Concept convergence process: A framework for improving product concepts

Computers & Industrial Engineering 59 (2010) 367–377

Contents lists available at ScienceDirect

Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie

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 b

Mechanical Engineering Department, Malaviya National Institute of Technology, Jaipur, India 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 2009 Received in revised form 22 April 2010 Accepted 13 May 2010 Available online 16 May 2010 Keywords: Concept selection Concept convergence Fuzzy logic Product 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 the final product depends on the selected concept. The exploration and evaluation of alternatives early in the product development (PD) process reduces the amount and magnitude of changes in later stages and increases the likelihood of success of new product development (NPD) projects. Though, currently available methods attempt to select the best concept from the available set of initial concepts, they do not help create an improved concept based on the learning and knowledge generated through the evaluation of initial concepts. The paper proposes a framework for selecting and/or evolving improved concepts through a rigorous concept evaluation and convergence process. The concept convergence process allows bringing together the best (desirable) traits from the initial set of concepts and creates a new set of hybrid concepts. The framework uses a fuzzy inference process for evaluating each initial concept against identified decision criteria, thus generating hybrid concepts to select the best feasible concept under given cost and technological constraints. The approach is demonstrated using a steering wheel concept generation example. Published by Elsevier Ltd.

1. Introduction Early design decisions during the PD process have become an increasingly important prerequisite competency to ensure corporate success in today’s global market environment. Decisions made early in the PD process significantly influence an organization’s capability to reduce development time and cost, and produce highly reliable products. Moreover, it helps organizations to move towards First Product Correct—getting it right the first time and every time—philosophy that is the ability to transition from design concept to a finished product with absolute certainty of a correct result (Yadav & Singh, 2008). With this in mind it seems particularly imperative to make early design decisions in the most optimal manner possible. The PD process is the sequence of steps or activities that an enterprise employs to conceive, design, and commercialize a product. This process starts with the initial creation of a wide set of alternative product concepts, followed by the subsequent narrowing of alternatives and increasing specifications of a product until the product can be reliably and repeatedly produced by the production system (Ulrich & Eppinger, 2000). In PD process, concept selection is one of the most important decisions, since success of the final product depends on the selected concept. A poor concept

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).

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

selection can rarely be compensated at later design stages and can give rise to a great expense of redesign costs (Pahl & Beitz, 1996). Many in the design community accept the notion that more than 70% of the final product quality and cost are determined in the conceptual design phase (Ishii, 1995; Nepal, Monplaisir, & Singh, 2005). Therefore, thorough exploration and evaluation of alternatives early in the design process can significantly help reduce the changes in later stages and increase the likelihood of success of new product development (NPD) projects (Chin & Wong, 1999). This paper intends to provide a structured methodology that helps create improved concepts based on the learning and knowledge generated through the evaluation of an initial set of generated concepts. Concept selection is the process of evaluating concepts with respect to customer needs and other relevant criteria, and selecting one or more concepts for further investigation and development. Concept screening and scoring are popular decision matrix based methods that are often used to narrow down the number of concepts to a select few. Unfortunately, the typical construction of decision matrices makes it difficult to ensure that promising concepts are not erroneously eliminated (Mullur, Mattson, & Messac, 2003). Additionally, detailed and precise information regarding product concepts is normally not available at this early stage of product development, and thus decisions are always made using qualitative information and judgment (Rosenman, 1993). Moreover, none of the existing concept selection methods address the issue of concept improvement. Mostly the focus is on elimination

368

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

of poor design concepts. Moreover, after the stage of concept selection, very little attention is paid to the concepts that are rejected. Nevertheless, there is always some possibility of these rejected concepts containing some traits, which if incorporated with the final concept, might contribute positively to further improve it. Although the existing methods have their own merits, none offers any structured mechanism to capture the knowledge generated through concept evaluation to improve design concepts. This paper proposes an effective methodology namely concept convergence process for selecting and/or evolving improved design concepts through a rigorous concept evaluation and convergence process. The methodology essentially involves evaluating an initial set of concepts against identified selection criteria and subsequently generating improved hybrid concepts. This makes the proposed approach radically different from the traditional evaluation techniques. The concept convergence process allows bringing together the best (desirable) traits from the initial set of concepts and creation of a new set of hybrid concepts. Later, the best feasible hybrid concept is selected against given cost and technological constraints. In order to deal with uncertainty and fuzziness in the evaluation process, fuzzy logic approach is used to aggregate the ratings given to concept alternatives against selection criteria. The rest of the paper is organized as follows: Section 2 provides a brief review of the existing literature on concept selection. Section 3 presents the proposed methodology for improving product concepts through the concept convergence process. Finally, Section 4 presents some concluding remarks.

2. Literature review Product concept selection is a very unique multi-criteria decision making problem where decisions are usually made based on highly imprecise knowledge regarding the decision criteria. Various researchers have attempted to address this unique problem of concept selection through the use of various multi-criteria decision making approaches, such as Quality Function Deployment (QFD) (Hauser & Clausing, 1988), Analytic Hierarchy Process (AHP) (Saaty, 1981), Pugh Matrix (Pugh, 1991), multi-criteria optimization (Ip, Yung, & Wang, 2004; Ebadian, Rabbani, Jolai, Torabi, & Moghaddam, 2008) and fuzzy logic (Zadeh, 1965). The most widely used methods in industry involve decision matrices (Pahl & Beitz, 1984). Decision matrix based methods generally involve assigning weights to each selection criteria; rating each product concept based on its estimated ability to satisfy each of those criteria; and summing up to achieve an overall score for each concept. These methods are highly suitable especially in those scenarios where decision making is mostly dominated by qualitative criteria. Among the matrix-based concept selection methodologies (CSMs) available in literature, the methodology given by Pugh (1991) is perhaps the most basic popular approach for concept selection. It has been employed for initial concept screening to eliminate highly infeasible concepts, when the number of initial concepts is very high. The Pugh’s method does not assign weights to the selection criteria (they all have equal weights) and each concept is rated as ‘‘better than,” ‘‘equal to,” or ‘‘worse than” a reference concept. Ulrich and Eppinger (2000) propose an extension to Pugh’s method to make a final selection from the concepts that have passed the Pugh’s screening process. In this case, weights are assigned to the selection criteria and concepts are given ratings from a rating scale. Takai and Ishii (2004) propose modifications to the Pugh’s methodology by introducing the concept of probability. Their approach involves evaluating the concept alternatives on the basis of their probability of achieving certain set targets. King and Sivaloganathan (1999) opine that one of the major shortcomings of matrix-based CSMs centered on the Pugh’s method is their

