In robust design, associated with each quality characteristic, the design objective often involves multiple aspects such as “bringing the mean of performance on target” and “minimizing the variations.” Current ways of handling these multiple aspects using either the Taguchi’s signal-to-noise ratio or the weighted-sum method are not adequate. In this paper, we solve bi-objective robust design problems from a utility perspective by following upon the recent developments on relating utility function optimization to a Compromise Programming (CP) method. A robust design procedure is developed to allow a designer to express his/her preference structure of multiple aspects of robust design. The CP approach, i.e., the Tchebycheff method, is then used to determine the robust design solution which is guaranteed to belong to the set of efficient solutions (Pareto points). The quality utility at the candidate solution is represented by means of a quadratic function in a certain sense equivalent to the weighted Tchebycheff metric. The obtained utility function can be used to explore the set of efficient solutions in a neighborhood of the candidate solution. The iterative nature of our proposed procedure will assist decision making in quality engineering and the applications of robust design.

1.
Athan
T. W.
, and
Papalambros
P. Y.
,
1996
, “
A Note on Weighted Criteria Methods for Compromise Solutions in Multi-Objective Optimization
,”
Engineering Optimization
, Vol.
27
, pp.
155
176
.
2.
Ballestro
E.
, and
Romero
C.
,
1991
, “
A Theorem Connecting Utility Function Optimization and Compromise Programming
,”
Operations Research Letters
, Vol.
10
, pp.
421
427
.
3.
Bazaraa, M. S., Sherali, H. D., and Shetty, C. M., 1993, Nonlinear Programming—Theory and Algorithms, John Wiley & Sons, New York.
4.
Bowman
V. J.
,
1976
, “
On the Relationship of the Tchebycheff Norm and the Efficient Frontier of Multiple-Criteria Objectives
,”
Lecture Notes in Economics and Mathematical Systems
, Vol.
135
, pp.
76
85
.
5.
Box
G.
,
1988
, “
Signal-to-Noise Ratios, Performance Criteria, and Transformations
,”
Technometrics
, Vol.
30
, No.
1
, pp.
1
18
.
6.
Bras
B. A.
, and
Mistree
F.
,
1995
, “
A Compromise Decision Support Problem for Robust and Axiomatic Design
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, No.
1
, pp.
10
19
.
7.
Cagan
J.
, and
Williams
B. C.
,
1993
, “
First-Order Necessary Conditions for Robust Optimality
,”
Advances in Design Automation
, ASME DE-Vol.
65-1
, pp.
539
549
.
8.
Chang, T. S., Ward, A. C., and Lee, J., 1994, “Distributed Design with Conceptual Robustness: A Procedure Based on Taguchi’s Parameter Design,” ASME Concurrent Product Design Conference, Gadh, R., ed., Chicago, IL, ASME, Vol. 74, pp. 19–29.
9.
Chen
W.
,
Allen
J. K.
, and
Mistree
F.
,
1996
a, “
System Configuration: Concurrent Subsystem Embodiment and System Syntheses
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
18
, No.
2
, pp.
165
170
.
10.
Chen
W.
,
Allen
J. K.
,
Mistree
F.
, and
Tsui
K.-L.
,
1996
b, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
118
, pp.
478
485
.
11.
Chen
W.
,
Allen
J. K.
, and
Mistree
F.
,
1997
, “
The Robust Concept Exploration Method for Enhancing Concurrent Systems Design
,”
Journal of Concurrent Engineering: Research and Applications
, Vol.
5
, No.
3
, pp.
203
217
.
12.
Das
I.
and
Dennis
J. E.
,
1997
, “
A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto set Generation in Multicriteria Optimization Problems
,”
Structural Optimization
, Vol.
14
, pp.
63
69
.
13.
Eggert
R. J.
, and
Mayne
R. W.
,
1993
, “
Probabilistic Optimal Design Using Successive Surrogate Probability Density Functions
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
115
, pp.
385
391
.
14.
Geoffrion
A. M.
,
1968
, “
Proper Efficiency and the Theory of Vector Optimization
,”
Journal of Mathematical Analysis and Application
, Vol.
41
, pp.
491
502
.
15.
Hazelrigg, G. A., 1996, Systems Engineering and Approach to Information-Based Design, Prentice Hall.
16.
