RETRACTED: Applying TRIZ and Fuzzy AHP to develop innovative design for automated manufacturing systems

Expert Systems with Applications 36 (2009) 8302–8312

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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Applying TRIZ and Fuzzy AHP to develop innovative design for automated manufacturing systems Te-Sheng Li a,*, Hsing-Hsin Huang b a b

Department of Industrial Engineering and Management, Minghsin University of Science and Technology, 1 Hsin-Hsin Rd., Hsin-Fong, Hsinchu 30401, Taiwan, ROC Department of Mechanical Engineering, Minghsin University of Science and Technology, 1 Hsin-Hsin Rd., Hsin-Fong, Hsinchu 30401, Taiwan, ROC

a r t i c l e

i n f o

Keywords: TRIZ Fuzzy analytical hierarchy process Contradiction matrix table Automated manufacturing system

a b s t r a c t Innovative design in the development of new product and process has become the core value in most business establishments. These innovative designs are often associated with the long-established trade-off compromises or conflicting performance parameters where speed and reliability, or quality and cost are readily acknowledged. The rate of change in technology and the commercial environment suggests that the opportunity for innovative design is accelerating, and systematic support for innovation process is needed. This study combines the Russian Theory of Inventive Problem Solving (TRIZ) and the fuzzy analytical hierarchy process (AHP) for designing the automated manufacturing systems. This study applied the contradiction matrix table, 40 innovative principles, and 39 engineering parameters to compromise the trade-off between design contradictions and engineering parameters. The design engineers can acquire more feasible solutions and inspiration through the proposed approach. However, due to vagueness and uncertainty in the decision-maker’s judgment, a fuzzy AHP is employed as a decision support tool that can adequately represent qualitative and subjective assessments under the multiple criteria decision making environment. Moreover, the proposed approach can help decision makers facilitate the selection and evaluation of innovative designs in the presence of intangible attributes and uncertainty. In short, the objectives of this research are to use TRIZ to propose the automated design alternatives under the innovative design consideration, and to use a fuzzy AHP to evaluate and select the best feasible alternative under multiple criteria. A case study of designing automated connector assembly line has been used to demonstrate the applicability of the proposed approach. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction The rapidly changing modern marketplace drives companies to seek competitiveness in product/process development in terms of innovation, high quality, and speed to market. Since innovative design decisions in the early design stages play a critical role in deciding the product development time, it is extremely important to make a systematic approach to design decisions in the early phase of design. The concept of trade-off, or conflicting performance parameters is a core element of design where speed and reliability, or quality and cost are readily acknowledged. These engineering designs are well documented and the trade-off parameters are balanced in the design process to achieve engineering optimization for a particular application. However, the practice of using trade-off parameters as a focus for systematic innovation in the mechanical design has only recently emerged from TRIZ (the Russian acronym for the ‘theory of inventive problem solving’). Numerous researchers have applied the concept of mechanical de* Corresponding author. E-mail address: [email protected] (T.-S. Li). 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.10.025

sign trade-offs to help acknowledge and manage conflicting performance parameters associated with manufacturing. For a design engineer, when he/she tries to solve an innovative design problem, he/she usually faces a systematic incompatibility or conflict design problem. As the design engineer changes certain parameters of the system in his/her thorny design problem, it might affect other parameters badly. Traditionally, the design engineer always compromises with this kind of contradictory situations and restricts him on performing innovative design tasks. The Russian Theory of Inventive Problem Solving (TRIZ) was originally proposed by Altshuller (1999). This method solves technical problems and offers innovative product structures by employing a knowledge base built from the analyses of approximately 2.5 million patents, primarily on mechanical design. TRIZ consists of three basic tools: (1) ‘the system conflict resolution principles’, which consists of 40 principles to effectively resolve the conflicts between customer requirements, (2) ‘effect’, which is a knowledge database system consisting of physical, chemical, and geometrical effects and rules for problem solving, and (3) the ‘substance-field model’ for modeling a technological problem in the form of ‘two materials’ and for deriving answers that make

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the above interaction change in the desired direction. In this way, TRIZ shows its potential as a support tool for creating the original idea in the ‘innovative design’ processes. The basic constituents of TRIZ are the contradictions, 40 inventive principles, the contradiction matrix (Domb, 1997, 1998; Zoyzen, 1997) and the laws of evolution (Petrov, 2002), the substance-field analysis modeling (Terninko, 2000), ideal final result (Domb, 1997), and substance field resources, scientific effects (Frenklach, 1998), and ARIZ (the Russian acronym for the ‘algorithm of inventive problem solving’) (Zlotin & Zusman, 1999). The core of TRIZ consists of 40 contradiction principles, and the matrix; other tools are auxiliary to assist design engineers in constructing the problem model and analyzing it. The TRIZ approach has applied to numerous design problem-solving such as CCD laser instrument for measuring complex 3D curved surfaces (Liu & Chen, 2001), auto-focus camera with lower response time (Jung, Bae, Suh, & Yi, 2006), CAD software integrating TRIZ into eco-design tool (Chang & Chen, 2004), integrating steering shaft lock for motorcycle (Mao, 2000), and Technology Forecasting of CCD and CMOS (Tompkins, Price, & Clapp, 2006). The most commonly applied tool is the matrix, which is composed of contradictions and 40 principles. The contradiction means that a worsening engineering parameter (avoiding degradation parameter, ADP) and an improving parameter (IP) exist simultaneously. There are 39 engineering parameters including the weight of object, the dimension of object, the force of object, and so forth. The matrix is a 39  39 matrix, which contains the zero to four most likely principles for solving design problems involving the 1482 most common contradiction types as shown partly in Table 1. The basic process of using TRIZ is as the following statement: For using TRIZ in the innovative design problem solving, the design engineer needs to first find the corresponding contradictions for his/her problem at hand. Next, the design engineer matches the meaning of each contradiction with two appropriate parameters from 39 engineering parameters defined in the matrix (Domb, 1997). The design engineer can find the inventive principles for solving the engineering innovative design problem from the matrix when he confirms the parameters of contradiction for an engineering system. Analytic hierarchy process (AHP) is one of the most popular methods used commonly in industry to aid in alternatives selection. In the conventional AHP developed by Saaty (1980), the pair-wise comparisons for each level with respect to the goal of the best alternative selection are conducted using a nine-point scale. The main advantage of AHP is its inherent ability to handle intangibles, which are predominant in any decision making process like the case presented in this paper. Also, less cumbersome mathematical calculations and comprehensibility makes the AHP an ideal technique that can be employed in the evaluation process. The AHP approach determines the weights qualitatively by constructing multi-level decision structures and forms pairwise comparison matrices. In the application of AHP, the decision maker’s

