An integrated framework for mechatronics based product development in a fuzzy environment

Applied Soft Computing 27 (2015) 376–390

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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

An integrated framework for mechatronics based product development in a fuzzy environment R. Parameshwaran a,∗ , C. Baskar b , T. Karthik c a b c

Department of Mechatronics Engineering, Kongu Engineering College, Perundurai 638052, Tamil Nadu, India Department of Mechanical Engineering, Kongu Engineering College, Perundurai 638052, Tamil Nadu, India Department of Automobile Engineering, Kumaraguru College of Technology, Coimbatore 641006, Tamil Nadu, India

a r t i c l e

i n f o

Article history: Received 17 January 2014 Received in revised form 12 August 2014 Accepted 14 November 2014 Available online 26 November 2014 Keywords: Mechatronics product design Fuzzy Delphi Method (FDM) Fuzzy Interpretive Structural Modeling (FISM) Fuzzy Analytical Network Process (FANP) Fuzzy Quality Function Deployment (FQFD) Fuzzy FMEA

a b s t r a c t New product development (NPD) is a term used to describe the complete process of bringing a new concept to a state of market readiness. Mechatronics based product requires a multidisciplinary approach for its modeling, design, development and implementation. An integrated and concurrent approach focusing on integrating the mechanical structure with basic three components namely sensors, controllers and actuators is required. This paper aims at developing a framework for a new Mechatronics product development. For conceptual design of Mechatronics system, various tools like Fuzzy Delphi Method (FDM), Fuzzy Interpretive Structural Modeling (FISM), Fuzzy Analytical Network Process (FANP) and Fuzzy Quality Function Deployment (FQFD) are used. Based on the prioritized design requirements, the functional specifications of the required components are developed. Then, Computer Aided Design and control system software are used to develop the detailed system design. Then, a prototype model is developed based on the integration of mechanical system with Sensor, Controller and Electrical units. Performance of the prototype model is monitored and Fuzzy failure mode and effect analysis (FMEA) is then used to rank the potential failures. Based on the results of fuzzy FMEA, the developed model is redesigned. The proposed framework is illustrated with a case study related to developing automatic power loom reed cleaning machine. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Products of Mechatronics Engineering are often based on the close interaction of mechanics, electrics/electronics, control engineering and computer sciences. Mechatronics systems are broadly classified into two categories. In the first category, a spatial integration of mechanics and electronics with an aim to reach a high density of mechanical and electronic functions within the available space focusing mainly on miniaturization, lower production costs and higher reliability is the focus. In the second category, controlled movements of multi-body systems with an aim to improve the behavior by using sensors, the control system and the system’s actuators is the focus [17]. It is important that the changes in the physical design and the controller choices must be evaluated simultaneously. A system with a proper controller and a badly designed mechanical system will never be able to give a good performance and the vice versa is also true [1]. Hence it is important that a strict

∗ Corresponding author. Tel.: +91 4294 226720; fax: +91 4294 220087. E-mail addresses: paramesh [email protected] (R. Parameshwaran), [email protected] (C. Baskar), [email protected] (T. Karthik). http://dx.doi.org/10.1016/j.asoc.2014.11.013 1568-4946/© 2014 Elsevier B.V. All rights reserved.

integration of mechanical, control, electrical, electronic and software aspects from the very beginning of the earliest conceptual design phase is required [47]. Many researchers have worked on Mechatronics system design. Hussein [22] proposed a geometrical approach for modeling both the physical and logical properties of Mechatronics system. The interconnection between these models is determined and a total model is built. The V-model for Mechatronics design consists of the following phases: functional requirement identification, system level specification, hierarchical system decomposition, definition of subsystems and components, verification and validation [46]. Moulianitis et al. [39] presented an approach for modeling the evaluation process in the conceptual design phase. The elements of the Mechatronics index are presented in terms of flexibility, intelligence and complexity. Hehenberger et al. [19] proposed an approach using hierarchical models in the design of Mechatronics systems. An extended variety and quality of principal solutions can be obtained from the utilization and proper combination of solution principles from different Mechatronics domains. The design engineer can use the specific “views of the object” as an interface to represent the relevant phenomena/effects of interest such as geometry, dynamics,

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stability or material. Beek et al. [3] proposed a modular design of Mechatronics systems with function modeling. The modularization approach makes use of the function–behavior–state (FBS) model and the design structure matrix (DSM). The approach integrates the DSM based modularization with the FBS modeling. Chhabra and Emami [11] proposed a holistic system approach for modeling in Mechatronics. The approach divides a Mechatronics system into three generic subsystems, namely generalized executive, sensory and control. These subsystems are linked together utilizing bond graph combinations and block diagrams. Energy, entropy and agility are used as design criteria and the obtained designs showed a superior performance compared to the existing ones. Cabrera et al. [6] proposed an architecture model to support cooperative design for Mechatronics products and illustrated the proposed approach with a development of control software. This approach provides proper product representation details, provides the required communication in the product development process and the required information association among the designers. Gausemeier et al. [17] proposed a model which deals with the stated problem by providing a generic procedure model and a specification technique for the integrative development of Mechatronics products and their production systems. The focus is to demonstrate how specific procedures can be derived from this generic procedure model. Sierla et al. [42] proposed the functional failure identification and propagation framework with a purpose to identify fault propagation paths in the conceptual design phase and determined the combined impact of several faults in software-based automation subsystems, electric subsystems and mechanical subsystems. Komoto and Tomiyama [26] proposed a framework for computer-aided conceptual design and its application to system architecting of Mechatronics products. The framework focuses on hierarchical system decomposition and consistency management of design information across different engineering disciplines. Gamage et al. [16] developed a design evolution framework to automate the evaluation and improvement of the design of an existing Mechatronics system. The developed system framework integrates Machine Health Monitoring System (MHMS) and Design Expert System (DES) with an Evolutionary Design Optimization System (EDOS) to obtain a design solution that satisfies the design specifications. An approach based on the mechatronic design quotient (MDQ) for systematic design of a Mechatronics system justifies that mechatronic design could be hierarchically separated into topological design and parametric design, and further “structured” into a multi-layered hierarchy [15]. A broad knowledge is required for developing multidisciplinary mechatronic systems/products. To manage the complexity of the product design of mechatronic systems adequate procedure models are necessary. At present, there is lack of integrated development methodologies and tools for mechatronic product design. No single “best” approach exists for the design of a Mechatronics system [19] and the development of Mechatronics systems is still a challenge due to its interdisciplinary nature [15]. Hence in this paper, a new approach for Mechatronics product design extensively focusing on conceptual design phase using NPD development tools like Fuzzy Delphi Method (FDM), Fuzzy Interpretive Structural Modeling (FISM), Fuzzy Analytical Network Process (FANP) and Fuzzy Quality Function Deployment (FQFD) and Fuzzy failure mode and effect analysis (Fuzzy FMEA) is proposed.

2. Background of techniques used The proposed model uses few techniques namely FDM, FISM, FQFD, FANP, Fuzzy FMEA. The following sections will describe each technique briefly.

