Although multiple responses are quite common in practical applications, the robust design problem is frequently dealt with by considering only one response. In this paper we present a general framework for the multivariate problem when data are collected from a combined array. Within the framework, both parameter and tolerance design are handled in an integrated way. The optimization criterion is based on a single value in terms of the quadratic loss function, and it is selected in order to incorporate both statistical information (such as correlation structure among responses and prediction uncertainty) and economic information relevant to the product or process (such as priorities and trade-offs among responses from the user's point of view). An illustrative application is presented on the design of the elastic element of a force transducer.
Key Words: Combined Array; Multiresponse Optimization; Quadratic Loss Function; Robust Parameter Design.
By DANIELE ROMANO, University of Cagliari, Piazza d'Armi, 09100 Cagliari, Italy
MARCO VARETTO and GRAZIA VICARIO, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
IN the past two decades, robust design has been an important subject for quality engineers, who are challenged to design products and processes which perform to design specifications regardless of their use and production conditions. This subject has also resulted in a lively debate among industrial statisticians (see, for example, the panel discussion edited by Nair (1992)). Interest may well increase in the future, as the growing practice of computer experiments and related research widen the potential of experimental statistics techniques and robust design even more. A major difficulty of conducting robust design experiments in the field is the control of noise factors, a problem which does not arise when experiments are run on a numerical model. The interested reader is referred to the discussion of a statistical framework for computer experiments provided by Sacks, Welch, Mitchell, and Wynn (1989), while their use in robust design is documented by Welch, Yu, Kang, and Sacks (1990) (see also Romano and Vicario (2002) and Romano, Alosi, Barbato, and Levi (1999)).
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