inability to deal with coupled decisions. QFD based CSMs appear to be a good solution to this problem. The interaction chart of the QFD matrix helps indicate those product concepts that can exist together and therefore reinforce each other. It also shows which concepts are highly incompatible with each other. King and Sivaloganathan (1999) propose the Flexible Design CSM, with emphasis on the importance of coupled decisions. This methodology follows a QFD like pattern, but with a significant difference that the interaction chart is replaced with a compatibility chart in the decision matrix. Although decision matrices provide a simple and systematic approach to the problem of concept selection, they fail in emphasizing on the relative importance of concept evaluation criteria. The evolution of AHP-based CSMs can be mostly attributed to the need to overcome this shortcoming (Okudan & Shirwaiker, 2006). The AHP, which was originally proposed by Saaty (1981), has been extensively used both in academic research as well as in industrial practice to solve multiple-criteria decision-making problems. It basically involves a systematic decomposition of a given problem into a hierarchical form to perform simple pair-wise comparisons and rankings for synthesizing importance weights at different levels of the hierarchy (Augustine, Jain, & Yadav, 2010). One of the notable AHP-based CSMs specifically aimed at design decision making was developed by Marsh, Moran, Nakui, and Hoffherr (1991). Mullens and Armacost (1995) propose a two-stage CSM wherein the Pugh’s method is used in the first stage for initial concept screening, and in the second stage, AHP is used for final quantitative evaluation of the concepts. Ayag and Ozdemir (2006) propose the use of Analytic Network Process (ANP) in concept selection, to accommodate for the variety of interactions, dependencies and feedback between higher and lower level elements of a hierarchy in a better way. AHP-based approaches have been the mainstay in multi-criteria decision making in the past few decades. However when it comes to handling uncertainties involved in weighting and scoring various criteria and alternatives, crisp numerical values do not suffice. The use of fuzzy logic (Zadeh, 1965) in conjunction with AHP has emerged as a solution to this problem. As an example of incorporating fuzzy logic in AHP, Ayag (2005) gives a fuzzy-AHP-based CSM for use in an NPD environment. There are many more interesting applications of fuzzy logic in the development of CSMs that can be observed in the literature. For instance Thurston and Carnahan (1992) propose the application of fuzzy set theory to a multiple-attribute engineering design evaluation process. Wang (2002) extends Pugh’s method with fuzzy set theory to measure the quality of a chosen concept. Jiao and Tseng (1998) propose a fuzzy ranking methodology for conceptual design evaluation in the context of mass customization. Wang (2001) provides fuzzy outranking models, where linguistic terms (fuzzy numbers) are set by the designer and used to compare various design concepts. Concepts that are outranked (dominated) are removed, leaving only those that merit further development. Another popular concept selection approach found in the literature is based on utility theory (Thurston, 1990). Utility theory is a multi-attribute decision making approach which in general involves the association of utility functions with decision criteria, and the evaluation of alternatives on their overall utility across the criteria. Pahl and Beitz (1984) were among the first to include utility theory into a systematic design method. Using utility theory in concept selection Thurston and Locascio (1994) attempt to build on the shortcoming of existing approaches in not being able to guide the decision-maker towards appropriate trade-offs. Although utility theory based CSMs have proved to overcome most of the limitations of CSMs based on other approaches, its acceptance in the engineering design community has not been very encouraging (Okudan & Shirwaiker, 2006). Another category of CSMs supports the notion of rigorous numerical and optimization techniques. Optimization-based approaches

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 selection have been proposed till date. Notable among these few include the CSM using s-pareto frontiers as given by Mattson and Messac (2002); using hypothetical equivalents and inequivalents as given by See and Lewis (2002); using genetic algorithm and combinatorial optimization as given by Crossley, Martin, and Fanjoy (2001); and using linear physical programming as given by Mullur et al. (2003). To summarize the discussion on existing CSMs, it can be said that although powerful in many cases, methods based on decision matrices may fail to aid designers in selecting potential concept alternatives. This is simply because decision matrices are based on an inadequate mathematical construct and it is possible to misinterpret the results of the concept selection process, as the weights may not be a true reflection of the decision-maker’s preferences (Mullur et al., 2003). Further, the existing methods do not have any mechanism to capture the knowledge and learning generated during concept evaluation process and to utilize it for further improvement of concepts. Although some variants of the Pugh’s methodology (e.g. Ulrich & Eppinger, 2000) have attempted concept improvement by combining individual concepts in the concept selection phase of the PD process, these are not generically applicable and failed in detailing out a structured procedure for improvement. On the other hand, multi-objective optimization methods can bring additional rigor to the concept selection process, but these methods are primarily used during the detailed phase of the design process. The research work presented in this paper derives motivation from the belief that rather than selecting the better among available alternatives, the progression towards better solutions by combining strengths of all available concepts within given constraints is a more robust approach for concept improvement. The proposed methodology is built on the existing decision matrix models but presents a different approach by assigning expectation levels to selection criteria instead of weights. Further it provides a mechanism to screen concept traits instead of whole concepts using the criteria expectation levels in order to identify superior traits or characteristics from each concept.