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2.1. Fuzzy Delphi Method (FDM) The Delphi method proposed by Dalkey and Helmer in 1963 facilitates forecasting by converging a value through the feedback of experts after several rounds. It is criticized because of its shortfalls such as repetitive questionnaires and evaluations, declining response rate of experts, inappropriate convergence, ambiguity and uncertainty in survey questions and more time consumption [9,31]. Hence fuzzy sets are incorporated into conventional Delphi method to tackle the above said problems. A few recent applications of FDM are: road safety performance indicators identification [36], lubricant regenerative technology selection [21], evaluating hydrogen production technologies [10], Six-Sigma project selection [49], ranking the sawability of ornamental stone [38] and new product development [31]. 2.2. Fuzzy Interpretive Structural Modeling (FISM) Interpretive structural modeling (ISM) proposed by Warfield (1974) enables individuals or groups to develop a map of complex relationships and to calculate adjacency matrix to present the relationship among a set of variables. A few recent applications areas of ISM are: the selection of reverse logistics provider [24], supplier selection process [34], analyze strategic products for photovoltaic silicon thin-film solar cell [29], wind turbine evaluation [30], mutual relationships identification among the enablers of tour value [33], modularizing and clustering the required parts [20]. ISM assumes a binary relation to exist, i.e., whether a definite relation exists or no relation between two elements. However, introducing fuzzy relations into conventional ISM will enhance the process of identifying the relationship between the variables [31]. The principle behind is to change the traditional binary value into a fuzzy binary relation. Thus FISM will provide interviewers the opportunity to express the strength or fuzziness of the relationship among elements. 2.3. Fuzzy Analytical Network Process (FANP) Analytical Network Process (ANP) is a popular multi-criteria decision making (MCDM) technique which is widely used because it considered ambiguity and dissension among decision makers and also interdependency over the use of various criteria and alternatives [34]. ANP requires the decision maker’s opinion to carry out pair-wise comparisons. The human assessment on qualitative attributes is always subjective and thus imprecise. Therefore, fuzzy sets are incorporated with the pair-wise comparison as an extension of ANP. The FANP approach allows a more accurate description of the decision making process. FANP is used in wide variety of problem areas: to measure the sectoral competition level of an organization [14], evaluating machine tool alternatives [2], SWOT analysis for the airline industry [41], to evaluate green suppliers [5], advanced-technology prioritization [44]. 2.4. Fuzzy QFD Quality function deployment (QFD) is a planning and problemsolving tool that is used for translating customer requirements (CRs) into design characteristics (DCs) of a product/service. Using crisp values for assessing the importance of customer needs, degree of relationship between customer needs and design requirements, and degree of relationship among the design requirements have been criticized by several authors [4,25]. Design requirements and part characteristics are the major phases for QFD in new product development activity. The imprecise design information can be represented effectively by means of linguistic variables and fuzzy set theory [40]. A few application areas where fuzzy set theory

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is incorporated into QFD are: new product development [13,18], shipping investment decisions [7], conceptual bridge design evaluation [37], manufacturing strategy development [23], credit card evaluation [48] and customer satisfaction determination [45].

2.5. Fuzzy FMEA FMEA is a technique used for defining, identifying and removing known and/or potential failures, problems, errors and so forth from the system, design, process, and/or service before they reach the customer [43]. The potential failure modes are identified and the failure causes are prioritized using FMEA. Risk priority number (RPN) which is the product of the occurrence (O), severity (S) and detection (D) of a failure is used to rank the failure modes. However, in reality, the risk factors O, S and D are difficult to be precisely estimated. The crisp RPNs have been considerably criticized for variety of reasons by various researchers. A few application areas are: assembly process at manufacturing facility in an automotive industry [28], to improve the purchase process in a public hospital [27]. From the literature, it is found that fuzzy rule-base system is the most popular method for prioritizing the failure modes, followed by gray theory, cost based model, AHP/ANP and linear programming [35]. Application of FDM, FISM, FANP-FQFD, Fuzzy FMEA for Mechatronic system design is rarely found in the literature.

3. Proposed methodology A systematic methodology that incorporates six stages namely need identification, conceptual design development via FDM, FISM, FANP–FQFD techniques, detailed design development using CAD modeling and control system software, prototype development, redesigning the developed prototype using fuzzy FMEA and commercialization are proposed in Fig. 1. The stages in the proposed framework are explained in the following sections. 3.1. Need identification A committee of experts is formed to define the Mechatronics product development problem. Initially customer requirements (CRs) are identified through interview, questionnaire or brainstorming session. All possible Engineering Characteristics (ECs) are then listed by the expert committee. 3.2. Conceptual design stage 3.2.1. Step I: Selection of potential CRs and ECs using FDM The Fuzzy Delphi Method is applied to select the most important CRs and ECs from the factors listed in the previous stage. The steps are as follows [31]:

Need identification for a new Mechatronics system-identifying the customer requirements and Engineering characteristics

Conceptual Design

Prioritization of the customer requirements (CRs) and engineering characteristics (ECs) through Fuzzy Delhi Method (FDM) and selection of critical factors

Identification of the relationships among the CRs, ECs and between CRs & ECs through Fuzzy Interpretive Structural Modeling (FISM)

Construction of House of Quality (HoQ) by integrating Fuzzy Analytic Network Process (Fuzzy ANP) and FISM results

Development of functional specifications of the required mechanical structure, sensors, actuators and controllers

Development of detailed designs using CAD software and control system software

Developing a prototype model based on the detailed design Alarming

Identifying and prioritizing the failure models of developed prototype model using Fuzzy FMEA

Redesigning the existing product based on FMEA results

Full production and commercialization Fig. 1. An integrated framework for a Mechatronics product development.

R. Parameshwaran et al. / Applied Soft Computing 27 (2015) 376–390 Table 1 Triangular fuzzy number for FISM [31].

di

Membership li

hi

1 Gray Zone

*

0 li l

li m h i l

si

li u

hi m

hi u

Fig. 2. Gray zone.

(i) Form a committee of experts and employ a questionnaire to ask experts for their most pessimistic (minimum) value and the most optimistic (maximum) value of the importance of each CR (EC) in the possible factor set Sc (Se ) in a range from 1 to 10. A score for a CR (EC) is denoted as: Ci = (lki , hik ),

i ∈ Sc

(1)

Ev = (lkv , hvk ),

v ∈ Se

(2)

where lki (lkv ) is the pessimistic index of factor i(v) and hik (hvk ) is the optimistic index of factor i(v), rated by expert k. (ii) The triangular fuzzy number for the most pessimistic index and the most optimistic index for each factor i(v) is determined. i The minimum value (lli (hil ) and llv (hvl )), the geometric mean (lm v (hv )) and the maximum value (li (hi ) and lv (hv )) of (him ) and lm m u u u u the experts’ opinions on the most pessimistic index and most i , li ), lv = (lv , lv , lv ) optimistic index are obtained, i.e., li = (lli , lm u l m u

v , hv ). and hi = (hil , him , hiu ), hv = (hvl , hm u (iii) The consensus of experts’ opinions are examined and the consensus significance value of each factor is calculated. The Gray Zone (Fig. 2) is the overlap section of li and hi and is used to examine the consensus of experts in each factor.

The consensus significance value of the factor i, si , is calculated by the following rules: • If there is no overlap between li and hi (no gray zone exists), then consensus significance value of the factor is i + hi lm m 2

(3)

• If a gray zone exists and the gray zone interval value of gi (g i = i ), i.e., lui − hil ) is less than the interval value of li and hi (di = him − lm gi ≤ di , the consensus significance value of the factor is calculated by (4) and (5).



F i (p) =



{min[li (p), hi (p)]}dp

,

i∈S

(4)

p i

s = {p/ max Fi (p),

i∈S

Linguistic variables

Triangular fuzzy numbers

Completely related Strongly related Fairly related Low related Unrelated

(0.75, 1, 1) (0.5, 0.75, 1) (0.25, 0.5, 0.75) (0.01, 0.25, 0.5) (0.01, 0.01, 0.01)

P Cognition Value

gi

si =

379

(5)

where Fi (p) is the area of the intersection of li and hi , and si is the cognition value (p) with the highest degree of membership (*) of the intersection of li and hi . • If a gray zone exists and gi > di , then a great discrepancy among the experts opinions arises. Above all steps need to be repeated until a convergence is obtained. The same procedure is carried out to calculate the consensus significance value of factor v, sv

(iv) Select factors from the factors list. Select factor i(v) if its consensus significance value is greater than or equal to threshold value TC (TE ) which is determined by the experts subjectively based on the mean of all si (sv ), i.e., select factor i(v) if si ≥ TC (sv ≥ TE ). 3.2.2. Step II: Identification of relationship among the factors by FISM A CR may have an impact on other CRs and similarly an EC may have an impact on other ECs. Hence the interdependence among CRs and among ECs must be studied. In addition, a CR can be fulfilled if one or more ECs are achieved. FISM is applied to determine the relationship and the steps involved are summarized below [32]:

(i) From the results of Step I, the selected CRs are defined as xi , i = 1, 2, 3, . . ., n. The relation between two CRs is obtained from the experts with a help of a questionnaire containing linguistic variables namely completely related, strongly related, fairly related, low related and unrelated. The triangular fuzzy numbers in Table 1 are used to define the relation between one CR to another. By applying the geometric mean approach to aggregate experts’ opinion, the relation from CAi to CAj is represented by a triangular fuzzy number, x˜ ij . (ii) ˛-cut technique is then used for preparing an aggregated fuzzy relation matrix, D˛ .