subjective judgments are quantified by assigning the corresponding numerical values based on the relative importance of alternatives under consideration to their parent component in the decision hierarchy. The next step is to repeat the AHP procedure to obtain the relative contributions of alternatives to the accomplishment of each improvement objective. The result is a set of weights for the manufacturing system alternatives that represents their contributions to the improvement objectives and the competitive strategy of the company. Wabalickis (1988) applied AHP as stand-alone method to justify the flexible manufacturing system. Datta, Samabasivarao, Kodali, and Deshmukh (1992) presented a generic decision making model and used AHP to justify manufacturing systems. Samabasivarao and Deshmukh (1997) used AHP as an integrated tool to select and justify advanced manufacturing technologies. Byun and Lee (2004) proposed a modified TOPSIS based decision support system to select a rapid prototyping process by employing AHP to determine criteria weights. Chan, Jiang, and Tang (2000) developed the intelligent tools, such as expert systems, fuzzy systems, neural networks and AHP, based on multi-criteria decision-making technique to aid the selection of most suitable FMS design. However, the above cited literature on the application of AHP to the selection or evaluation problem reveal that most of them employ conventional or crisp AHP, which does not address the issue of uncertainty. Fuzzy AHP is an extension of conventional AHP and employs fuzzy set theory to handle uncertainty. The main purpose of this article is to evaluate the contradiction check in the engineering design, check fuzzy judgment matrices, derive priorities from fuzzy judgment matrices, and make a final decision under group experts using fuzzy AHP. This article demonstrates the application of weighted geometric mean and arithmetic mean to aggregate the individual priorities in the fuzzy AHP to reach group consensus. All of these issues and evaluation of engineering design are illustrated with a numerical example. The fuzzy AHP technique has been employed to develop the decision-making support tool for numerous industrial applications including FMS design and analysis (Chan et al., 2000), resources allocation enhancements (Ariel & Reich, 2003), quantitative measurement for design freedom (Wood & Agogino, 2005), and engineering design concept selection (Ullman, 2002). Furthermore, Frey, Jahangir, and Engelhardt (2000), for example, offer a more reliable calculation of decoupled designs with Axiomatic Design. Xiao, Zeng, Allen, Rosen, and Mistree (2005) apply game theory to collaborative design environments and use design capability indices to quantify some uncertainties in the outcome. Saaari and Siebery (2004) apply geometric tools to consider the quality of pairwise comparisons. Ayag (2005) integrated the simulation with fuzzy AHP method to evaluate the conceptual design alternatives in a new product development. Ayag and Ozdemir (2006) proposed fuzzy AHP and Benefit/Cost (B/C) ratio analysis to select the best machine tool under the multiple-criteria decision making environment. Jaganathan, Erinjeri, and Ker (2007) discussed three issues

Table 1 Partial cells of contradiction matrix. IP

ADP 1

2

3

4



11

1 2 3 4 12 .. . 39

#15, #35, #10, #14

39

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that are critical to fuzzy AHP while the manufacturing organizations made complex decisions in regard to investment in new manufacturing technologies. Singh, Khilwani, and Tiwari (2007) justified and quantified the reconfigurable manufacturing system using fuzzy AHP that aid in rapidly adjusting their capability to production functionality. Scott (2007) quantified the uncertainty in multicriteria concept selection method using fuzzy AHP for an engineering design. The paper is organized as follows. Section 2 is dedicated to the introduction of some fundamentals about TRIZ. Section 3 describes the basic theory of fuzzy AHP and steps. Section 4 proposes the approach for solving the design problem. A case study is illustrated for designing the automated manufacturing system in Section 5, while Section 6 provides a detailed discussion. Finally, the last section highlights the most relevant results of the authors work and suggests possible extensions. 2. The TRIZ TRIZ, an acronym for the Theory of Inventive Problem Solving, began in 1946 when Altshuller, a mechanical engineer, began to study patents in the Russian Navy. This approach has widely been taught in Russia, but did not emerge in the West until the late 1980s. Several different solution systems have been derived by abstracting inventive principles from the ongoing analysis of patent data. Several of these solutions focus on contradictions or trade-offs in identifying innovative solutions. There are three premises on which the theory may be viewed: (i) the ideal design with no harmful functions is a goal, (ii) an inventive solution involves wholly or partially eliminating a contradiction and (iii) the inventive process can be structured. Each of these premises will be dealt with in turn. Finding the ideal solution to a needed function or effect with no harmful or negative effects is referred to in TRIZ circles as Ideality:

Ideality ¼

All useful functions or effects All harmful functions or effects

ð1Þ

One may argue that there is little new in this, as a similar emphasis on improving functionality is also evident in widely established approaches such as Value Engineering. However, the difference is that this thinking is central to TRIZ and numerous supporting tools have been developed that specifically concentrate on improving the functionality through innovation rather than the traditional cost cutting or sub-optimization focus. Altshuller’s (1999) early work on patents resulted in classifying inventive solutions into five levels, ranging from trivial to new scientific breakthroughs. Although there is potential to structure the inventive process around trade-off contradictions leading to several developments, only the technical contradiction solution system and physical contradiction solution system are introduced here. Fig. 1 illustrates this abstraction process, which classifies problems and solutions in seeking correlation that enables a set of generic problem solving operators or principles to be identified. 2.1. Technical contradiction solution system After having identified the significance of contradictions, Altshuller went on to classify them into 39 parameters and 40 common principles that are repeatedly used in patented solutions. To display the possible technical contradiction combinations, he produced a 39  39 matrix and identified which of the 40 inventive principles were more commonly associated with specific combinations of contradiction parameters (see Table 1). This matrix is called the Technical Contradiction Matrix.