369

odology in a step-wise manner along with a suitable example involving a 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 consideration to cost is a futile exercise. A concept may be very good as far as the performance is concerned; it is not a very promising concept if the customer rejects the product due to its high cost. Therefore, cost consideration must be incorporated in any concept generation and selection methodology. Although, there may be instances when cost is not at all an important factor compared to high performance demand. In such cases, the stage of the methodology where treatment of the cost factor is carried out may be bypassed. It is therefore better to keep a provision for cost consideration in a methodology to generalize it. In the first step, it is proposed to establish a cost ceiling for screening the initial set of concepts as well as the final set of hybrid concepts. This helps us to screen those concepts whose estimated cost value lies below the pre-determined cost ceiling and take them to the next step. Market potential and competition analysis are useful techniques that the team could use to arrive at a suitable cost ceiling for their product. This involves clearly identifying the market segment to be targeted. The identified segment of the market is then placed on an economic scale to find out the paying power of the customers. To do this, a market survey may be conducted to find the average income of the target market. This set of information along with the price range of competing products can be taken as the basis for a rough estimate of the cost ceiling value. The detailed discussion on estimation of cost ceiling is beyond the scope of this paper. To demonstrate the applicability of the proposed framework, we consider an example of a steering wheel concept selection process for a luxury car. Based on market potential and competition analysis, the team has decided on a cost ceiling value that has allowed four concepts from the initial set of concepts generated by the design team to pass through. Fig. 2 and Table 1 provide detailed information on the four steering wheel concepts. 3.2. Step-II: identify evaluation criteria

3. Proposed approach The proposed methodology suggests a new approach for bringing out the preferences of decision-makers for each decision criteria. In the proposed approach, the criteria are treated like sieves, and the importance of each criterion is reflected in its sieve pore size. In a way, the sieve pore size of a criterion represents its expectation level regarding the set of concept alternatives. Higher the expectation level of a given criterion, smaller will the pore size be, and hence finer (better) a given concept has to be to pass through that criterion sieve. Another unique feature of the proposed methodology is in the way ratings are assigned to individual concepts with respect to the selection criteria. Each criterion is decomposed into its sub-criteria and is represented as a tree structure. The concepts are rated with respect to the lower level sub-criteria because it is fairly easy to make more accurate comparison and judgment at lowest level. These ratings are then aggregated towards the top of the tree to assign a final rating to the given main criterion. In the final stages of the methodology, the concept traits that have passed through sieves successfully are used to generate hybrid concepts. These new concepts generated out of the initial set of concepts will almost certainly exceed the expectations of the decision-maker in all performance aspects. Fig. 1 illustrates the overall concept convergence and selection methodology, and the following sections delineate the proposed meth-

To effectively evaluate concepts, identification of appropriate evaluation criteria is an essential and key step in concept selection process. Generally, these criteria should manifest customer, corporate, and regulatory requirements as well as manufacturing constraints and limitations. At this stage, the design team must make sure that the criteria that are decided upon are as generalized as possible. For example, suppose one of the criteria decided upon by the team is ease of steering, and another is ease of access to features, then instead of taking these two criteria separately, the team should find a more general way of expression, let us say ease of use. This will encompass both the above-mentioned separate criteria as well as many more of their sort. In short, the team should make sure that none of the identified selection criteria are in any way a part of any other criterion that has already been included in the list. Henceforth the criteria identified in this step will be addressed to as ‘main criteria’. The design team has decided to include 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 into sub-criteria, which may further be decomposed to lower level subcriteria. This decomposition process continues until a set of sub-criteria that could be easily rated based on available information is

370

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

Identify selection criteria

Establish cost ceiling and screen generated concepts with the ceiling

Customer viewpoint

Company viewpoint

Decompose each main criterion into sub-criteria (sieves)

Benchmarking viewpoint Establish a ‘sieve pore size’ for each criterion (Xj) This final set of hybrids can be taken up for further development by the team

Rate concepts with respect to each subcriterion

Aggregate the ratings of each concept with respect to the sub-criteria to get its main ratings. (Zij)

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

Extract the set of technically feasible hybrids For all i & a given j, is Zij > Xj?

YES Take Zij to form Concept roots

Form the set of all theoretically possible Hybrid roots

NO

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

Teak wood rim cover Power switch for stereo/radio Soft leather cover

Urethane covering Button for changing channels Light switch

(a) Steering wheel concept-I

Switch for rim heater Power switch for stereo/radio Switch for A.C/heater blower Granulated thick plastic rim cover

Button for changing channels Metallic color coated plastic cover Light switch

(b) Steering wheel concept-II

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

Soft, smooth, ultra high quality urethane rim cover

Soft, smooth, ultra high quality urethane cover over center

Soft, smooth, ultra high quality urethane cover on spokes

(c) Steering wheel concept-III

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

Steering wheel concept-IV Fig. 2. CAD drawing of four concepts.

achieved. Therefore, while decomposing these criteria into sub-criteria, the team must make sure that each main criterion is broken down 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 four main criteria, into their respective lower level sub-criteria.