⎡

0

⎢ [x˛ , x˛ ] ⎢ 21L 21U ⎣

....

˛ ˛ [x1nL , x1nU ]

0

....

˛ ˛ [x2nL , x2nU ]⎥

˛ ˛ [xn2L , xn2U ]

....

D˛ = ⎢

˛ ˛ , xn1U ] [xn1L

⎤

˛ ˛ [x12L , x12U ]

⎥ ⎥ ⎦

(6)

0

where 0 < ˛ < 1 ˇ (iii) An aggregated defuzzified relationship matrix, D˛ with ˛-cuts and index of optimism ˇ is obtained using Eq. (7). ˛ˇ

˛ ˛ xij = (1 − ˇ)xijL + ˇxijU ,

∀ˇ ∈ [0, 1]

(7)

The aggregated defuzzified relation matrix with ˛-cuts and index of optimism ˇ in generalized form is given as:

⎡

˛ˇ

x11

˛ˇ

x12

. .

˛ˇ

x1n

⎤

⎢ ˛ˇ ˛ˇ ⎥ ˛ˇ ⎢x x22 . . x2n ⎥ 21 ⎢ ⎥ ˇ ⎥ D˛ = ⎢ ⎢ . . . . . ⎥ ⎢ ⎥ ⎣ . . . . . ⎦ ˛ˇ

xn1

εˇ

xn2

. .

(8)

˛ˇ

xnn

(iv) A binary relation matrix, D is prepared to determine whether there is a relation between two CRs. A threshold value is deter˛ˇ mined by the experts. If xij is higher than the threshold value,

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xj is deemed reachable from xi and it is assumed that ij = 1, otherwise ij = 0. The binary relation matrix for CR–CR is: x1

x1 x2 D=

. . .

⎡

x2 0

...

...

1n

0

...

2n ⎥

.

. . .

0

. . .

n1

n2

...

0

⎥, ⎥ ⎦

i = 1, 2, . . ., n; j = 1, 2, . . ., n

,

(9)

where ij denotes the relation between the ith row and jth column CRs. (v) The initial reachability matrix, M is obtained by the addition of the binary relation matrix, D and the identity matrix, I: M =D+I

(10)

The final reachability matrix is obtained by increasing the power of the initial reachability matrix until the condition M* = Mb = Mb+1 is satisfied. The value of b should be always greater than one. In the final reachability matrix, M* a convergence can be met to reflect the transitivity of the contextual relation among the criteria for determining the interdependencies.

x1 x2 M∗ =

. . . xn

x2

...

11

∗ 12

...

∗ 1n

∗ 22

...

∗ ⎥ 2n

.

. . .

. . .

. . .

∗ n1

∗ n2

...

∗ nn

⎡ ∗

∗ ⎢ 21 ⎢ ⎢ . ⎣ .

xn

Extremely strong Intermediate Very strong Intermediate Strong Intermediate Moderately strong Intermediate Equally strong

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

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

(iii) Fuzzy pairwise comparison matrices are constructed using ˜ k ) with pairwise comparison of the imporTable 2. A matrix (A tance of CRs for expert k can be obtained: CR1

⎡ CR1 CR2

⎤ ⎥, ⎥ ⎦

.. . i = 1, 2, . . ., n; j = 1, 2, . . ., n

,

CRn

(12)

where n is the order of the matrix and max is the largest eigen vector. Consistency Index Random Index

CR2 1

⎢ ⎢ 1/˜a12k ⎢ ⎢ . ⎢ . ⎢ . ⎢ ⎢ .. ⎢ . ⎢ ⎢ ⎢ .. ⎢ . ⎢ ⎢ ⎢ .. ⎢ . ⎣ 1/˜a1nk

(i) HoQ is constructed using the relationship between CRs and ECs, inner dependence among CRs and among ECs obtained through FISM procedure. A check is entered if there is an influence of one factor to another factor. (ii) A questionnaire using Satty’s nine-point scale of pairwise comparison for ANP is prepared and the domain experts are asked to fill out the questionnaire. The relationship between CRs and ECs, the inner dependence among CRs and the inner dependence among ECs required for HOQ construction are obtained. Pairwise comparison matrix of each part of the questionnaire from each expert is examined for consistency using Eqs. (12) and (13). If an inconsistency is present, the expert is asked to revise the part of the questionnaire. max − n n−1

.. .

(11)

3.2.3. Step III: Prioritizing ECs using FANP-QFD Using the above result of FISM, the relationship between the customer requirements (CR–CR), relationship between the Engineering characteristics (EC–EC) and relationship between the engineering characteristics (EC) and customer requirements (CR) (i.e.) (CR–EC) are finalized. The House of Quality (HoQ) is then constructed and ECs are prioritized by applying FANP. The procedure of the FANP is as follows [32]:

Consistency Ratio =

Positive reciprocal triangular fuzzy numbers

˜ k = CRi A

The same procedures are used to determine the interdependence among ECs and the influence of CRs on ECs.

Consistency Index =

Positive triangular fuzzy numbers

.. .

The generalized form of M* is given as x1

Linguistic variables

⎤

12

⎢ 21 ⎢ ⎢ . ⎣ .

xn

xn

Table 2 Triangular fuzzy numbers for FANP [31].

(13)

...

...

CRj

...

CRn

⎤

a˜ 12k

...

...

... ...

a˜ 1nk

1

...

...

... ...

a˜ 2nk ⎥

.. .

1

...

... ...

...

.. .

.. .

1

a˜ ijk . . .

...

.. .

.. .

1/˜aijk

1 ...

...

.. .

.. .

.. .

.. .

1

...

1/˜a2nk

.. .

.. .

.. .

.. .

1

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ (14) ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

where n is the number of CRs. (iv) Fuzzy aggregated pairwise comparison matrices are constructed. Using geometric mean approach, the fuzzy pairwise comparison matrices from all experts are combined. There are a total of k sets of pairwise comparison matrices to represent the relationship between CRs and ECs, and also for the inner dependence among CRs and for the inner dependence among ECs for k experts. There are k triangular fuzzy numbers for each pairwise comparison between two elements. A synthetic triangular fuzzy number is obtained by geometric mean approach: a˜ ij = (˜aij1 ⊗ a˜ ij2 ⊗ · · · ⊗ a˜ ijk )1/k

(15)

where a˜ ijk = (lijk, mijk , uijk ) The fuzzy aggregated pairwise comparison matrix is as follows:

⎡

1

⎢ ⎢ 1/˜a12 ⎢ ⎢ . ⎢ . ⎢ . ⎢ ⎢ . ˜ = ⎢ .. A ⎢ ⎢ ⎢ .. ⎢ . ⎢ ⎢ ⎢ .. ⎣ . 1/˜a1j

⎤

a˜ 12

...

...

...

...

a˜ 1j

1

...

...

...

...

a˜ 2j ⎥

.. .

1

...

.. .

.. .

1

.. .

.. .

1/˜aij

.. .

.. .

.. .

1/˜a2j

...

...

⎥ ⎥ ⎥ ⎥ ... ... ...⎥ ⎥ ⎥ a˜ ij . . . . . . ⎥ ⎥ ⎥ ⎥ 1 ... ...⎥ ⎥ ⎥ ⎥ .. 1 ...⎦ . ...

...