Correlation Operators Generic Problem Category

Generic Solution

Classification

Classification

Specific Problem

Category

Specific Solution

Fig. 1. The general case for abstracting a solution system.

2.2. Physical contradiction solution system Over a period of time Altshuller identified a further level of abstraction from the technical contradictions. He found that, in many cases, the technical contradiction could be presented as two extremes of one feature, which he called a physical contradiction. More formally, a physical contradiction requires mutually exclusive states as they relate to a function, performance or a component. Typical physical contradictions include: fast vs. slow; solid vs. porous; moveable vs. stationary; hot vs. cold, etc. The relationship between the technical and physical contradictions can be described as follows. A technical contradiction between parameter A and B has further abstracted to present the contradiction in terms of common variable parameter C, which represents the physical contradiction. Altshuller found that by defining the contradiction around one parameter with mutually exclusive states the correlation operators used to detect a solution could be more generic and there are four separation principles used to help resolve this type of contradiction. The separation principles can be summarized as: (i) separation of opposite requirements in space, (ii) separation of opposite requirements in time, (iii) separation within a whole and its parts, and (iv) separation upon condition. Fig. 2 briefly illustrates the relationship between these two levels of abstraction. Fig. 2 illustrates the relationship between these two levels of abstraction. If one considers the aircraft example, the technical contradictions are speed and adaptability (e.g. take-off and landing distances) and look for another common parameter displaying mutually exclusive states. Such a parameter in this example might be the wing area. A small wing area is required for speed, but for take-off, landing and general maneuverability a larger wing area is required. The four separation principles would then be considered and, in this case, ‘separation in time’ naturally leads to the possible option of variable wing geometry. 3. Fuzzy AHP 3.1. Fuzzy set theory Fuzzy set theory was introduced by Zadeh in 1965, to solve the problems involving the absence of sharply defined criteria (Zadeh, 1994). If the uncertainty (fuzziness) of human decision-making is not taken into account, the results can be misleading. The key idea of fuzzy set theory is that an element has a degree of membership in a fuzzy set (Negoita, 1985; Zimmermann, 1996). A fuzzy set is defined by a membership function (all the information about a fuzzy set is described by its membership function maps elements (crisp inputs) in the universe of discourse (interval that contains all the possible input values) to elements (degree of membership) within a certain interval which is usually [0, 1]). Then, the degree of membership specifies the extent to which a given element belongs to a set or is related to a concept. The most commonly used range

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Separation Principles

Generic Problem (physical contradiction)

Generic Solutions (Selected separation Principles)

Specialization

Classification Contradiction Matrix

Generic Problem (technical contradiction)

Generic Solutions (Selected from 40 Principles)

Specialization

Specialization

Classification Specific Problem

Specific Solution

Fig. 2. The first and second levels of abstraction.

for expressing the degree of membership is the unit interval [0, 1]. Fuzzy theory thus is used to solve such kind of problems, and it has been applied in a variety of fields in the last four decades. Theory of fuzzy sets has evolved in various directions, and treating fuzzy sets as precisely defined mathematical objects subject to the rules of classical logic and the linguistic approach are the two distinct directions. The underlying logic of linguistic approach is that the truth-values are fuzzy sets and the rules of inference are approximate rather than exact (Gupta, Saridis, & Gaines, 1977). In this ~ 9, ~ are used to represent subjecstudy, triangular fuzzy number, 1— tive pairwise comparisons of selection process in order to capture the vagueness. A fuzzy number is a special fuzzy set A = fðx; uA~ ðxÞÞ; x 2 Rg, where x takes it values on the real line, R : 1 < x < þ1 and uA~ is a continuous mapping from R to the closed interval [0, 1]. As shown in Fig. 3, the triangular fuzzy num~ = (a, b, c), where a 6 b 6 c, and the membership function is ber A defined as

8 xc > < ac ; c  x  a; xb uA~ ¼ ab ; a  x  b; > : 0; otherwise; 0  c  a  b

ð2Þ

AHP, the pairwise comparison, is made by using a ratio scale. A frequently used scale is the nine-point scale (Saaty, 1989, see Table 2) which shows the participants’ judgments or preferences among the options such as equally important, moderately more important, strongly more important, very strongly more important, and extremely more important. Even though the crisp scale of 1–9 has the advantages of simplicity and easiness for use, it does not take into account the uncertainty associated with the mapping of one’s perception or judgment to a number. The triangular fuzzy number, ~ 9, ~ are utilized to improve the conventional nine-point scaling 1— scheme. In order to take imprecision of human qualitative assess-

μ A~ ( x)

Table 2 Definition and membership function of fuzzy number. Intensity of importance

Fuzzy number

Definition

Membership function

Reciprocal scale

1 3

~ 1 ~ 3

(1,1,2) (2,3,4)

5

~ 5

7

~ 7

9

~ 9

(1/2,1,1) (1/4,1/3,1/ 2) (1/6.1/5,1/ 4) (1/8,1/7,1/ 6) (1/10,1/9,1/ 8)