371

M. Augustine et al. / Computers & Industrial Engineering 59 (2010) 367–377 Table 1 Detailed description of four steering wheel concepts. Concept 1 Spokes Rim Main features

Two in numbers, rectangular section, urethane covering Hollow tubular, teak wood covering, urethane cover at intersection with spokes Horn at center, air bag within center with soft leather cover

Accessory features

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

Concept-II Spokes Rim Main features

Three in number, rectangular section, soft plastic cover (metallic color coating) Hollow tubular, soft, thick plastic covering with granulated surface Fixed center; air bag within center with soft plastic cover (metallic color); horn in center

Accessory features

Concept-III Spokes Rim Main features Accessory features Concept-IV Spokes Rim Main features Accessory features

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 of the fixed center

Three in number, rectangular section, soft smooth, ultra high quality urethane covering Hollow tubular; soft, smooth, ultra high quality urethane covering Air bag beneath center with soft, smooth, and ultra high quality urethane cover over center; horn on each spoke beneath cover AC/heater blower ON/OFF with depressible center

Two in numbers; rectangular section; polished teak wood covering Hollow tubular; urethane covering except at intersection with spokes; intersections having teak wood covering; soft leather strip wound over the rim 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 Visual display screen on upper half of the center showing the rear side view while in reverse gear

Aesthetics

Convenience of use

Gloss

Grip

Sophisticated look Orientation beauty of spokes

Durability

Safety

Durability of surface finish

Reliability of air bag module

Ergonomic advantage gained by accessory features

Durability of rim cover

Risk from rim cover material

Accessibility of features

Reliability of features

Risk from protrusions

Accessibility of main features

Reliability of main features

Accessibility of accessory features

Reliability of accessory features

Fig. 3. Hierarchical decomposition of main criteria.

3.4. Step-IV: allocate a ‘‘sieve pore size” to each main criterion From this step onwards, each main criterion is treated as a sieve. These sieves act as gates to screen out the concept traits, which do not meet the expectation levels of the design team. It is therefore important to establish expectation levels for each criterion of the product concept. Higher the importance of a given criterion, higher will be the expectation level for that criterion. Each criterion (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. The finer sieve pore size for any given criterion means higher expectation levels and therefore, these finer sieves will stop concepts from passing through if their rated scores do not meet expectation levels. On the contrary, a low score indicates a liberal sieve, which will allow most of the concepts to pass through.

The problem of establishing an expectation level (sieve pore size) for each main criterion should encompass different perspectives. In this study, we suggest to include three main perspectives namely: customer’s perspective – how important that criterion is from customer’s point of view; company’s perspective – capability of the manufacturing firm in achieving the given criterion and its match with the company’s overall market strategy; and benchmarking perspective – the current rating of the product among existing competitor’s products and future target for a given criterion. The outcome of this step will be a sieve pore size for each main criterion considered in the concept selection problem. In the example of steering wheel concept selection, the design team first assigned expectation levels to each main criterion, keeping in mind these three different perspectives and thus arrived at three different ratings for each criterion. The overall expectation level

372

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

Decision maker’s knowledge & expertise Fuzzification

Fuzzy rule base

Fuzzy inference process

Defuzzification

Crisp inputs

Crisp output

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

8 9 6:00 > > > > > < 6:50 > = Xj ¼ > 7:50 > > > > > : ; 8:00 where Xj represents expectation level (sieve pore size) for jth main criterion.

3.5. Step-V: rate all concepts with respect to each sieve The purpose of this step is to rate each concept against each lower level sub-criterion and then to aggregate these sub-criteria ratings to arrive at main criteria rating scores. Interestingly, at early stage of PD processes, no quantitative information is available for objective rating of concepts. We, therefore, propose to use a suitably defined rating scale of 0–10 to solicit expert’s opinion to rate each concept against identified sub-criteria. Nevertheless, this rating process relies more on subjective assessment, which could be imprecise seeing that it is almost impossible to have complete knowledge about concept characteristics. This motivates us to seek the help of fuzzy logic to account for, to some extent, the fuzzy nature of the human decision making process in rating the concepts, and in combining these ratings to arrive at main criteria ratings. We, therefore, propose to use fuzzy logic system to deal with qualitative or imprecise concept rating scores and combine them to achieve main criteria rating scores. Fig. 4 provides the structure of a Mamdani type fuzzy logic system (FLS) which is the most commonly used fuzzy inference methodology. For detailed discussion and understanding of fuzzy logic systems, readers are advised to refer Yadav, Singh, Chinnam, and Goel (2003) and Chen, Lin, and Huang (2006). Since the process involves aggregating multiple inputs into a single output (i.e. the main criterion rating score), we are therefore dealing with the MISO (multiple input–single output) topology of fuzzy systems. Each input (i.e. each lower-level subcriterion rating score) as well as the output of the FLS is considered as a fuzzy linguistic variable. A linguistic variable takes values from a set of fuzzy sets which are labeled with linguistic terms like ‘‘very low”, ‘‘low”, ‘‘medium”, ‘‘high”, etc.

Very low

Low

Medium

High

Very high

1 Membership

can be achieved by combining these three ratings. Presently, the team arrived at final expectation levels for each criterion by soliciting the responses from three experts each representing the different perspective and assigning equal weights to each perspective. It is important to mention here that the weight assigned to each perspective could vary, depending on the competitive strategy of the company. Moreover, there are different well established methods that can be used to combine different ratings and arrive at final expectation level. Fuzzy logic (Zadeh, 1965) and AHP (Saaty, 1981) are well tested methods to arrive at sieve pore sizes based on the given criteria and perspectives. The final expectation levels for aesthetics, convenience of usage, durability, and safety respectively are given below in matrix form:

0

0.8

1.6 2.4

3.2

4.0 4.8

5.6

6.4

7.2 8.0

8.8

10

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

These linguistic variables are defined on a base variable that specifies the universe of discourse (rating scale 0–10) in both input and output spaces. Triangular membership functions have been considered to define linguistic variables (see Fig. 5). Triangular membership functions have the advantage of simplicity, and are also the most widely and frequently used (Yadav et al., 2003; Bowles & Pelaez, 1995). The set of all linguistic variables associated with the inputs constitute the input space of the FLS. The output space of the FLS is defined by a single linguistic variable associated with the main criterion. Carefully chosen membership functions, associated fuzzy sets, and fuzzy rules can efficiently tackle the problem of prioritizing the inputs as desired by the team. Tables 2 and 3 describe in an increasing order, the fuzzy sets and their associated linguistic labels that were used for the input and output variables respectively for the main criterion: ‘Aesthetics’ (refer Fig. 6). The fuzzy IF-THEN rules provide a natural framework for expressing human knowledge and dealing with imprecise information. Experts often find fuzzy rules to be a convenient way to ex-

