team decided to focus their initialefforts on ‘T-hybrid-1’ concept only.

4. Conclusions

The paper presents a structured methodology for improving andselecting product concepts through a concept convergence process.The new methodology puts more emphasis on converging existingconcepts into new hybrid (improved) concepts rather than select-ing the best available concept from the initial set of concepts. Inthis effort, the initial set of concepts is evaluated against selectioncriteria to identify superior traits from these concepts. The evalua-tion process of the proposed method deviates considerably fromthe traditional approaches wherein weights are assigned to eachselection criterion, and instead establishes expectation levels for

each main criterion by capturing expectations of all the stakehold-ers. These expectation levels (sieve pore sizes) provide much betterreflections of the decision-maker’s preferences and the resultingsieves are utilized to isolate superior concept traits. The fuzzy logicapproach is used to deal with uncertainty in concept ratings. Theconcept convergence approach brings the superior traits from aninitial set of concepts together and creates a set of hybrid conceptsby exploring all possible combinations of these traits. The finaldecision of selecting hybrid concepts for further development ismade by considering clearly defined economical and technicalconstraints.

The development of hybrid or improved concepts through theconcept convergence process generally improves the PD processeffectiveness and enhances product reliability and hence customersatisfaction. The proposed framework extends the existing work ondecision matrix models in concept selection and supports the ‘‘set-based concurrent engineering” philosophy devised by Toyota (So-bek, Liker, & Ward, 1999). However, the results still depend onthe quality of information derived through the concept rating pro-cess and expert’s judgment in building the rule base. As with anymodeling framework, one has to exercise great care to ensure thatthe data and inputs presented to the methodology are of goodquality without which the results could be biased. The proposedmethod is particularly sensitive to the fuzzy rule base that aggre-gates the lower level sub-criteria ratings into top level criteria. Thismethod is most beneficial during early stages of the product devel-opment, where one is generally constrained from collecting ade-quate quantitative data to accurately rate concepts against givenselection criteria. The test and validation of the proposed frame-work and development of computer-based framework are to bestudied in our future work. Cost estimation method at early stagesof PD process needs to be explored further when information andknowledge regarding concept features is imprecise or qualitative.The development of heuristic approaches to enumerate and testpossible hybrid combination is another potential area for futureresearch.

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T-Hybrid-1Spokes Two in numbers, rectangular cross section, polished teak wood coveringRim Hollow tubular; soft, smooth, ultra high quality urethane covering, except at intersection with spokes where covering is teak wood; soft leather strip

wound over rim coverMain features Fixed center (divided into two halves – upper and lower); air bag beneath the lower half of fixed center, with soft, smooth, ultra high quality urethane

covering over lower half of center; horn on both spokes beneath coverAccessory

featuresVisual display screen on upper half of fixed center to show the rear side view while in reverse gear, along with display of obstacle proximity statistics(for help in parking, especially in dark)



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Concept convergence process: A framework for improving product concepts

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