2,4,6,8

~ 4; ~ 6; ~ 8 ~ 2;

Equally important Moderately more important Strongly more important Very strongly more important Extremely more important Intermediate values

(6,7,8) (8,9,10)

ments into consideration, the five triangular fuzzy numbers and the reciprocal scale are defined with the corresponding membership function as shown in Table 2 and Fig. 4, respectively. 3.2. Fuzzy AHP Most of the basic steps involved in fuzzy AHP are similar to crisp AHP. However, the use of fuzzy numbers instead of crisp numbers and the process of extracting priorities from the pairwise comparison differentiate fuzzy AHP from crisp AHP. The six steps that are common to both AHP and fuzzy AHP are listed in the following (Cheng, 1999; Chi & Kuo, 2001): 1. Define the unstructured problem and state clearly the objectives and outcomes. 2. Decompose the complex problem into a hierarchical structure with decision elements (criteria, detailed criteria, and alternatives).

u A~

Equally

Moderately

~ 3

~ 1

Strongly

~ 5

Very strongly

Extremely

~ 9

~ 7

1.0

1

1

0

(4,5,6)

c

a

b

~ ¼ ða; b; cÞ. Fig. 3. Membership function of a triangular fuzzy number A

2

3 4 5 6 7 Intensity of importance

Fig. 4. Fuzzy membership function.

8

9

10

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3. Employ pairwise comparisons among decision elements and form comparison matrices. 4. Use the eigenvalue method to estimate the relative weights of the decision elements. 5. Check the consistency property of matrices to ensure that the judgments of decision makers are consistent. 6. Aggregate the relative weights of decision elements to obtain an overall rating for the alternatives. The fuzzy AHP approach works in a similar way that of crisp AHP. The basic difference lies in the comparison of elements at a given level in giving their relative weights in relation to the element at the immediate upper level. Here, instead of using a crisp ratio scale, triangular fuzzy numbers are used to represent the subjective pairwise comparison of alternatives in order to capture vagueness. In fuzzy AHP, triangular fuzzy numbers are utilized to improve the scaling scheme in the judgment matrices and fuzzy arithmetic is used to solve the fuzzy value (Ayag, 2005; Cheng & Mon, 1994). The overall procedure of this approach is given in the following steps. ~ 9) ~ to an element indi1. Assign a triangular fuzzy number (1— cating the relative strength of each pair of elements present in the hierarchy. 2. Construct a hierarchy using these triangular fuzzy numbers that represents the pairwise comparison of the elements at a cer~ ij Þ is constructed as given below: tain level. The matrix Aða

2

1 6 . 6 .. ~¼6 A 6 . 6 . 4 . ~n1 a

~13 a .. . .. . ~n3 a

~12 a .. . .. . ~n2 a

where aij ¼



3 ~1n  a .. 7  . 7 7 .. 7 7  . 5  1

ð3Þ

(

aijl ¼

aaiju ¼

~ ~ij ¼ 1 a ~ 9 ~ ~ij  xÞ þ xa; a ~ij ¼ 2— ða ~ ~ij ¼ 9 a ~ 8 ~ ~ij þ xÞ  xa; a ~ij ¼ 1— ða

~ ij ; a

~aij ¼ l  a ~aiju þ ð1  lÞ  a ~aijl ; a

ð4Þ

ð5Þ

8 l 2 ½0; 1

ð6Þ

Based on the above equation, the matrix obtained for a particular value of a is given as

1 6 . 6 . . ~a ¼ 6 A 6 . 6 . 4 . ~an1 a

!1=3 M kij

2 !1=3 31 n n X Y k 5 4 M ij

j¼1

i¼1

ð8Þ

j¼1

Q To obtain nj¼1 Mkij , fuzzy multiplication is performed for a particular matrix at a certain level such that n Y j¼1

Mkij ¼

n Y

~aijl ; a

j¼1

n Y j¼1

~aij ; a

n Y

! ~aiju a

ð9Þ

j¼1

Then the fuzzy addition operation for that level matrix and the weight of factors underlying that matrix are calculated using the equation

W ki ¼ ðwkij ; wkim ; wkiu Þ 20  1=3 1 0  1=3 1 0  1=3 13 n n n Q Q Q a a a ~ ~ ~ a a a 6B C B C B C7 ij iju ijl 6B C B C B C7 j¼1 j¼1 j¼1 ¼ 6B  1=3 C; B  1=3 C; B  1=3 C7 n n n 4@Pn Q A @Pn Q A @Pn Q A5 a a a ~ a iju

j¼1

i¼1

~ a ij

j¼1

i¼1

~ a ij

j¼1

l

~a12 a .. . .. . ~an2 a

~a13 a .. . .. . ~an3 a

3 ~a1n  a .. 7 7  . 7 .. 7 7  . 5 

5. The priority weight of each alternative is obtained by synthesizing the priorities of each level using fuzzy addition and multiplication. Finally, a crisp weight is calculated that decides the superiority of an alternative. 4. The proposed approach

Here, x is the maximum range of judgment and a represents the ~aij , decision maker’s confidence in his/her judgment. Further, a the most likely value of the fuzzy number, is estimated by setting the index of optimism, i.e. l. This index l, representing the degree of satisfaction of the decision maker, is used to evaluate the value of ~aij using the following equation a