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

L

LM

M

MH

H

(0, 0, 2.5)

(0, 2.5, 5)

(2.5, 5, 7.5)

(5, 7.5, 10)

(7.5, 10, 10)

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

L (0, 0, 1)

L+1 (0, 1, 2)

L+2 (0.5, 1.5, 2.5)

L+3 (1, 2, 3)

Linguistic term Fuzzy set

M4 (1.5, 2.5, 3.5)

M3 (2, 3, 4)

M2 (2.5, 3.5, 4.5)

M1 (3.5, 4.5, 5.5)

Linguistic term Fuzzy set

M+1 (4.5, 5.5, 6.5)

M+2 (5.5, 6.5, 7.5)

M+3 (6, 7, 8)

M+4 (6.5, 7.5, 8.5)

Linguistic term Fuzzy set

H3 (7, 8, 9)

H2 (7.5, 8.5, 9.5)

H1 (8, 9, 10)

H (9, 10, 10)

373

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

Gloss

Inputs 8.5

8

Sophisticated look

7

9.5

8.8

9.5

5

Orientation beauty of spokes

9.99

8

9

9

9

FLS Aesthetics

Output 6.35

7.85

6.35

8.66

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

press their knowledge about the relationship between input and output variables. Therefore, fuzzy IF-THEN rules are developed to combine imprecise ratings of lower level sub-criteria to achieve main criteria ratings. Few sample rules are given below: Rule 1: IF ‘Gloss’ is L, AND ‘Sophisticated look’ is L, AND ‘Beauty of orientation of spokes’ is L, THEN ‘Aesthetics’ is L. Rule 2: IF ‘Gloss’ is L, AND ‘Sophisticated look’ is L, AND ‘Beauty of orientation of spokes’ is LM, THEN ‘Aesthetics’ is L + 2. However, in the case of MISO topology of fuzzy systems, there has to be an appropriate mechanism to capture the relative importance of the inputs if a priority structure exists among them. To incorporate the priority structure existing among the inputs in the respective fuzzy rule bases, we devised an ‘incremental pull method’. In this method, the inputs are assigned pulling powers depending on their relative weights or priorities. The higher priority input gets more pulling power. The rules are then formulated in such a way that an increment in the antecedent for a relatively important input across the rules would pull the consequent (output of fuzzy rule) towards the higher or lower side in the output space. The direction of pull depends on whether the increment is positive or negative, and magnitude of pull is always proportional to the pulling power of the corresponding input.

To further explain the incremental pull method; let us consider the priority structure of lower level sub-criteria for the main criterion ‘Aesthetics’. Suppose the sub-criterion ‘sophisticated look’ is the most important one, and the sub-criterion ‘gloss’ is the least important. The final priority structure is given as ‘sophisticated look’ > ‘beauty of orientation of spokes’ > ‘gloss’. Keeping in mind the priority structure, we assign pulling powers 3:2:1 to ‘sophisticated look’, ‘beauty of orientation of spokes’, and ‘gloss’ respectively. 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 rule 2, the antecedent of the same is the fuzzy set ‘LM’. Note that the antecedent part related with the rest of the two variables is the same for both the rules. This is considered as an increment of one fuzzy set in the antecedent of the rule related with the input variable ‘beauty of orientation of spokes’; since ‘LM’ is the fuzzy set next to ‘L’ in the increasing order of fuzzy sets of that input variable in the FLS for ‘Aesthetics’ (refer Table 2). Now observe that the consequent of rule 1 is the fuzzy set ‘L’ while that of rule 2 is the fuzzy set ‘L + 2’, which is an increment of two fuzzy sets (refer Table 3). Hence, an increment of one fuzzy set in the antecedent part related with the given input variable while keeping the same for the other two variables constant causes a shift or increment of two fuzzy sets in the consequent across the two fuzzy rules. The

Table 4 Input and output values for each main criterion. Input rating scores Grip

Output

Accessibility of features Main features

Ergonomic advantage

Aggregated score for ‘convenience of use’

8 9 6 9

4.73 6.65 6.55 6.8

Accessory features

a. Input and output data for ‘convenience of use’ Concept-I 6 6 Concept-ll 8 6 Concept-Ill 8 8.5 Concept-IV 9 8.5

8 7.5 7.5 9.5

Input rating scores Reliability of air bag module b. Input and output data for ’safety’ Concept-I 9 Concept-ll 9 Concept-Ill 9 Concept-IV 9

Output Hazardous effects of rim cover material

Risk from protruding features

Aggregated score for ‘safety’

6 8 9.5 8

7 8 9.5 8

7.53 7.84 8.34 7.84

Input rating scores Durability of surface finish

c. Input and output data ‘durability’ Concept-I 6 Concept-ll 7 Concept-Ill 8 Concept-IV 7.5

Output Durability of rim cover

8 9 9 9

Durability of features

Aggregated score for ’durability’

