Statistical Modelling 4 (2004), 249–264
A strategy of robust parameter design for multiple responses
Sonja Kuhnt and Martina Erdbrügge
Department of Statistics, University of Dortmund,
D-44221 Dortmund,
Germany
eMail:
kuhnt@statistik.uni-dortmund.de
Abstract:
In this article, we provide a strategy for the simultaneous
optimization of multiple responses. Cases are covered where
a set of response variables has finite target values and
depends on easy to control as well as on hard to control
variables. Our approach is based on loss functions, without
the need for a predefined cost matrix. For each element of a
sequence of possible weights assigned to the individual responses,
settings of the easy to control parameters are determined, which
minimize the estimated mean of a multivariate loss function. The
estimation is based on statistical models, which depend only on
the easy to control variables. The loss function itself takes
the value zero, if all responses are on target with zero variances.
In each case, the derived parameter settings are connected to a
specific compromise of the responses, which is graphically
displayed to the engineer by so called joint optimization plots.
The expert can thereby gain valuable insight into the production
process and then decide on the most sensible parameter setting.
The proposed strategy is illustrated with a data set from the
literature and new data from an up to date application.
Keywords:
multiple responses; robust parameter design; simultaneous
optimization; Taguchi methods
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