| Summary: | 博士 === 淡江大學 === 管理科學研究所 === 70 === This dissertation emphasizes ranking and selection approach to multiple statistical decision problems in the following areas:
PART A: Design of experiments.
PART B: Reliability analysis.
PART C: Regression analysis.
For the incomplete prior information decision problems, I-optimal criterion, which is the compromise of minimax criterion and Bayes criterion, has received great attention. By employing this criterion for the class of natural selection rules, it allows us to determine optimal sample size for selecting the best population or the better populations among several competing populations for PART A. B and C respectively.
Next, "local optimality" is also discussed. Recently, the attention has been increasingly given to the construction of optimal decision rules for selecting all good populations that aresuperior to a control population. Some investigations have been studied for the unequal sample size case. But the optimality has seldom been considered. By using "local optimality", it allows usto control the error probabilities and maximize the efficiency in picking out the superior populations even for the unequal sample size case. Furthermore, hypothesis testing approach is also studied from the selection point of view. Our approach can solve some difficulties which arise from the traditional methods.
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