Main features

Accessory features

8.5 8.5 8.5 8.5

9 8.5 8 7

7.00 7.48 7.99 7.91

374

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

reason for this is that the pulling power allocated to the input variable ‘beauty of orientation of spokes’ is 2. Had the pulling power of this input variable been 3, the consequent of the second rule would have been ‘L + 3’. The incremental pull method thus offers a convenient solution to the problem of incorporating any priority structure that may exist among the inputs of an FLS with a MISO topology in the conventional combinatorial rule base generation procedure. After enumerating the complete fuzzy rule base, the fuzzy logic toolbox of MATLAB is used to develop fuzzy logic system for each main criterion. Fig. 6 illustrates the process of combining sub-criteria ratings into the rating for the main criterion ‘Aesthetics’ for all four concepts. For example, the grey shaded boxes show the final ratings given to concept-I with respect to the three sub-criteria and corresponding output in terms of aggregated rating of main criterion ‘aesthetics’. These final ratings are obtained by taking the average of multiple assessments (three evaluators) and presented as single input of each characteristic for a concept. The final ratings assigned to concept-I are: 8.5 for ‘gloss’, 8.8 for ‘sophisticated look’, and 8 for ‘beauty of orientation of spokes’. The FLS treats these ratings as fuzzy inputs and provides the final output rating for the given main criterion. However, the final output of the FLS is also a fuzzy set and it needs to be converted into a crisp value. The centroid of area (defuzzification) method is used here to convert the fuzzy set output into a crisp value (Yadav et al., 2003). The final aggregated crisp value is 6.35, which represents the overall rating for concept-I against ‘aesthetics’ criterion. The similar approach is used for other main criteria as well. Table 4a–c gives input and output values of remaining three main criteria for all four concepts. The output of fuzzy logic system represents concept ratings for each given criterion and concept. These ratings are called ‘fineness scores’ Zij, where i = 1, 2, . . . , k represents number of initial concepts considered in the evaluation process and j = 1, 2, . . . , n represents number of main criteria. For our steering wheel example, we had considered four concepts and these concepts were evaluated against four main criteria. The fineness scores are arranged in a matrix 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 positive aspect of a sub-criterion/criterion. A higher criterion rating means a better concept against that particular criterion. For example, the high rating of 9.5 given to the concept-III with respect to the sub-criterion ‘risk from protruding features’ (see Table 4b)

means that the risk is very low for the concept-III, and not the other way round. 3.6. Step-VI: screen all concepts through each sieve and record the ones that pass through This step involves the comparison of fineness scores of all concepts with the expectation level (sieve pore size) for each main criterion. The comparison is done by taking each row of the ‘fineness score matrix’ (one at a time) and checking each element of the row for the condition; IsZ ij P X j ? A concept is said to have passed through successfully if the corresponding concept rating in the jth row satisfies the given condition. Passing through successfully means the concept has satisfied the minimum level of expectations for the jth criterion. This process is analogous to separating finegrained particles from coarse-grained particles using a suitable sieve. Here the particles are the concept rating scores and the sieve pore size represents the expectation level of the main criterion. The condition imposed for successful passing ensures that only those particles (concept scores) with grain sizes finer than or equal to the sieve pore size (expectation level) of the main criterion are allowed to pass through. Larger the Zij score of a given concept, finer the grain size of the particle (concept). Similarly, larger the Xj value of a given sieve, smaller the sieve pore size of that sieve. It may be noted here that this is in no way a concept screening process. Though a given concept may fail to pass through one sieve; it may pass successfully through another. Fig. 8 shows the process of screening concept traits by passing concept scores through the sieves and recording successful concept traits. 3.7. Step-VII: form ‘concept roots’ The concept scores (Zij) that have successfully passed through the sieves refer to those traits that meet or exceed the minimum expectation levels of the stakeholders in the PD process. Fig. 9 shows the number of traits (rating scores) of each concept meeting minimum level of expectations. These successful traits are now referred to as ‘concept roots’. To form concept roots, all the main criteria (sieves) are arranged in descending order of sieve pore sizes (Xj), so that the topmost sieve has the maximum value of (Xj). This arrangement ensures that the criterion having higher expectation level is listed first and the one having lower most expectation level

Steering wheel Concepts III 8.34

IV

Safety

I

Durability

7.99

7.91

6.65

6.55

6.80

7.85

6.35

8.66

Steering Wheel Concepts I

II

III

IV

Durability

6.35 4.73 7.00

7.85 6.65 7.48

6.35 6.55 7.99

8.66 6.80 7.91

Safety

7.53

7.84

8.34

7.84

Aesthetics Convenience of Usage

Convenience of usage Aesthetics

Fig. 7. Fineness score matrix.

6.35

II

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

‘Fineness Score’ Matrix

‘Sieve pore size’ Matrix

6.35

7.85

6.35

8.66

6.00

4.73

6.65

6.55

6.80

6.50

7.00 7.53

7.48 7.84

7.99 8.34

7.91 7.84

7.50 8.00

Passed Concept Scores

6.35

Fig. 8. Screening of concept traits.

7.85

6.35

8.66

6.65

6.55

6.80

7.99 8.34

7.91

375

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

Root-1

Root-2

Root-3

Root-4

8.34

6.35

j=1

8.34

7.99

7.91

j=2

7.99

6.65

6.55

6.80

j=3

6.80

7.85

6.35

8.66

j=4

8.66

Empty root template

Hybrid root

Concept roots

Fig. 10. Hybrid root formation.

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

k = 1 to M; k = 1

Start

T-Hybrid-k

Is technically feasible?

k = (k + 1)

No

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

In this step, we generate new (hybrid) concepts from the concept roots identified in the previous step. This is done by grafting the nodes of concept roots corresponding to each criterion onto empty root templates (see Fig. 10) to form what we now refer to as ‘Hybrid roots’. These hybrid roots, if technically feasible, would be new concepts generated by bringing together desirable traits from the initially generated concepts. The new hybrid concepts thus formed would exceed, or at least meet, all expectation levels of the stakeholders that were set in the form of sieve pore sizes. Fig. 10 illustrates the process of hybrid roots formation from an initial set of concept roots. The aim of this process is to develop superior concepts by selecting feasible combinations of desirable traits. Owing to the fact that the initial concept traits are used to converge upon new (and better) concepts, we call this whole process as ‘concept convergence process.’ Since there are many concept root nodes available, theoretically one can explore a large number of combinations that will result in the formation of several hybrid concepts. The overall performance measure called ‘hybrid rating’ (HR) of the hybrids thus formed is given by following equation:

ðHRÞi ¼

n X

Z ij  X j

ð1Þ

No Is cost below cost ceiling?