(16)

1

where a˜ ij = (lij, mij , uij ) (v) Defuzzified aggregated pairwise comparison matrices are constructed using the center of gravity defuzzification

R. Parameshwaran et al. / Applied Soft Computing 27 (2015) 376–390

method. The comparison between elements i and j is defuzzified using the following equation:



aij =



(uij − lij ) + (mij − lij ) 3

+ lij

(17)

The defuzzified aggregated pairwise comparison matrix is:

⎡

1

⎢ ⎢ 1/a12 ⎢ ⎢ . ⎢ . ⎢ . ⎢ ⎢ .. A=⎢ ⎢ . ⎢ ⎢ .. ⎢ . ⎢ ⎢ ⎢ .. ⎣ . 1/a1j

⎤

a12

...

...

...

...

a1j

1

...

...

...

...

a2j ⎥

.. .

1

...

.. .

.. .

1

.. .

.. .

1/aij

.. .

.. .

.. .

1/a2j

...

...

⎥ ⎥ ⎥ ⎥ ... ... ...⎥ ⎥ ⎥ aij . . . . . . ⎥ ⎥ ⎥ ⎥ 1 ... ...⎥ ⎥ ⎥ ⎥ .. . 1 ...⎦ ...

...

(18)

1

(vi) The consistency of the defuzzified aggregated pairwise comparison matrices is checked. A local priority vector is derived for each defuzzified aggregated comparison matrix as an estimate of the relative importance of the elements. A · w = max · w

(19)

where A is the defuzzified aggregated pairwise comparison matrix, w is the eigenvector; max is the largest eigen value of A. The consistency property of each defuzzified aggregated pairwise comparison matrix can be examined as explained earlier. (vii) An unweighted super matrix is formulated. Priority vectors are entered in the appropriate columns of a matrix to represent the relationships in the HOQ.

G

⎡

G

CR

EC

I

M unweighted = CR

⎣ WCG WCC

EC

WEC

⎤ ⎦

(20)

WEE

where WCG is a vector that represents the impact of the goal on CRs, WEC is a matrix that represents the impact of CRs on ECs, WCC indicates the interdependency of CRs, WEE indicates the interdependency of ECs, I is the identity matrix, and entries of zeros correspond to those elements that have no influence. (viii) A weighted super matrix is calculated. The stochastic unweighted super matrix is obtained by giving equal weights to the blocks in the same column to make each column sums to unity. Then the limit super matrix is calculated by raising the weighted super matrix to the power of 2k + 1 and the final priorities of ECs are obtained. The priority weights of ECs can be found in the EC-to-goal block in the limit super matrix. 3.2.4. Step IV: Development of functional specifications Based on the prioritized ECs, the functional specifications of the required mechanical structure, sensors, actuators and controllers are determined. The required components are selected based on the characteristics like reliability, maintainability, serviceability, upgradeability and disposability. 3.3. Development of detailed design The detailed design for mechanical systems is developed by considering the effect of forces that act on the system and their corresponding motions with the help of CAD packages. The developed

381

system is analyzed from structural, thermal, fluid power and power transmission perspective. The electrical components frequently used are classified into three types: input modules (sensors, signal conditioning and impedance matching circuits), control modules (Microcontrollers, PLC and computer based controllers) and output modules (mechanical and electrical actuators like motors, contact devices like relays, circuit breakers, etc.). The signals from sensors are fed to the controller module and controllers compare it with the set point and actuate the output modules accordingly. The required analysis for electrical systems is performed using software like SPICE, OrCAD, Proteus, RSLogix, LabVIEW, MATLAB, etc. 3.4. Prototype development Prototyping is the process of replacing non-computer subsystems with actual hardware. Based on the detailed design from the previous stage, the required mechanical system is fabricated. The real time interfacing of mechanical system with sensors, controllers and actuators are to be carried out. In mechatronics system design, the main purpose of real-time interface system is to provide data acquisition and control functions for the computer. The real time interfacing includes analog to digital (A/D) and digital to analog (D/A) conversion, analog signal conditioning circuits and sampling theory. 3.5. Analysis of the developed prototype and redesigning The developed prototype model is checked for reproducing the reality. The unmodeled errors are identified and prioritized using Fuzzy FMEA. In this paper, fuzzy FMEA based on fuzzy TOPSIS integrated with fuzzy AHP [28] is used for prioritizing the errors. Chang’s extent analysis method for fuzzy AHP is utilized to determine the weight vector of three risk factors namely severity, occurrence and detectability. Chen’s fuzzy TOPSIS is utilized to obtain most critical errors by using the linguistic scores of risk factors for each design error. The detailed procedure for this fuzzy FMEA approach is as follows: (i) A group of decision makers identifies the errors in the prototype model. (ii) Fuzzy AHP is used to obtain the weights of the risk factors. The procedure for AHP is as follows [8]: Let X = {x1 , x2 ,. . ., xn } be an object set, and U = {u1 , u2 , . . ., un } be a goal set. According to the method of extent analysis, each object is taken and extent analysis for each goal is performed, respectively. Therefore, m extent analysis values for each object can be obtained ˜ 1,M ˜ 2 , . . ., M ˜ j , where, all the M ˜ j (i = with the following signs: M gi gi gi gi 1, 2, . . ., n; j = 1, 2, . . ., m) are Triangular Fuzzy Numbers (TFNs). The steps of extent analysis are as follows: Step 1: The value of fuzzy synthetic extent with respect to the ith object is defined as:

S˜ i =

m

⎡ ⎤−1 m n

˜ j ⊗⎣ ˜j ⎦ M M gi gi

j=1

i=1 j=1

(21)



m ˜ j perform the fuzzy addition operation of m To obtain M j=1 gi extent analysis values for a particular matrix such that m

j=1

⎡ ⎤−1 m m m

˜j =⎣ M lj , mj , uj ⎦ gi j=1

j=1

j=1

(22)

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R. Parameshwaran et al. / Applied Soft Computing 27 (2015) 376–390 Table 3 Fuzzy evaluation scores for the weight vector.

˜ 1 and M ˜ 2. Fig. 3. The intersection between M



˜j = M gi

i=1 j=1

Fuzzy score

Absolutely strong (AS) Very strong (VS) Fairly strong (FS) Slightly strong (SS) Equal (E) Slightly weak (SW) Fairly weak (FW) Very weak (VW) Absolutely weak (AW)

(2, 5/2, 3) (3/2, 2, 5/2) (1, 3/2, 2) (1, 1, 3/2) (1, 1, 1) (2/3, 1, 1) (1/2, 2/3, 1) (2/5, 1/2, 2/3) (1/3, 2/5, 1/2)



n m ˜ j the fuzzy addition operation M ˜ j (j = and to obtain M i=1 j=1 gi gi 1, 2, . . ., m) values is performed such as m n

Linguistic terms

 n n

li ,

i=1

mi ,

n

i=1



ui

(23)

i=1

and then inverse of the above vector is computed such as

⎡ ⎤−1  m n

1 j ⎦ ⎣ ˜ = n M gi

u i=1 i

i=1 j=1

,

1

n

i=1

mi

,



1

n

As shown above, the value of the fuzzy synthetic extent with respect to the ith object is defined and S1 , S2 , etc. are calculated. ˜ 1 and M ˜ 2 are two triangular fuzzy numbers, the degree Step 2: As M ˜2 ≤M ˜ 1 is defined as: of possibility of M



˜2 ≥M ˜ 1 ) = supy≥x min  ˜ (x), min  ˜ (y) V (M M M 1

Rating

Probability of occurrence

Fuzzy number

Very high (VH) High (H) Moderate (M) Low (L) Remote (R)

Failure is almost inevitable Repeated failures Occasional failures Relatively few failures Failure is unlikely

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

(24)

l i=1 i



Table 4 Fuzzy ratings for occurrence of a design error.