2

¼

n Y

ð10Þ 1 i¼j 1 ~ 1 ~ ~ ~ 1—9or 1 —9 ; i–j

~ ij ; a

(

W ki

i¼1

3. The next step is to calculate the lower and upper limit of the ~ij with respect to a certain value of a, corresponding h i fuzzy h number i a ~¼ a ~aijl; a ~aij , a ~aiju , where ~aij ¼ a i.e. A a

quently the overall inconsistency of the hierarchy. The consistency index (CI), which is a measure of inconsistency, is given by CI = ðkmax  nÞ=ðn  1Þ, where kmax is the largest eigenvalue of ma~ a and n is the dimension of the matrix (Kwong & Bai, 2003). trix A The consistency ratio (CR) is used to directly estimate the consistency of pairwise comparison. It is computed by dividing the CI by a value known as the random index (RI), i.e. CR = CI/RI. When CR becomes greater than 10%, the problem and judgment are revised (Saaty, 1986). 4. After calculating the consistency ratios of the entire matrix and making it below 0.1, the next step is to calculate the weight vector for each factor lying at different levels of the hierarchy. This is calculated using the equation

In this paper, an innovative design approach, TRIZ and a fuzzy AHP, is employed as an integrated methodology for the selection of an appropriate manufacturing system. Here, TRIZ is applied by breaking up the complex design problem into a contradiction matrix as well as incentive principles. In addition, a fuzzy AHP is conducted by decomposing the structure of decision process into a hierarchical sequence in order to determine the relative importance of each alternative manufacturing system through pairwise comparisons. The common design parameters for selecting a suitable manufacturing system, including productivity, safety and environment, quality, flexibility, and cost are taken into account. By trading off among these tangible and intangible engineering parameters and manufacturing system alternatives, a design strategy towards a best manufacturing system is achieved. In this paper, the proposed approach is adopted for the evaluation and selection of new generation manufacturing systems. The integrated approach as shown in Fig. 5 comprises of the following steps.

ð7Þ

1

To assign the intensity importance to the factor, it is necessary to find the consistency of the decision maker’s judgment and subse-

4.1. Analyze the existing manufacturing system Firstly, the proposed approach incorporated engineering parameters and strategic managerial parameters to analyze the existing manufacturing system. The related decision makers

T.-S. Li, H.-H. Huang / Expert Systems with Applications 36 (2009) 8302–8312

Analyze the existing manufacturing system

Identify the attributes for evaluating the manufacturing system

Construct the Contradiction Matrix and propose the related inventive principles

8307

propose the guidelines for the design of product, process and manufacturing system. On the other hand, Falkner and Benhajla (1990) present an article on the process and methodology for establishing and choosing criteria. They enlist nine major dimensions like flexibility, competition, and inventory that will enable the decision making process to capture tactical and strategic objectives of the company. The topmost level in the hierarchical structure for the evaluation problem is the goal to achieve the best manufacturing system design. The second and third levels are with the set of chosen criteria and sub-criteria, respectively. The last level comprises available alternatives.

Construct the hierarchy of fuzzy AHP 4.5. Collect the relevant data (questionnaire)

Collect the relevant data

The next step involves the collection of expert opinions through a questionnaire survey. The expertise comprises plant manager, shop floor manager, and design engineers.

Prioritizing subjective criteria using fuzzy AHP

4.6. Prioritizing subjective criteria using fuzzy AHP, and calculating the weights for each level of hierarchy

Find the final evaluation and select the best manufacturing system Fig. 5. Flowchart of the proposed approach.

propose their ideas for planning and designing the manufacturing system to fulfill the requirements of the company. In the process of selection and evaluation of the manufacturing system, the decision making panel mainly comprises the plant manager, the shop floor manager and the manufacturing designers. 4.2. Identify the attributes for evaluating the manufacturing system Secondly, the proposed approach establishes the link between each managerial parameter and engineering parameters. Especially, the relationship of each managerial parameter element with the 39 engineering parameters of TRIZ is examined. For example, the productivity improvement of the manufacturing system can be obtained by worsening the reliability of the system. This means that improving the ease of manufacturing system may worsen the precision of manufacturing. Therefore, the problem of improving the managerial functions is transferred to TRIZ problem. Thus, Table 1 illustrates the relationship between all elements of 39 engineering parameters and the corresponding 40 principles of TRIZ. To examine the contradiction matrix Table 1 is to identify the available engineering parameters with respect to the managerial function of the manufacturing system. 4.3. Construct the Contradiction Matrix and propose the related inventive principles The essential managerial functions for the manufacturing system include productivity, flexibility, precision, reliability, safety and environment. Basically, the contradiction matrix can help design engineers to realize the conflict of the engineering problem, and obtain the feasible inventive principles through the patent database. 4.4. Construct the hierarchy of fuzzy AHP One of the most critical components in the decision making process is choosing the criteria against which alternatives will be evaluated. TRIZ, 39 engineering parameters and 40 inventive principles

The proposed fuzzy AHP assists decision makers in structuring the multi-criteria strategic decision making for the potential design of manufacturing system. Once the hierarchy is structured, pairwise comparison among the different elements of a level is performed with respect to a particular higher level element. Usually, a nine-point fuzzy number as suggested by Saaty (1981) is used for comparing various levels which are translated into pairwise comparison judgment matrices. 4.7. Find the final evaluation and select the best manufacturing system In the final phase of evaluation, weight vectors for the individual levels of hierarchy are evaluated using the methodology given in the ranking. On the basis of their weights, the final alternatives are ranked using the ranking value. However, if two alternatives have a similar ranking value, then they are compared using the most likely value and finally the alternative with the largest OV– PV will be selected. OV stands for the optimistic value (upper value), and PV represents the pessimistic value (lower value).