No

k = M?

Yes Yes Select for further development

Stop

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

the main criteria ‘safety’, two concepts meet ‘durability’ criteria, three concepts exceed the expectation level of ‘convenience of use’, and all four concept scores meet the expectation level of ‘aesthetics’ criteria. Therefore, theoretically 1  2  3  4 = 24 combinations of hybrid roots are possible. The hybrid rating is calculated using Eq. (1). A sample calculation of hybrid rating for one 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  6:50Þ þ ð8:66  6:00Þ ¼ 222:805

j¼1

Here, n is number of sieves, Zij is the grafted ‘fineness score’ of the ith concept corresponding to the jth sieve (criterion), and Xj is the ‘sieve pore size’ of the jth sieve. In Eq. (1) the multiplication of Zij and Xj can be considered akin to weighting of rating scores in conventional approaches. The only difference is that the weighting parameter Xj takes values from the interval [0, 10] instead of the traditionally used interval [0, 1]. The team should form all the possible hybrid roots and arrange them in descending order of hybrid ratings. This is purely a theoretical step and involves only simple operations of choosing and placing the available concept root nodes onto the root templates (i.e. making all possible combinations from among the available root nodes), and is not at all time consuming if a simple algorithm is developed for doing the job. The outcome of this step is the set of all theoretically possible hybrid concepts that can be generated from hybrid roots. As shown in Fig. 9, only one concept rating score meets the expectation level of

3.9. Step-IX: check the ‘hybrid roots’ for technical feasibility and against the cost ceiling It is not necessary that simply by grafting together various nodes, a feasible concept will be generated. By grafting the nodes from different concept roots onto a hybrid, we are essentially trying to generate a new concept by combining different concept traits that are considered to be better and meeting expectation levels. However, it is not always true that these nodes taken from different concepts will be technically compatible with each other. If the nodes are found to be mutually compatible, i.e. the hybrid is found to be technically feasible, then the next step is to make a fair estimate of its expected cost. On the other hand, if the hybrid is not found to be technically feasible, then the next best hybrid is checked for its feasibility. This process is repeated until a feasible hybrid concept is found. If the estimated cost of a technically fea-

376

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

Table 5 Descriptions of final hybrid concept. T-Hybrid-1 Spokes Rim Main features Accessory features

Two in numbers, rectangular cross section, polished teak wood covering 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 cover 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 cover Visual 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)

sible hybrid concept is found to be lower than the pre-determined cost ceiling (established in the first step of the methodology), then this hybrid concept is selected for further development. If the estimated cost is above the ceiling, then the next best feasible hybrid is selected and this process is repeated until the required numbers of feasible hybrid concepts are selected for further development. The overall process involved in this step can be presented as a heuristic/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 (that was involved in generating the initial set of concepts) along with the description of the concept trait combinations for each hybrid. The design team is supposed to revert back with a set of hybrid solutions that are technically feasible; these may be slightly different from the actual theoretical hybrids, since the design team may have considered some minor trade-offs to make a theoretical hybrid technically feasible which otherwise was not so in its actual form. 3. The set of technically feasible hybrids is then analyzed to make a rough cost estimate for each technically feasible hybrid. 4. These hybrids are then screened with the cost ceiling, so that the team is finally left with a set of technically feasible hybrid solutions that have cost estimates below the pre-determined cost ceiling. These hybrid concepts may be taken for further development by the team. 5. If the final set of hybrid concepts is a null set, then the initial concepts are again taken into consideration by changing expectation levels and repeat the whole process. Based on the design team’s analysis, ‘T-hybrid-1’ was found to be technically feasible by the design team after making some minor trade-offs. The final description of ‘T-hybrid-1’ as sent back to the selection team is given in Table 5. This hybrid solution was found to be having a cost estimate below the pre-determined cost ceiling, and hence was selected for further development. Although there were three more hybrid concepts, which satisfied both technical and economical constraints, the team decided to focus their initial efforts on ‘T-hybrid-1’ concept only.

4. Conclusions The paper presents a structured methodology for improving and selecting product concepts through a concept convergence process. The new methodology puts more emphasis on converging existing concepts into new hybrid (improved) concepts rather than selecting the best available concept from the initial set of concepts. In this effort, the initial set of concepts is evaluated against selection criteria to identify superior traits from these concepts. The evaluation process of the proposed method deviates considerably from the traditional approaches wherein weights are assigned to each selection criterion, and instead establishes expectation levels for

each main criterion by capturing expectations of all the stakeholders. These expectation levels (sieve pore sizes) provide much better reflections of the decision-maker’s preferences and the resulting sieves are utilized to isolate superior concept traits. The fuzzy logic approach is used to deal with uncertainty in concept ratings. The concept convergence approach brings the superior traits from an initial set of concepts together and creates a set of hybrid concepts by exploring all possible combinations of these traits. The final decision of selecting hybrid concepts for further development is made by considering clearly defined economical and technical constraints. The development of hybrid or improved concepts through the concept convergence process generally improves the PD process effectiveness and enhances product reliability and hence customer satisfaction. The proposed framework extends the existing work on decision matrix models in concept selection and supports the ‘‘setbased concurrent engineering” philosophy devised by Toyota (Sobek, Liker, & Ward, 1999). However, the results still depend on the quality of information derived through the concept rating process and expert’s judgment in building the rule base. As with any modeling framework, one has to exercise great care to ensure that the data and inputs presented to the methodology are of good quality without which the results could be biased. The proposed method is particularly sensitive to the fuzzy rule base that aggregates the lower level sub-criteria ratings into top level criteria. This method is most beneficial during early stages of the product development, where one is generally constrained from collecting adequate quantitative data to accurately rate concepts against given selection criteria. The test and validation of the proposed framework and development of computer-based framework are to be studied in our future work. Cost estimation method at early stages of PD process needs to be explored further when information and knowledge regarding concept features is imprecise or qualitative. The development of heuristic approaches to enumerate and test possible hybrid combination is another potential area for future research.

