| Summary: | 碩士 === 國立中山大學 === 應用數學研究所 === 82 === Motivated by a problem concerning the productivity and
stability of two production lines in a plant,optimum
experimental designs for estimating parameters of multiresponse
models with some common factors at the same levels are
considered. The $D$-and $A$- criteria for constructing optimal
designs under these models are presented and the equivalence
theorem for each criterion is formulated. Based on the
equivalence theorems, we find that product designs are $D$-($
A$-)optimal in additive and product models under some
restrictions. The models concerning discrete factors are also
discussed. We show product designs are also $D$-optimal in the
linear additive models with both discrete factors and
continuous factors, where continuous factors are the common
factors in the two models. Finally, a sample size reduction
method for the experiment is illustrated.
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