Chen. W., M. Wiecek, and J. Zhang, 1999, "Quality Utility: A Compromise Programming Approach to Robust Design," ASME Journal of Mechanical Design, 121, 2, pp. 179-187.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and the small robustness di#erence between the neighboring minima. Nevertheless, the result provides a qualitative picture about the trade o# between performance and robustness, from which a user can make a decision and choose a preferred solution. The second test problem is taken from reference [19]. The original objective function to minimize is as follows: f(x) x 1 5.0) 10.0, 24) subject to g(x) x 2 6.45 0, 25) 10, 26) 10. 27) The standard deviation of the function can be derived as follows, assuming the standard deviation of x 1 and x 2 are the ....

....the standard deviation of x 1 and x 2 are the same: # f (x) # x (3.0(x 1 4.0(x 1 ) 2.0(x 2 5.0) 28) where # x is the standard deviation of both x 1 and x 2 , which is set to: # x = 1 #x, 29) where #x is the maximal variation of x 1 and x 2 . According to [19], the search for robust optimal solutions can be formulated as follows, assuming the maximal deviation of both variables is 1: minimize f 1 = f, 30) f 2 = # f , 31) subject to g(x) x 2 8.45, 32) 9, 33) 9. 34) We call the objective for robustness in equation (31) the ....

W. Chen, M. Wiecek, and J. Zhang. Quality utility: A compromise programming approach to robust design. Journal of Mechanical Design, 121(2):179--187, 1999.

....2. 0 2 4 6 8 10 0 2 4 6 8 10 1.5 1 0.5 0 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 (a) b) Fig. 7. a) The 2 dimensional function of the test problem 1. b) The Pareto front obtained using robust measure 2. The second test problem is taken from reference [16]. The original objective function to minimize is as follows: f(x) x 1 5.0) 10.0, 25) subject to g(x) x 2 6.45 0, 26) 10, 27) 10. 28) The standard deviation of the function can be derived as follows, assuming the standard deviation of x 1 and x 2 are the ....

....the standard deviation of x 1 and x 2 are the same: # f (x) # x (3.0(x 1 4.0(x 1 ) 2.0(x 2 5.0) 29) where # x is the standard deviation of both x 1 and x 2 , which is set to: # x = 1 #x, 30) where #x is the maximal variation of x 1 and x 2 . According to [16], the search of robust optimal solutions can be formulated as follows, assuming the maximal deviation of the both variables is 1: minimize f 1 = 31) f 2 = 32) subject to g(x) x 2 8.45, 33) 9, 34) 9, 35) where = 5.1046 and # = 0.4168 are the ideal solutions ....

W. Chen, M. Wiecek, and J. Zhang. Quality utility: A compromise programming approach to robust design. Journal of Mechanical Design, 121(2):179--187, 1999.

....be achieved by simultaneously optimizing the mean performance and minimizing the performance variance . Modeling the tradeoff between these two aspects has been widely studied in the literature (Sudaresan, et al. 1993; Bras and Mistree, 1995; Chen, et al. 1996; Iyer and Krishnamurty, 1998; Chen, et al. 1999). In general, objective robustness is an issue related to how to better model a designer s preference structure when making tradeoffs between the mean and variance attributes. No matter what objective expression we use to achieve the robustness of product performance, it is even more critical to ....

....the best achievable optimal solution of s and s s , respectively. Here we use the weighting factor method to formulate the multiple objective function, though other advanced mathematical programming approaches can be used to better illustrate the tradeoff between the mean and variance attributes (Chen et al. 1999). For the purpose of illustration, we use weighting factors w 1 =w 2 =0.5. The optimal solutions from using with different formulations of the constraint in Eqn. 3.8) are presented in Table 2. They are also marked as 1, 2, 3, etc. in Fig. 7. To compare the accuracy and to confirm the design ....

Chen, W., Wiecek and M.M, Zhang, J., 1999, "Quality Utility: A Compromise Programming Approach to Robust Design", ASME Journal of Mechanical Design, Vol. 121, No. 2, pp.179-187.

....variance . Modeling the tradeoff between these two aspects has been widely studied in the literature (Sudaresan, et al. 1993; Bras and Mistree, 1995; Chen, et al. 1996a; Iyer and Krishnamurty, 1998) In recent developments, a multiobjective mathematical programming approach has been proposed (Chen, et al. 1998) to overcome the limitations of Taguchi s signal to noise ratio approach and the simplistic weighted sum method. In general, objective robustness is an issue related to how to better model a designer s preference structure when making tradeoffs between the mean and variance attributes. No matter ....