5. The case study 5.1. Problem description To validate the applicability of the proposed approach, the approach is implemented in a real case of manufacturing system selection problem. In this research, an electronic connector manufacturer located in Taiwan has been taken into consideration. The company is engaged in the production of a variety of connectors for communication devices, computers and consumer electronics. Although the company uses semi-automated production line, it still lacks the efficiency to cope with a change in product design due to its existing production line. Taking into account the current trends in business and future needs, the company is committed to achieving a planned technological development. In order to maintain the company’s competitive advantage in the market place, the aforementioned TRIZ and fuzzy AHP approach provide a methodology to select the best alternative from the substitutes present in their domain, based on certain subjective and objective aspects. In our study, the plant manager, the shop manager and the manufacturing designer are set up with the decision makers for this project. Initially, the decision makers classify the criteria and sub-criteria influencing their judgment and collect the relevant data using the innovative design tool, TRIZ. On the contrary, in

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order to prioritize the relative importance of each manufacturing system alternatives, the strategic variables of the present complex decision-making problem are structured into a multilevel hierarchy.

(1) Improving the production speed (#9), and avoiding the degradation system reliability (#27) and accuracy of measurement (#28). (2) Improving the ease of manufacturing (#32), simplifying the production process and avoiding the degradation system functions (#35). (3) Improving the productivity (#39) and avoiding the degradation of accuracy of manufacturing (#29).

5.2. The innovative design tool and Fuzzy AHP Above, a TRIZ combined with a fuzzy AHP approach to the evaluation of the manufacturing system alternative has been presented. In this section, the following research steps are carried out in accordance with the steps illustrated in the proposed flowchart (see Fig. 5). Step 1: Analyze the existing manufacturing system The communication connector consists of insert component, copper lead and housing component. The material of insert component is plastic, L cubic type with 8 pressed slots (width = 0.45 mm). The complexity of combining insert component with copper lead will be challenging for the designer. The introduction of automated mechanism may tackle this difficulty and partial area electroplating can reduce the material cost. Initially, the designer observes the existing manual operation system and converts the manual system into the automated manufacturing system via redesigning the flow process and mechanism. The existing manual system has the following problems: (1) The complex manual operations make the cycle time longer and cannot meet the requirement of production. In addition, it causes higher production cost. (2) The deficiency of efficiency is caused by the boring manual operations with respect to the connector mass production. (3) Too many work-in-processes stacked with the side of the production line makes the production inefficient. (4) Combining the insert component with housing component via manual operation may easily scratch the surface of electroplating, causing more defective products. Step 2: Identify the attributes (engineering parameters) for redesigning the manufacturing system According to the existing problems in the system, the designer discussed with the shop manager and plant management, and found some manufacturing contradictions existing in the manual system. The designer identified three major contradictions in the manufacturing system.

Step 3: Construct the contradiction matrix and propose the related inventive principles From step 2, the design engineer identifies three major contradictions and then finds the corresponding engineering parameters and incentive principles from Table 1. The three contradictory features and related feasible solutions are listed in Tables 3–5, respectively. The innovative design is shown in Fig. 6. Step 4: Construct the hierarchy of fuzzy AHP The evaluation of automated manufacturing systems is conducted by fuzzy AHP methodology in this research project. The designer suggests the project team that the manufacturing system design not only considers the innovative design rules (e.g. productivity, reliability, precision, etc.) but also considers the environment safety and cost of the manufacturing system. Fig. 6 shows the hierarchical structure used. The goal of the fuzzy AHP model is to choose the best automated manufacturing system for a company. First level criteria include productivity, flexibility, precision, reliability, safety & environment and cost. The sub-criteria of system function include production rate, auto loading/unloading, lead time and machine utilization. The sub-criteria of flexibility are parts type, routings, and transfer mechanism. The sub-criteria of precision are position sensor, repeatability and feasibility. The sub-criteria of reliability are system stability, repeatability, and Table 4 Contradiction combination (II) and related incentive principles. IP

ADP

Related incentive principles

(#32) (Ease of manufacture)

(#35) (Adaptability)

#2 Extract 1. Avoid using the bulk wires and assemble wiring with housing simultaneously. Thus, it can increase the production speed and avoid wire intertangling

Table 3 Contradiction combination (I) and related incentive principles. IP

ADP

Related incentive principles

(#9 Speed)

(#29) (Accuracy of measurement)

#10:Prior action1. Put the insert, housing and wiring parts into auto-feeder in advance, for feeding and orientation of automatic parts more conveniently for the next operation2. Put the insert subassembly with wiring on the front of the cylinder, and wait for mother parts to the fixed position and drive the cylinder to finish operation3. Redesign the cutting tool and put it vertically on the top side of the wiring. The prior actions of cutting operation include cutting the right-hand side of carrier, insert the wiring, and cutting the left-hand side of carrier, then bend the wiring #25:Self-service1. Put the insert and housing components into the auto-feeder machine2. Auto error detection, use position sensor to detect the cylinder position3. Preset the sensor on the front of insert and housing feeding position, avoid running out of parts and automatically detect the error #28:Replacement of a mechanical system1. Use a spray nozzle to deliver the finished goods and avoid the metal surface scrap2. Utilize the electronic signal to inspect the quality #11: Cushion in advance1. The actuator is combined with the redesigned mechanism and the bolt is positioned to enhance the cutting force of the cutting tool to avoid any damage to the parts to be inserted2. Preset the cutting tool on the vertical overhead of the wiring and combine the parts to be inserted with the wiring firmly. In contrast to the manual assembly, automatic assembly can predefine the cutting position and avoid surface scratches3. Due to the high speed of feeding the part to be inserted and the difficulty of positioning, suggest using the position sensor to detect the insertion parts and avoid running out of parts4. Consider the firm of the subassembly insert part with the wiring, additionally design the diamond tenon on the insert part, and also change the special material for avoiding crash5. Wiring carrier avoids wire spreading upon processing the insetting operation #27: An inexpensive short-life object instead of an expensive durable one1. Substitute the partial electroplating wiring for overall electroplating wiring and reduce the cost2. Wiring carrier is disposable after processing #28: Replacement of a mechanical system1. Provide the sensors to confirm accurately the cylinder position along with the suitable mechanism and design the sequence control system for coordinating the subsystem operation