(25)

2

the fuzzy numbers are defuzzified into crisp numbers through the following Eq. (31): ˜ =M= P(M)

m1 + 4m2 + m3 6

(31)

Each value in the matrix is defuzzified and consistency ratio of the matrix is calculated and checked whether it is less than or equal to 0.1 or not.

and can be equivalently expressed as follows:

˜2 ≥M ˜ 1 ) = (d) = V (M

⎧ 1, ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

if m2 ≥ m1

0,

if l2 ≥ u2

l1 − u2 (m2 − u2 ) − (m1 − l1 )

otherwise

(26)

where d is the ordinate of the highest intersection point D between ˜ 1 and M ˜ 2 , both values M˜ and M˜ as shown in Fig. 3. To compare M 1 2 ˜2 ≥M ˜ 1 ) and V (M ˜1 ≥M ˜ 2 ) are needed. of V (M d (Ai ) = min V (S˜ i ≥ S˜ K )

(27)

The formulae required to compare two triangular fuzzy numbers are given in Step 2 and the degree of possibility is calculated in the Step 3. Step 3: The degree of possibility for a convex fuzzy number to be ˜ i can be defined by greater than k convex fuzzy numbers M ˜ ≥M ˜ 1, M ˜ 2 , . . ., M ˜ k ) = min V (M ˜ ≥M ˜ i ), where i = 1, 2, . . ., k. V (M (28) Assume that d (Ai )

= min V (S˜ i ≥ S˜ K ) for k = 1, 2, . . ., k = / i. Then the weight vector is given by

W  = (d (A1 ), d (A2 ), . . ., d (An ))

T

(29)

where Ai (i = 1, 2, . . ., n) are n elements. Step 4: Via normalization, the normalized weight vectors are W = (d(A1 ), d(A2 ), . . ., d(An ))

T

(iii) Fuzzy TOPSIS is used to rank the errors according to the closeness co-efficient [12]. The decision makers use linguistic variables to evaluate the ratings of alternatives with respect to criteria. Tables 4–6 give the linguistic scale fuzzy ratings for evaluation of the alternatives with respect to three criteria namely occurrence, severity and detection. The ratings of alternatives with respect to each criterion by K experts can be calculated as: x˜ ij =

 1 1 x˜ + x˜ ij2 + · · · + x˜ ijK K ij

where x˜ ijk is the rating of the Kth decision maker for the ith alternative with respect to jth criterion. Table 5 Fuzzy ratings for severity of a design error. Rating

Severity of effect

Fuzzy number

Hazardous without warning (HWOW) Hazardous with warning (HWW) Very high (VH)

Very high severity ranking without ranking Severity ranking with ranking

(9, 10, 10)

High (H)

(30)

where W is a non-fuzzy number. Weight vector of risk factors can be obtained using pair-wise comparison method. The decision makers use the linguistic variables in Table 3 to evaluate the weight vector risk factors. The consistency ratio of the comparison matrix has to be checked. The graded mean integration approach is utilized for this purpose and

(32)

Moderate (M) Low (L) Very Low (VL) Minor (MR) Very minor (VMR) None (N)

System inoperable with destructive failure System inoperable with equipment damage System inoperable with minor damage System inoperable without damage System operable with significant degradation of performance System operable with some degradation of performance System operable with minimal interference No effect

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

R. Parameshwaran et al. / Applied Soft Computing 27 (2015) 376–390

The distance of each alternative from A* and A− can be currently calculated as:

Table 6 Fuzzy ratings for detection of a design error. Rating

Likelihood of detection

Fuzzy number

Absolute uncertainty (AU) Very remote (VR) Remote (R) Very low (VL) Low (L) Moderate (M) Moderate high (MH) High (H) Very high (VH) Almost certain (AC)

No chance Very remote chance Remote chance Very Low chance Low chance Moderate chance Moderate high chance High chance Very high chance Almost certainty

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

di∗ =

n



⎢ x˜ ⎢ 21 D=⎢ ⎢ . ⎣ .. x˜ m1

x˜ 12

···

x˜ 1n

x˜ 22

···

x˜ 2n

di− =

n



.. .

.. .

(46)

where d(. , .) is the distance measurement between two fuzzy numbers calculating with the following formula d (, ) =

1 [(1 − 1 )2 + (2 − 2 )2 + (3 − 3 )2 ] 3

(47)

A closeness coefficient is defined to determine the ranking order of all alternatives once the di∗ and dj− of each alternative Ai (i = 1, 2,. . ., m) are calculated. The closeness coefficient of each alternative is calculated as

(33) CCi =

· · · x˜ mn

x˜ m2



d v˜ ij , v˜ − , i = 1, 2, . . ., m, j

j=1

⎤

⎥ ⎥ ⎥ .. ⎥ . ⎦

(45)

j=1

The fuzzy multi-criteria decision-making problem is expressed in matrix format after obtaining weights of the criteria and fuzzy ratings of alternatives with respect to three criteria as: x˜ 11



d v˜ ij , v˜ ∗j , i = 1, 2, . . ., m,



⎡

383

dj− dj∗ + dj−

,

i = 1, 2, . . ., m

(48)

The linguistic variables are described by triangular fuzzy numbers: x˜ ij = (aij , bij , cij ). The linear scale transformation is used to transform the various criteria scales into a comparable scale. The ˜ is obtained. normalized fuzzy decision matrix R

(iv) Based on the closeness co-efficient value, the design errors/failures are prioritized. These inputs are fed back to the conceptual design stage and redesigning of the system is carried out. The steps in the above said stages are repeated until the proposed design meets the customer requirements and functional specifications.

˜ = r˜ij R

3.6. Full production and commercialization

W = [w1 , w2 , . . ., wn ],

where j = 1, 2, 3. . ., n

 

 r˜ =

 r˜ =

(34)

(35)

mxn

a˜ ij b˜ ij c˜ij , , cj∗ cj∗ cj∗



b− cj− a− j j , , cij bij aij

j ∈ B;

,

(36)

 j ∈ C;

,

(37)

where C is the set of cost criteria and B is the benefit criteria

In this stage, the new product is developed based on the final design which satisfies all the requirements. The full production and commercialization of the new product is then taken up. The product is launched at this stage and associated advertisements are created and implemented and the initial feedback is received.

cj∗ = maxcij ,

if j ∈ B

(38)

4. Case study related to power loom ream cleaning machine design

a− j

if j ∈ C

(39)

4.1. Need identification

i

= minaij , i

The normalization method mentioned above is to preserve the property that the ranges of normalized triangular fuzzy numbers belong to (0, 1). Considering the different importance of each criterion, the weighted normalized fuzzy decision matrix is constructed:

 

V˜ = v˜ ij

m×n

,

i = 1, 2, . . ., m; j = 1, 2, . . ., n,

(40)

where

v˜ = r˜ij (·)d(Cj ).

(41)

According to the weighted normalized fuzzy decision matrix, the elements v˜ ij ∀ i, j are normalized as positive triangular fuzzy numbers and their ranges belong to the closed interval (0, 1). Then, the fuzzy positive-ideal solution (FPIS, A*) and fuzzy negative-ideal solution (FPIS), A− are defined as: ∗



−



A = A =

v˜ ∗1 , v˜ ∗2 , . . ., v˜ ∗n



,

 −

v˜ − ˜− ˜n 1,v 2 , . . ., v

(42) (43)

,

Where v˜ ∗j = (1, 1, 1) and v˜ − = (0, 0, 0), j

j = 1, 2, . . ., n.

(44)

A power loom is a mechanized loom powered by a line shaft and is used to weave cloth. The basic purpose of any loom is to hold the warp threads under tension to facilitate the interweaving of the weft threads. The major components of the loom are the warp beam, heddles, harnesses, shuttle, reed and take-up roll. The major problems in the power looms are: cotton gets deposited in the reed when it is used for longer period and the rust is formed. To use the reed further, it should be cleaned from both dust and rust. At present, the cleaning process is done manually. Initially reed will be cleaned by a needle to remove cotton as shown in Fig. 4 and then it will be rubbed with brush to remove dust as shown in Fig. 5. This process consumes more labor hour. Hence it is required to develop an automated reed cleaning machine which will solve the above said problems. 4.2. Conceptual design stage 4.2.1. Step I: Selection of factors by using FDM CRs and ECs are collected from the experts in the power loom industries. FDM is applied to CRs and ECs to find consensus significance value ((sv )a ). The results of FDM for CRs are shown in Table 7. With TE for CRs is set at 6, five CRs are shortlisted out of 11. The

384

R. Parameshwaran et al. / Applied Soft Computing 27 (2015) 376–390

Fig. 4. Reed cleaned by needle.