Keeney, R. L., and Raifa, H., 1976, Decisions with Multiple Objective: Preferences and Value Tradeoffs, John Wiley and Sons, New York.
17.
Messac
A.
,
1996
, “
Physical Programming: Effective Optimization for Computational Design
,”
AIAA Journal
, Vol.
34
, No.
1
, pp.
149
158
.
18.
Mistree, F., Hughes, O. F., and Bras, B. A., 1993, “The Compromise Decision Support Problem and the Adaptive Linear Programming Algorithm,” Structural Optimization: Status and Promise, AIAA, Washington, D.C, pp. 247–286.
19.
Miura, H., and Chargin, M. K., 1996, “A Flexible Formulation for Mult-Objective Design Problems,” American Institute of Aeronautics and Astronautics, pp. 1187–1192.
20.
Nair
V. N.
,
1992
, “
Taguchi’s Parameter Design: A Panel Discussion
,”
Technometrics
, Vol.
34
, No.
2
, pp.
127
161
.
21.
Otto, K. N. and Antonsson, E. K., 1991, “Extensions to the Taguchi Method of Product Design,” Third International Conference on Design Theory and Methodology, (Stauffer, L. A., Ed,), Miami, Florida, pp. 21–30.
22.
Parkinson
A.
,
Sorensen
C.
, and
Pourhassan
N.
,
1993
, “
A General Approach for Robust Optimal Design
,”
Transactions of the ASME
, Vol.
115
, pp.
74
80
.
23.
Phadke, M. S., 1989, Quality Engineering Using Robust Design, Prentice Hall, Englewood Cliffs, New Jersey.
24.
Ramakrishnan, B., and Rao, S. S., 1991, “A Robust Optimization Approach Using Taguchi’s Loss Function for Solving Nonlinear Optimization Problems,” Advances in Design Automation, ASME DE-32-1, pp. 241–248.
25.
Siddall, J. N., 1984, “A New Approach to Probability in Engineering Design and Optimization,” Vol. 106, March, 1984, pp. 5–10.
26.
Steuer, R. E., 1986, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley & Sons, New York.
27.
Su
J.
, and
Renaud
J. E.
,
1997
, “
Automatic Differentiation in Robust Optimization
,”
AIAA Journal
, Vol.
35
, No.
6
, pp.
1072
1072
.
28.
Sundaresan
S.
,
Ishii
K.
, and
Houser
D. R.
,
1993
, “
A Robust Optimization Procedure with Variations on Design Variables and Constraints
,”
Advances in Design Automation
, ASME DE-Vol.
69-1
, pp.
379
386
.
29.
Taguchi, G., 1993, Taguchi on Robust Technology Development: Bringing Quality Engineering Upstream, ASME Press, New York.
30.
Thurston
D. L.
,
1991
, “
A Formal Method for Subjective Design Evaluation with Multiple Attributes
,”
Research in Engineering Design
, Vol.
3
, pp.
105
122
.
31.
Tind, J., and Wiecek, M. M., 1997, “Augmented Lagrangian and Tchebycheff approaches in multiple objective programming,” to appear in Journal of Global Optimization.
32.
Tsui
K.-L.
,
1992
, “
An Overview of Taguchi Method and Newly Developed Statistical Methods for Robust Design
,”
IIE Transactions
, Vol.
24
, No.
5
, pp.
44
57
.
33.
von Neumann, J., and Morgenstern, O., Theory of Games and Economic Behavior, 2nd ed. Princeton University Press, Princeton, N.J. 1947.
34.
Yu, J., and Ishii, K., 1994, “Robust Design by Matching the Design with Manufacturing Variation Patterns,” ASME Design Automation Conference, September 1994, Minneapolis, MN, DE-Vol. 69-2, pp. 7–14.
35.
Yu
P. L.
,
1973
, “
A Class of Solutions for Group Decision Problems
,”
Management Science
, Vol.
19
, pp.
936
946
.
36.
Yu
P. L.
, and
Leitmann
G.
,
1974
, “
Compromise Solutions, Dominations Structures, and Salukvadze’s Solution
,”
Journal of the Optimization Theory and Applications
, Vol.
13
, pp.
362
378
.
37.
Zeleny, M., 1973, Compromise Programming, in: Multiple Criteria Decision Making, eds: J. L. Cochrane and M. Zeleny, University of South Carolina Press, Columbia, SC, pp. 262–301.
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