(#27) (Reliability)

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T.-S. Li, H.-H. Huang / Expert Systems with Applications 36 (2009) 8302–8312 Table 5 Contradiction combination (III) and related incentive principles. IP

ADP

Related incentive principles

(#39) (Productivity)

(#29) (Accuracy of measurement)

#10: Prior action1. Put the insert, housing and wiring parts into the vibratory bowl feeder location in advance, for automatic parts feeding and orienting that are more convenient for the next operation2. Put the insert subassembly inset with wiring on the front of cylinder, wait for mother parts to the fixed position and drive the cylinder to finish the operation3. Redesign the slot in the transfer system that it makes the insert parts move to the correct position for insertion. Thus, the number of operations will be eliminated and also can reduce the cost#18: Mechanical vibration1. Using vibratory bowl feeder for feeding insert and housing parts can automatically adjust parts feeding and orienting reducing time and cost. Adding sensors in the auto-feeder also can control the capacity of the feeder

Fig. 6. The innovative design, NO. I–V present the cylinders.

reliability of transfer system. The sub-criteria of safety and environment are operational environment, ergonomics requirement and safety equipment. The sub-criteria of cost are system cost, labor cost and equipment cost. Thus, the AHP approach decomposes a problem into the elements. Then, the criteria are assessed by pairwise comparisons. The last level is the manufacturing system alternatives labeled here as alternative A, B and C, respectively. In fuzzy AHP, pairwise comparisons use triangular fuzzy membership, in the sense that the decision makers need to express their preferences in an approximate way by judgment or by stating a ~ 9 ~ comparison scale. single number taken from the 1— Step 5: Collect the relevant data Fig. 7 shows a diagram of main criteria with their sub-criteria used for the selection of manufacturing system. The next step involves the collection of expert opinions from the questionnaire ~ 9). ~ The expertise comprises using triangular fuzzy numbers (1— of plant manager, shop floor manager, and design engineers. One of the expert opinions of pairwise comparison matrix for the main criteria using fuzzy numbers is given in Table 6. The lower limit and upper limit of the fuzzy numbers with respect to the a were defined by applying Eqs. 5 and 6 as follows:

~ a ¼ ½1 þ 2a; 5  2a; ~ a ¼ ½1; 3  2a; 3 1 ~ a ¼ ½3 þ 2a; 7  2a; 7 ~ a ¼ ½5 þ 2a; 9  2a 5   1 1 ~ 1 ¼ ~ a ¼ ½7 þ 2a; 11  2a; 3 ; 9 ; a 5  2a 1 þ 2a     1 1 1 1 ~ 1 ¼ ~ 1 ¼ ; ; 5 ; 7 ; a a 7  2a 3 þ 2a 9  2a 5 þ 2a   1 1 ~ 1 ¼ ; 9 a 11  2a 7 þ 2a

Then, we substituted the values, a = 0.5 and l = 0.5 into fuzzy comparison matrices, and obtained all the a-cuts fuzzy comparison matrices as follows:

2 6 6 6 6 a ~ ¼6 A 6 6 6 4

1 ½1=4; 1=2 ½2; 4 1

½1; 2

½2; 4

3

7 7 7 7 7 ½6; 8 ½4; 6 7 7 7 1 ½1=4; 1=2 5

½2; 4 ½1=4; 1=2 ½4; 6 1 ½1=4; 1=2 ½4; 6 1

½4; 6 ½6; 8 ½1; 2

1 Step 6: Prioritizing subjective criteria using fuzzy AHP, and calculating the weights for each level of hierarchy After structuring the hierarchy, we implement a fuzzy AHP approach using a triangular fuzzy number. The assessment starts with a pairwise comparison among the main criteria by expertise in order to prioritorize the impact of each design system function and managerial consideration. Then we acquire the fuzzy comparison matrices for each level of the hierarchy with reference to the elements belonging to the previous level. We first calculated the geometric mean of each cell and the eigenvalue of the matrix. The kmax was calculated to be 6.317 of the main criteria of comparison matrix. The dimension of the matrix, n is six and the random index, RI(n) is 1.24. We then calculated the consistency index (CI) and the consistency ratio (CR) of the matrix that were 0.0634, and 0.0511, respectively. We also calculated the consistency ratios for all the sub-criteria and observed that they were all less than 0.1. As a result of this calculation, we have shown that the consistency of the judgments in each comparison matrix was acceptable. Table 7 illustrates the fuzzy comparison matrix of alternatives with respect to the sub-criteria production rate. Then, we substituted

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Production rate Auto loading/unloading Productivity

Lead time Machine utilization Parts type

Flexibility

Routings Transfer mechanism

Position sensor Precision

Repeatability System precision

Goal To select a Manufacturing System design

System stability Reliability

Repeatability Reliability of Transfer

Operation environment

Safety & Environment

Ergonomics requirement Safety equipment

System cost Cost

Labor cost Equipment cost

Fig. 7. Automated manufacturing system hierarchy.

Table 6 Fuzzy comparison matrix of main criteria using triangular fuzzy numbers. Criteria

C1

C2

C3

C4

C5

C6

C1 C2 C3 C4 C5 C6

1

~ 1 3 1

~ 3 ~ 3

~ 1 ~ 1 3 ~ 1 3

~ 3 ~ 5 ~ 5 ~ 7

~ 5 ~ 7 ~ 1 ~ 5 ~ 1 3

1

1

1

Table 8 The a-cut fuzzy comparison matrix for alternatives with respect to the first subcriteria production rate a = 0.5 and l = 0.5. Alternatives

A

B

C

A B C

1.00 [1/2, 1] [1/6, 1/4]

[1, 2] 1.00 [1/4, 1/2]

[4, 6] [2, 4] 1.00

1

Table 7 Fuzzy comparison matrix for alternatives with respect to the first sub-criteria production rate using triangular fuzzy number. Alternatives

A

B

C

A B C

1 ~ 1 1 ~ 1 5

~ 1 1 ~ 1 3

~ 5 ~ 3

Thus, the global weights for main and sub-criteria were listed in Table 9. From Table 9, the ranking of the main criteria were productivity > reliability > flexibility > precision > environment safety > cost. In addition, the results of the weights and final aggregation are summarized in Table 10. Based on the aggregated weights, the alternatives were ranked as alternative C > alternative A > alternative B.