Fig. 5. Reed rubbed with brush.

results of FDM for ECs are shown in Table 8. Here TE for ECs is set at 6.5. So, five ECs are shortlisted out of 8. From FDM, the selected CRs are: Efficiency of cleaning (CR1 ); Easy to operate (CR2 ); Minimum cycle time for cleaning (CR3 ); less skilled labor requirement (CR4 ) and Low machine cost (CR5 ). Similarly the selected ECs are: PLC based control mechanism (EC1 ); selection of suitable brushes and lead screw mechanism (EC2 ); selection of suitable motor (EC3 ); selection of sensors and relays (EC4 ) and automation for stopping the cleaning process (EC5 ). 4.2.2. Step II: Identification of relationships among factors by using FISM FISM is then applied to identify the interdependence among CRs, the interdependence among ECs and the relationship between

CRs and ECs. A questionnaire is prepared on shortlisted CRs/ECs to obtain these relationships. With ˛ = 0.5 and ˇ = 0.3, ˛-cut method is applied to arrive at the crisp values. The influences among CRs and ECs are shown in Tables 9 and 10, respectively. Table 11 shows the influence of CRs on ECS.

The integrated relation matrix between CRs-CRs is derived as shown in Table 12. The integrated relation matrix between ECs-ECs is derived as shown in Table 13. The integrated relation matrix between CRs-ECs is derived as shown in Table 14.

Table 7 FDM for CRs. S. No.

1 2 3 4 5 6 7 8 9 10 11

Customer requirements

Easy to operate Less weight Low machine cost High efficiency of cleaning Less skilled labor requirement High reliability of machine Low maintenance Less vibration during operation Minimum Cycle time for cleaning Noise free operation Compact size

Pessimistic value

Optimistic Value

lli

i lm

lui

hil

him

hiu

4 2 5 5 5 2 3 1 3 1 2

5.43 4.14 6.14 6.55 5.79 4.26 4.22 2.16 4.64 1.77 3.69

7 6 8 8 8 7 7 5 6 4 6

7 6 8 8 7 5 5 3 7 4 5

8.31 7.32 8.97 9.35 8.31 6.89 6.98 4.92 8.94 4.68 6.52

10 8 10 10 10 9 10 8 10 6 9

a

di − gi

(sv )

2.88 3.18 0.83 2.8 1.52 0.63 0.76 0.76 3.04 2.91 1.83

6.72 5.51 7.42 7.83 7.34 5.82 5.81 3.92 6.44 2.89 5.37

Table 8 FDM for ECs. S. No.

1 2 3 4 5 6 7 8

Engineering characteristics

PLC based control mechanisms Selection of suitable brushes and lead screw mechanisms Selection of suitable motors Selection of sensors and relay Proper material selection for Mechanical structures Automated controls for stopping the cleaning process Proper signal conditioning unit Emergency controls

Pessimistic value

Optimistic value

lli

i lm

lui

hil

him

hiu

4 3 5 4 4 5 4 1

6.07 5.28 6.21 5.65 5.24 5.57 5.19 2.15

8 7 8 8 6 7 7 5

8 7 7 8 6 7 6 4

8.62 8.28 8.57 8.62 7.56 7.96 7.56 5.77

10 9 10 10 9 9 9 8

a

di − gi

(sv )

2.55 3 1.36 2.97 2.32 2.37 1.37 2.62

7.23 6.61 7.53 6.98 6.29 6.67 6.42 4.86

R. Parameshwaran et al. / Applied Soft Computing 27 (2015) 376–390 Table 9 Influence of a CR on another CR. CRi

 

Geometric mean x˜ ij

Influence on CRj

385

˛ˇ

˛-Cut

xij

l

m

u

˛ xijL

˛ xijU

CR1

CR2 CR3 CR4 CR5

0.1101 0.4546 0.0293 0.0293

0.4546 0.7214 0.1079 0.1079

0.7214 0.9086 0.9457 0.9457

0.2823 0.588 0.0686 0.0686

0.588 0.815 0.5268 0.5268

0.3740 0.6561 0.2061 0.2061

CR2

CR1 CR3 CR4 CR5

0.1557 0.5728 0.6555 0.0100

0.5727 0.8256 0.9086 0.0857

0.7939 1 1 0.136

0.3642 0.6992 0.7820 0.0478

0.6833 0.9128 0.9543 0.1108

0.4599 0.7633 0.8337 0.0667

CR3

CR1 CR2 CR4 CR5

0.3153 0.4546 0.3972 0.0100

0.5727 0.7214 0.6555 0.0293

0.8256 0.9086 0.9086 0.0369

0.4444 0.5888 0.5263 0.0196

0.6991 0.815 0.7820 0.0331

0.5205 0.6561 0.6031 0.0237

CR4

CR1 CR2 CR3 CR5

0.0293 0.1557 0.1359 0.2503

0.1079 0.5726 0.5204 0.5003

0.1557 0.7939 0.7939 0.7502

0.0686 0.3641 0.3281 0.3753

0.1318 0.6832 0.6571 0.6253

0.0876 0.4598 0.4268 0.4503

CR5

CR1 CR2 CR3 CR4

0.0100 0.0293 0.0857 0.0100

0.0857 0.1079 0.1359 0.0293

0.1359 0.1557 0.1782 0.0369

0.0479 0.0686 0.1108 0.0196

0.1108 0.1318 0.1571 0.0331

0.0667 0.0876 0.1247 0.0237

Table 10 Influence of an EC on another EC. ECi

 

Geometric mean x˜ ij

Influence on ECj

˛ˇ

˛-Cut

xij

l

m

u

˛ xijL

˛ xijU

EC1

EC2 EC3 EC4 EC5

0.3972 0.0293 0.5204 0.6555

0.6555 0.3153 0.7939 0.9086

0.9086 0.5727 0.9086 1

0.5264 0.1723 0.6571 0.7820

0.7820 0.444 0.8512 0.9543

0.6031 0.2538 0.7154 0.8337

EC2

EC1 EC3 EC4 EC5

0.1079 0.3153 0.3972 0.3972

0.4579 0.5727 0.6555 0.6555

0.7214 0.8256 0.9086 0.9086

0.2829 0.444 0.5263 0.5263

0.5896 0.6991 0.7820 0.7820

0.3749 0.5205 0.6031 0.6031

EC3

EC1 EC2 EC4 EC5

0.0100 0.0857 0.0369 0.0369

0.0293 0.3972 0.3609 0.3609

0.1359 0.6555 0.6302 0.6302

0.0196 0.2414 0.1989 0.1989

0.0826 0.5263 0.4955 0.4955

0.0385 0.3269 0.2879 0.2879

EC4

EC1 EC2 EC3 EC5

0.6555 0.1875 0.0100 0.6555

0.9086 0.8256 0.0857 0.9086

1 1 0.1359 1

0.7820 0.5065 0.0478 0.7820

0.9543 0.9128 0.1108 0.9543

0.8337 0.6284 0.0669 0.8337

EC5

EC1 EC2 EC3 EC4

0.4546 0.1359 0.0293 0.4546

0.7214 0.5204 0.1079 0.7214

0.9086 0.7939 0.1556 0.9086

0.5888 0.3281 0.0686 0.588

0.815 0.6571 0.1317 0.815

0.6561 0.4269 0.0875 0.6561

A threshold value is taken as 0.5 to identify whether the two factors are dependant or not [47]. The adjusted relation matrixes are:

