碩士 ; 國立政治大學 ; 統計學系 ; 84354016 ; 在行列設計(row-column design)的架構下，當行總和與列總和皆為總試驗處理數的倍數時，我們考慮行效果與列效果的相互比較之最適性。延續Shah和Sinha(1993)的結果，在給定行總和及列總和的情況下，我們導出達成齊一最適設計(uniformly optimal design)的充分條件。此外，當總實驗單位固定時，達成全域最適設計(universally optimal design)的充分條件亦被求出。我們同時列舉許多相關的設計排列法。 ; We consider the problem of comparing row effects and column effects in the row-column design setup when the row sizes and column sizes are all multiples of the number of treatments. Following the work of Shah and Sinha (1993), we derive a sufficient condition for uniformly optimal designs for given values of the row sizes and column sizes. We also derive a sufficient condition for universally optimal designs when the total number of experimental units is fixed. Several examples of designs with high efficiencies are provided. ; ACKNOWLEDGMENT --- i CONTENTS --- ii ABSTRACT --- iii 1. INTRODUCTION --- 1 2. PRELIMINARIES --- 5 3. OPTIMAL DESIGNS FOR FIXED ROW SIZES (n.j.) ANDCOLUMNSIZES(n.k) --- 11 4. OPTIMAL DESIGNS FOR FIXED TOTAL NUMBER OFEXPERIMENTALUNITS(n) --- 27 REFERENCES --- iv