1

6. Discussion the value, a = 0.5 and l = 0.5 in the above expression into fuzzy comparison matrices, and obtained the a-cuts fuzzy comparison matrix in Table 8. Step 7: Finding the final evaluation and selecting the best manufacturing system

The method proposed in section 3 seems that it is easy to utilize contradiction matrix with the engineering parameters. However, TRIZ has a basic problem: some matrix elements of the contradiction matrix of TRIZ include no principle of invention. If these matrix elements are crucial for the design problem, it might be

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T.-S. Li, H.-H. Huang / Expert Systems with Applications 36 (2009) 8302–8312 Table 9 The relative importance and ranking of criteria and sub-criteria. Goal

Criteria

Wt.

Rank

Sub-criteria

Relative weight (%)

Wt.

Rank

Automated manufacturing system

Productivity

0.213

1

Flexibility

0.195

3

Precision

0.146

4

Reliability

0.203

2

Environment safety

0.127

5

Cost

0.116

6

Production rate Auto loading/unloading Lead time Machine Utilization Parts type Routings Transfer mechanism Position sensor Repeatability System precision System stability Wiring Reliability of transfer system Operation environment Ergonomics requirement Safety equipment System cost Labor cost Equipment material cost

33.2 23.7 30.3 12.8 29.6 24.5 45.9 31.3 44.7 24.0 48.9 15.7 35.4 25.9 44.2 29.9 45.8 23.1 31.1

0.0707 0.0505 0.0645 0.0273 0.0577 0.0478 0.0895 0.0457 0.0653 0.0350 0.0993 0.0319 0.0719 0.0329 0.0561 0.0380 0.0531 0.0268 0.0361

4 10 6 18 7 11 2 12 5 15 1 17 3 16 8 13 9 19 14

Table 10 The final ranking of manufacturing system design alternatives. Goal

Criteria

Sub-criteria

Wt.

A

B

C

CR

Automated manufacturing system

Productivity

Production rate Auto loading/unloading Lead time Machine Utilization Parts type Routings Transfer mechanism Position sensor Repeatability System precision System stability Wiring Reliability of transfer system Operation environment Ergonomics requirement Safety equipment System cost Labor cost Equipment material cost

0.0707 0.0505 0.0645 0.0273 0.0577 0.0478 0.0895 0.0457 0.0653 0.0350 0.0993 0.0319 0.0719 0.0329 0.0561 0.0380 0.0531 0.0268 0.0361

0.529 0.532 0.318 0.222 0.299 0.399 0.289 0.303 0.251 0.253 0.235 0.285 0.205 0.350 0.288 0.432 0.458 0.551 0.401 0.34

0.355 0.193 0.293 0.404 0.332 0.285 0.195 0.243 0.286 0.298 0.297 0.305 0.397 0.246 0.350 0.341 0.335 0.235 0.426 0.30

0.116 0.275 0.389 0.375 0.368 0.316 0.516 0.454 0.463 0.449 0.468 0.410 0.398 0.404 0.361 0.228 0.207 0.214 0.173 0.36

0.086 0.042 0.085 0.070 0.086 0.014 0.057 0.060 0.048 0.098 0.056 0.013 0.009 0.071 0.043 0.010 0.025 0.014 0.013

Flexibility

Precision

Reliability

Environment safety

Cost

Evaluation for alternatives

useful to relate the features of the contradiction matrix to the principles of invention directly without contradiction information. In this paper, criteria evaluation is based on weighting evaluation. In general, two issues related to weighting evaluation must be considered in validating the weighting factors and the assumption of linearity. Regarding the first issue, the weighting factors are derived based on the TRIZ contradiction matrix and fuzzy AHP, and are thus generally reliable. However, linearity is assumed in our method and is an important issue. When linearity is assumed, the superior evaluation results of some evaluation aspects can cancel out the inferior evaluation results of other aspects. In addition, the effects of solution ideas can cancel out one another. In real situations, however, the effects of solution ideas may not add up or cancel out easily. In such cases, it becomes necessary to merge solution ideas with the same evaluation. In the proposed fuzzy AHP approach, a design engineer set the degree of uncertainty of feasibility of a solution idea and the weighting factor, and the design uncertainty is then calculated using fuzzy AHP corresponding to the degree of their uncertainties. It may be possible to set the uncertainty of them by using an engineering management database or an engineering knowledge base.

7. Conclusion The research described in this paper demonstrates that the development of innovative design for automated manufacturing system is now within the realms of possibility. If a design project includes a contradiction structure to be overcome, it is necessary to generate a novel solution idea at the system viewpoint. For this purpose, an idea generation approach has been proposed in which the TRIZ contradiction matrix is adopted based on the expertise knowledge. The method enables the knowledge incorporated in TRIZ to be used for innovative design. The design of automated manufacturing system is employed with an innovative approach, TRIZ. Though more than one design is probable, a multi-criteria decision making handling with uncertainty, fuzzy AHP, is able to evaluate and suggest the most suitable design. The integration of innovative design tool, TRIZ and multicriteria decision making, fuzzy AHP is tested in this research, and indicates that it is likely to be a reliable and promising methodology in process design. To summarize, the current research has demonstrated that the use of an integrated methodology of innovative design and mul-

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