Chen, W., Wiecek and M.M, Zhang, J., 1998, "Quality Utility: A Compromise Programming Approach to Robust Design", 1998 ASME Design Technical Conference, paper no. DAC5601, Atlanta, GA. In press, ASME Journal of Mechanical Design.

....analysis. An interactive multiobjective robust design procedure was earlier proposed by the authors to solve bi objective robust design (BORD) problems under the notion that a reliable mathematical representation of the decision maker s actual utility function may not always be available (Chen et al. 1999). The procedure was developed to allow a designer to exercise his her preference structure of the multiple aspects of robust design, locally approximate the efficient frontier and interactively explore alternative solutions in a neighborhood of a solution of interest. The exploration is performed ....

....is proposed in Section 3. The methodology is illustrated on examples in Section 4 and Section 5 concludes the paper. 2. THE INTERACTIVE ROBUST DESIGN PROCEDURE For a detailed description of the interactive robust design procedure, the reader is referred to the authors previous publication (Chen et al. 1999). In brief, the bi objective robust design (BORD) problem is solved using the compromise programming (CP) approach for 4 a given preference structure assigned by the weights w 1 and w 2 representing the relative importance of two objectives f 1 = f and f 2 = s f : minimize b subject to b D ....

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Chen, W., Wiecek, M., and Zhang, J., 1999, "Quality Utility: A Compromise Programming Approach to Robust Design," ASME Journal of Mechanical Design, Vol. 121-2, pp. 179-187.

....support decision making. An interactive multiobjective robust design procedure was proposed by the authors to solve bi objective robust design (BORD) problems under the notion that a reliable mathematical representation of the decision maker s actual utility function may not always be available (Chen et. al 1998). The proposed robust design procedure follows upon the recent developments on relating utility function optimization to a multiobjective programming method. It is developed to allow a designer to exercise his her preference structure of the multiple aspects of robust design and to explore ....

....derivation of the quality utility at a candidate solution by means of a quadratic function in a certain sense equivalent to the weighted Tchebycheff metric. It was then proposed to further use this utility function to explore the efficient solutions in a neighborhood of the candidate solution. In Chen et al. 1998, the advantages of the CP approach over the WS method in locating the efficient multiobjective robust design solutions (Pareto points) Steuer, 1986) are thoroughly illustrated both in principle and through the example problems. The derivation of a family of quadratic utility functions at the ....

[Article contains additional citation context not shown here]

Chen, W., Wiecek, M. M, Zhang, J., 1998, "Quality Utility: A Compromise Programming Approach to Robust Design", 1998 ASME Design Technical Conference, paper no. DAC5601, Atlanta, GA. In press, ASME Journal of Mechanical Design.

....of attributes that cannot be directly converted to a common metric. One difficulty associated with using the utility function approach is that, in practice, it is often impossible to obtain a reliable mathematical representation of the decision maker s actual utility function. One of the authors, Chen et al. 1998) used a combination of the rigorous multiobjective mathematical programming method and the principles of decision analysis to address the multiple aspects of the objective in robust design. One of the major elements of the proposed approach is associated with the use of the Compromise Programming ....

....The basic idea of the CP method is to identify an ideal solution (utopia point) where each attribute under consideration achieves its optimum value. In the case of a conflict among the different attributes, the designer seeks a solution, which is the closest possible to the ideal solution. In Chen et al. 1998, the advantages of the CP approach over the WS method in locating the efficient multiobjective robust design solutions (Pareto points) Steuer, 1986) are thoroughly illustrated both in principle and through example problems. Following upon the advancements in the area of multicriteria ....

[Article contains additional citation context not shown here]

Chen, W., Wiecek, M. M, Zhang, J., 1998, "Quality Utility: A Compromise Programming Approach to Robust Design", 1998 ASME Design Technical Conference, paper no. DAC5601, Atlanta, GA. In press, ASME Journal of Mechanical Design.

No context found.

Chen. W., M. Wiecek, and J. Zhang, 1999, "Quality Utility: A Compromise Programming Approach to Robust Design," ASME Journal of Mechanical Design, 121, 2, pp. 179-187.

No context found.

Chen. W., Wiecek, M., and Zhang, J., Quality Utility: A Compromise Programming Approach to Robust Design, ASME Journal of Mechanical Design, Vol. 121, No. 2, 1999, pp.179-187.

No context found.

Chen. W., Wiecek, M., and Zhang, J., "Quality Utility: A Compromise Programming Approach to Robust Design", ASME Journal of Mechanical Design, Vol. 121, No. 2, 1999, pp.179-187.

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