⎡0 0 1 0 0⎤ ⎡0 1 0 1 1⎤ ⎢0 0 1 1 0⎥ ⎢0 0 1 1 1⎥ DCR = ⎢ 1 1 0 1 0 ⎥ DEC = ⎢ 0 0 0 0 0 ⎥ ⎣ ⎦ ⎣ ⎦ 0 0

0 0

0 0

0 0

DCR&EC

0 0

⎡1 1 0 0 ⎢0 1 0 1 = ⎢0 0 0 0 ⎣ 0 0

0 0

0 0

1 1

1 1 1 0 ⎤ 0 1⎥ 0⎥ ⎦ 1 0

0 0

0 1

1 0

The initial reachability matrixes M are:

⎡

0 0 ⎢ MCR = D + I = ⎣ 1 0 ⎡0 0 0 ⎢ MEC = D + I = ⎣ 0 1 1 ⎡ 1 1 ⎢0 1 MCR&EC = ⎣ 0 0 0 0 0 0

0 0 1 0 0 1 0 0 1 0 0 0 0 0 0

1 1 0 0 0 0 1 0 0 0 0 1 0 1 1

⎤ ⎡

1 0 0 0 ⎥ ⎢ 0⎦+⎣0 0 0 0⎤ ⎡0 1 1 0 1 ⎥ ⎢ 0⎦+⎣0 1 0 0⎡ 0 1 0 0 1 ⎥ ⎢0 1 0⎦+⎣0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1⎤

0 1 0 0 0 0 1 0 0 0 0 0 1 0 0

0 0 1 0 0 0 0 1 0 0 0 0 0 1 0

⎤ ⎡

1 0 0 0 ⎥ ⎢ 0⎦=⎣1 0 0 1⎤ ⎡0 0 1 0 0 ⎥ ⎢ 0⎦=⎣0 0 1 1⎡ 1 1 1 0 0 ⎥ ⎢0 1 0⎦=⎣0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0⎤

0 1 1 0 0 1 1 0 1 0 0 0 1 0 0

1 1 1 0 0 0 1 1 0 0 0 1 0 1 1

0 1 1 1 0 1 1 0 1 1⎤

0 1 ⎥ 0⎦ 1 1

⎤

0 0 ⎥ 0⎦ 0 1⎤ 1 1 ⎥ 0⎦ 1 1

386

R. Parameshwaran et al. / Applied Soft Computing 27 (2015) 376–390

Table 11 Influence of a CR on EC. CRi

 

Geometric mean x˜ ij

Influence on ECj

˛ˇ

˛-Cut

xij

l

m

u

˛ xijL

˛ xijU

CR1

EC1 EC2 EC3 EC4 EC5

0.5724 0.75 0.25 0.0292 0.01

0.8255 1 0.5001 0.1077 0.0855

1 1 0.7502 0.1554 0.1357

0.6990 0.8750 0.3751 0.0685 0.0478

0.9128 1.0000 0.6252 0.1316 0.1106

0.7631 0.9125 0.4501 0.0874 0.0666

CR2

EC1 EC2 EC3 EC4 EC5

0.01 0.6552 0.085 0.5723 0.3149

0.01 0.9086 0.3968 0.8255 0.5723

0.01 1 0.6552 1 0.8255

0.0100 0.7819 0.2409 0.6989 0.4436

0.0100 0.9543 0.5260 0.9128 0.6989

0.0100 0.8336 0.3264 0.7631 0.5202

CR3

EC1 EC2 EC3 EC4 EC5

0.01 0.0293 0.01 0.01 0.0292

0.0292 0.1079 0.0292 0.0855 0.1077

0.0368 0.9457 0.0368 0.1357 0.1554

0.0196 0.0686 0.0196 0.0478 0.0685

0.0330 0.5268 0.0330 0.1106 0.1316

0.0236 0.2061 0.0236 0.0666 0.0874

CR4

EC1 EC2 EC3 EC4 EC5

0.01 0.085 0.25 0.5723 0.3149

0.0292 0.3968 0.5001 0.8255 0.5723

0.0368 0.6552 0.7502 1 0.8255

0.0196 0.2409 0.3751 0.6989 0.4436

0.0330 0.5260 0.6252 0.9128 0.6989

0.0236 0.3264 0.4501 0.7631 0.5202

CR5

EC1 EC2 EC3 EC4 EC5

0.01 0.0293 0.1079 0.5723 0.01

0.01 0.3153 0.4579 0.8255 0.0855

0.01 0.5727 0.7214 1 0.1357

0.0100 0.1723 0.2829 0.6989 0.0478

0.0100 0.4440 0.5897 0.9128 0.1106

0.0100 0.2538 0.3749 0.7631 0.0666

Table 12 Integrated relation matrix among CRs.

CR1 CR2 CR3 CR4 CR5

Table 14 Integrated relation matrix between CR–ECs.

CR1

CR2

CR3

CR4

CR5

0 0.4599 0.5205 0.0876 0.0667

0.3740 0 0.6561 0.4598 0.0876

0.6561 0.7633 0 0.4268 0.0237

0.2061 0.8337 0.6031 0 0.1247

0.2061 0.0667 0.0237 0.4503 0

The final reach ability matrixes M* are:

0 0

0 0

1 0 0 1

4 MCR&EC

⎡1 1 0 1 ⎢0 1 0 1 = ⎢0 0 1 0 ⎣ 0 0

0 0

0 0

1 1

CR1 CR2 CR3 CR4 CR5

1 1 1 1 1 1 1 1 1 1 ⎤ 1 1⎥ 0⎥ ⎦ 1 1

EC2

EC3

EC4

EC5

0.0873 0.8336 0.7630 0.0236 0.01

0.9125 0.01 0.5201 0.5201 0.7630

0.7630 0.3264 0.0236 0.01 0.5201

0.6027 0.0236 0.7630 0.4500 0.7630

0.0666 0.5201 0.5201 0.5201 0.0666

CR1

CR2

CR3

CR4

CR5

1 0.143 0.333 0.333 0.25

7 1 5 3 3

3 0.2 1 0.333 0.333

3 0.333 3 1 3

4 0.333 3 0.333 1

max = 5.4249; Consistency ratio = 0.0894.

Based on M* , the relationship between the factors are depicted in Fig. 6. 4.2.3. Step III: Prioritizing ECs using FANP-QFD A questionnaire using Satty’s nine-point scale of pairwise comparison for ANP is prepared based on the relationship among the

factors in HoQ. The defuzzified aggregated pairwise comparison matrixes are shown in Tables 15–17, respectively. These pairwise comparison matrixes are examined for consistency using Eqs. (12) and (13). These priorities are entered into the designated places in the unweighted supermatrix as shown in Table 17. The unweighted supermatrix is transformed into a weighted supermatrix and the Table 16 Pairwise comparison matrix for ECs-ECs.

Table 13 Integrated relation matrix among ECs.

EC1 EC2 EC3 EC4 EC5

EC1

Table 15 Pairwise comparison matrix for CRs-CRs.

⎡1 1 1 1 0⎤ ⎡1 1 1 1 1⎤ ⎢1 1 1 1 0⎥ ⎢1 1 1 1 1⎥ 3 =⎢ 4 ⎥ ⎢ ⎥ MCR ⎣ 1 1 1 1 0 ⎦ MEC = ⎣ 0 0 1 0 0 ⎦ 0 0

CR1 CR2 CR3 CR4 CR5

EC1

EC2

EC3

EC4

EC5

0 0.3749 0.0385 0.8337 0.6561

0.6031 0 0.3269 0.6284 0.4269

0.2538 0.5205 0 0.0667 0.0875

0.7158 0.6031 0.2879 0 0.6561

0.8337 0.6031 0.2879 0.8337 0

EC1 EC2 EC3 EC4 EC5

EC1

EC2

EC3

EC4

EC5

1 3 7 3 3

0.333 1 3 0.333 0.333

0.143 0.333 1 0.333 0.333

0.333 3 3 1 0.333

0.333 3 3 3 1

max = 5.4205; Consistency ratio = 0.0885.

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387

Fig. 6. House of Quality (HoQ).