References Augustine, M., Jain, R., & Yadav, O. P. (2010). A fuzzy-AHP-based framework for prioritising benchmarks in the service sector. International Journal of Productivity and Quality Management, 5(4), 452–472. Ayag, Z. (2005). A fuzzy AHP-based simulation approach to concept evaluation in a NPD environment. IIE Transaction, 37, 827–842. Ayag, Z., & Ozdemir, R. G. (2006). An analytic network process-based approach to concept evaluation in a new product development environment. Journal of Engineering Design, 1, 18. Bowles, J. B., & Pelaez, C. E. (1995). Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis. Reliability Engineering and System Safety, 50, 203–213. Chen, C., Lin, C., & Huang, S. (2006). A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, 102(2), 289–301. Chin, K., & Wong, T. N. (1999). Integrated product concepts development & evaluation. International Journal of Computer Integrated Manufacturing, 12(2), 179–190.

M. Augustine et al. / Computers & Industrial Engineering 59 (2010) 367–377 Crossley, W. A., Martin, E. T., & Fanjoy, D. W. (2001). Conceptual aircraft design environment: Case study evaluation of computing architecture technologies. AIAA Paper 2001-5247, Oct. 2001. Ebadian, M., Rabbani, M., Jolai, F., Torabi, S. A., & Moghaddam, R. A. (2008). A new decision-making structure for the order entry stage in make-to-order environments. International Journal of Production Economics, 111(2), 351–367. Hauser, J., & Clausing, D. (1988). The house of quality. Harvard Business Review (May–June), 67–73. Ip, W. H., Yung, K. L., & Wang, D. (2004). A branch and bound algorithm for subcontractor selection in agile manufacturing environment. International Journal of Production Economics, 87(2), 195–205. Ishii, K. (1995). Life-cycle engineering design. Journal of Mechanical Design, 117, 42–47. Jiao, J., & Tseng, M. M. (1998). Fuzzy ranking for concept evaluation in configuration design for mass customisation. Concurrent Engineering: Research & Application, 6(3), 189–206. King, A. M., & Sivaloganathan, S. (1999). Development of a methodology for concept selection in flexible design strategies. Journal of Engineering Design, 10, 329–349. Marsh, S., Moran, J. V., Nakui, S., & Hoffherr, G. (1991). Facilitating and training in quality function deployment. GOAL/QPC, Methuen, MA. Mattson, C. A., & Messac, A. (2002). Development of a Pareto-based concept selection method. In 43rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Paper No. AIAA 2002-1231, Denver, CO, April 22–25. Mullens, M. A., & Armacost, R. L. (1995). A two-stage approach to concept selection using the analytic hierarchy process. International Journal of Industrial Engineering, 2(3), 199–208. Mullur, A. A., Mattson, C. A., & Messac, A. (2003). Pitfalls of the typical construction of decision matrices. In AIAA 40th aerospace sciences meeting and exhibit, Paper Number AIAA – 2002-0466. Nepal, B., Monplaisir, L., & Singh, N. (2005). Integrated fuzzy logic-based model for product modularization during concept development phase. International Journal of Production Economics, 96, 157–174. Okudan, G. E., & Shirwaiker, R. A. (2006). A multi-stage problem formulation for concept selection for improved product design. In Proceedings of PICMET’06, July 9–13, Istanbul, Turkey.

377

Pahl, G., & Beitz, W. (1984). Engineering design. London: Design Council. Pahl, G., & Beitz, W. (1996). Engineering design: A systematic approach (2nd ed., pp. 178–187). London: Springer-Verlag. Pugh, S. (1991). Total design (pp. 67–85). New York: Addison-Wesley. Rosenman, M. A. (1993). Qualitative evaluation for topological specification in conceptual design. Applications and Techniques of Artificial Intelligence in Engineering, 2, 311–326. Saaty, T. L. (1981). The analytical hierarchy process. New York: McGraw-Hill. See, T.K., & Lewis, K., (2002), ‘Multiattribute decision making using hypothetical equivalents. In Proceedings of ASME DETC’02, September 29–October 2, 2002, Montreal, Canada. Sobek, D. K., II, Liker, J. K., & Ward, A. C. (1999). Toyota’s principles of set-based concurrent engineering. Sloan Management Review, winter 1999. Takai, S., & Ishii, K. (2004). Modifying Pugh’s design concept evaluation methods. In Proceedings of ASME DETC’04, September 28–October 2, 2004, Salt Lake City, Utah, USA. Thurston, D. (1990). Subjective design evaluation with multiple attributes. ASME DTM, 27, 355–361. Thurston, D. L., & Carnahan, J. V. (1992). Fuzzy ratings and utility analysis in preliminary design evaluation of multiple attributes. Journal of Mechanical Design, 114, 648–658. Thurston, D. L., & Locascio, A. (1994). Decision theory for design economics. The Engineering Economist, 40(1). Ulrich, K. T., & Eppinger, S. D. (2000). Product design and development (2nd ed., pp. 138–159). Boston: McGraw-Hill, Inc. Wang, J. (2001). Ranking engineering design concepts using a fuzzy outranking preference model. Fuzzy Sets and Systems, 119, 161–170. Wang, J. (2002). Improved engineering design concept selection using fuzzy sets. International Journal of Computer Integrated manufacturing, 15(1), 18–27. Yadav, O. P., Singh, N., Chinnam, R. B., & Goel, P. S. (2003). A fuzzy logic based approach to reliability improvement estimation during product development. Reliability Engineering and Systems Safety, 80, 63–74. Yadav, O. P., & Singh, N. (2008). Perspective and challenges for product reliability assurance during product development process. International Journal of Product development, 5(1/2), 4–16. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.