Table 17 Unweighted supermatrix. Nodes

Goals

CR1

CR2

CR3

CR4

CR5

EC1

EC2

EC3

EC4

EC5

Goals CR1 CR2 CR3 CR4 CR5 EC1 EC2 EC3 EC4 EC5

1 0.454 0.046 0.257 0.098 0.146 0 0 0 0 0

0 0.525 0.056 0.279 0.139 0 0.091 0.476 0 0.275 0.158

0 0.525 0.056 0.279 0.139 0 0 0.274 0.476 0.158 0.092

0 0.525 0.056 0.279 0.139 0 0 0 0 0 0

0 0 0 0 0 0 0.066 0.257 0 0.53 0.146

0 0 0 0 0 0 0.135 0 0 0.584 0.281

0 0 0 0 0 0 0.053 0.249 0.437 0.159 0.101

0 0 0 0 0 0 0.053 0.249 0.437 0.159 0.101

0 0 0 0 0 0 0 0.274 0.476 0.158 0.092

0 0 0 0 0 0 0.053 0.249 0.437 0.159 0.101

0 0 0 0 0 0 0.053 0.249 0.437 0.159 0.101

Table 18 Limit supermatrix. Nodes

Goals

CR1

CR2

CR3

CR4

CR5

EC1

EC2

EC3

EC4

EC5

Goals CR1 CR2 CR3 CR4 CR5 EC1 EC2 EC3 EC4 EC5

1 0.005 0.001 0.003 0.001 0 0.029 0.258 0.449 0.158 0.096

0 0.006 0.001 0.003 0.002 0 0.029 0.258 0.449 0.158 0.096

0 0.006 0.001 0.003 0.002 0 0.029 0.258 0.449 0.158 0.096

0 0.006 0.001 0.003 0.002 0 0.029 0.258 0.449 0.158 0.096

0 0.005 0.001 0.003 0.001 0 0.029 0.261 0.454 0.159 0.097

0 0.005 0.001 0.003 0.001 0 0.029 0.261 0.454 0.159 0.097

0 0.005 0.001 0.003 0.001 0 0.029 0.261 0.454 0.159 0.097

0 0.005 0.001 0.003 0.001 0 0.029 0.261 0.454 0.159 0.097

0 0.005 0.001 0.003 0.001 0 0.029 0.261 0.454 0.159 0.097

0 0.005 0.001 0.003 0.001 0 0.029 0.261 0.454 0.159 0.097

0 0.005 0.001 0.003 0.001 0 0.029 0.261 0.454 0.159 0.097

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Fig. 7. CAD model for the proposed product.

Fig. 8. Prototype model of the power loom reed cleaning machine.

weighted supermatrix is raised to powers to capture all the interactions and finally the limit supermatrix is obtained as shown in Table 18. The priority weights of ECs from limit supermatrix are:

WEC

EC1 EC2 = EC3 EC4 EC5

⎡ 0.029 ⎤ ⎢ 0.258 ⎥ ⎢ 0.449 ⎥ ⎣ ⎦ 0.158 0.096

4.2.4. Stage IV: Development of functional specifications Automatic power loom reed cleaning machine is designed according to the prioritized FANP-QFD based results: selection of suitable motor (EC3 ); selection of suitable brushes and lead screw mechanism (EC2 ); selection of sensors and relays (EC4 ); automation for stopping the cleaning process (EC5 ); PLC based control mechanism (EC1 ). With the help of detailed design calculations, the following components are identified for developing further design: AC motor, DC motor, lead screw, bearing, wire brush, proximity sensor, PLC, relay and power supply.

4.4. Prototype development With the help of CAD model and PLC programming developed using RSLogix software, the prototype model has been developed and it is shown in Fig. 8. 4.5. Analysis of the developed prototype and redesigning Using Fuzzy FMEA, unmodeled errors in the developed prototype are identified and prioritized for further redesigning purpose. Since Mechatronics system involves integrating various modules like hardware and software, this process is highly essential. The various failure modes identified in the prototype model are: Vibrations in AC motors (FM1 ); Vibrations in lead screw arrangements (FM2 ); Excessive cycle time for cleaning process (FM3 ); Improper brush size (FM4 ); Weight of motor holding setup (FM5 ); Improper selection of AC motor (FM6 ) and Improper selection of DC motor (FM7 ). Fuzzy AHP is used to obtain the weights of the risk factors. Fuzzy TOPSIS is used to rank the errors according to the closeness Table 19 Evaluations of experts in linguistic variables and weights of the risk factors.

4.3. Development of detailed design

Risk factors

Severity (S)

Occurrence (O)

Detection (D)

Weight vector

Based on the functional specifications and design calculations, the CAD model for the proposed system is developed and is shown in Fig. 7.

Severity Occurrence Detection

E, E, E – –

FS, VS, VS E, E, E –

SS, SS, FS SS, FW, E E, E, E

0.547 0.168 0.283

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Table 20 Fuzzy evaluations of each risk factor with respect to each failure mode. Severity (S) FM1 FM2 FM3 FM4 FM5 FM6 FM7

7.67 5.33 7 8.33 4.67 5.67 6

Occurrence (O) 8.67 6.33 8 9.33 5.67 6.67 7

9.33 7.33 9 9.67 6.33 7.67 8

6.67 3.33 4 6.67 2.33 5.67 3.33

Detectability (D) 7.67 4.33 5 7.67 3.33 6.67 4.33

8.67 5.67 6.67 8.67 5 8 5.67

9.33 6.67 7.67 9.33 6 8.67 6.67

7.33 4.67 7 4.33 6 7.33 6

8.33 5.67 8 5.33 7 8.33 7

9.33 6.67 9 6.33 8 9.33 8

Table 21 Ranking of failure modes. Failure mode

FM1

FM2

FM3

FM4

FM5

FM6

FM7

Closeness co-efficient Ranking

0.2948 1

0.2085 7

0.2681 3

0.2750 2

0.2105 6

0.2547 4

0.2229 5

co-efficient. The importance of the risk factors (S, O and D) is determined by using FAHP method. The linguistic variables from three experts are obtained using Table 3. The corresponding weight vector for the risk factors calculated using FAHP are shown in Table 19. The three experts also evaluate the risk factors with respect to each failure modes using the linguistic variables from Tables 4–6. Using geometric mean approach, the fuzzy evaluations of each risk factor with respect to each failure mode is shown in Table 20. The closeness co-efficient values found using FAHP-Fuzzy TOPSIS method and the ranking are shown in Table 21. The prioritized failure modes are: vibrations in AC motors (FM1 ); improper brush size (FM4 ); excessive cycle time for cleaning process (FM3 ); improper selection of AC motor (FM6 ); improper selection of DC motor (FM7 ); Weight of motor holding setup (FM5 ); Vibrations in lead screw arrangements (FM2 ). By analysing the developed prototype through fuzzy FMEA, the potential failures are identified and ranked. Based on this ranking, the product is redesigned. The vibration in AC motor setup should be reduced by selecting proper motor capable of running at slow speed. The suitable size of the brush is to be selected according to width of the reed. Because of smaller size brush, the cycle time is increased. Proper DC motor should be selected to drive the lead screw efficiently. If the weight of the AC motor holding setup is reduced, then the vibrations will be in control. 5. Conclusions Development of Mechatronics system is a challenging process due to its interdisciplinary nature. Initial design verification is a significant requirement of a new product development, since early design phase account for a major portion of lifecycle costs. Hence, a strict integration of mechanical, control, electrical, electronic and software aspects from the very beginning of the conceptual design phase is required. The proposed model provides a methodology for solving Mechatronics design issues right from the conceptual design phase and helps to reduce the product development costs. Fuzzy based QFD and FMEA take care of customer requirements and failure analysis in the designs respectively. In this paper, a systematic framework that incorporates FDM, FISM, FANP–QFD and fuzzy FMEA for a Mechatronics product development is proposed. The customer requirements and their related engineering characteristics are identified and the critical factors are prioritized through FDM. The FISM is then applied to determine the relationship among the factors. These results are used to construct HoQ and the engineering characteristics are ranked through FANP based QFD. Based on the prioritized engineering characteristics, the functional specifications of the required mechanical structure,

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