【摘要】 <正> [1]研究过正交试验设计的优良性问题,得到在仅仅考虑主效应时,正交设计是A-,D-,E-最优的结论。[2](1978)推广了[1]的结果,证明了在一级交互效应下,正交设计也是A-,D-,E-最优的。[3]提出泛最优性的概念,给出了判定泛最优设计的定理。利用[3]的结果,[5](1980)证明了仅仅考虑主效应时,正交设计是泛最优的,而AF-,D-,E-最优性都不过是泛最优性的特例,从而蕴涵了[1]的结果。然而,在具有交互作用的情更多还原

【Abstract】 We consider the problem on optimality of the factor experiment design with any order interaction effects.In this paper,the term of broad optimality (B-optimality)is introduced and a sufficient condition on B-optimality is obtained.By computing the generalized inverse matrix of the information matrix for estimating main effects as well as interaction effects,the B-optimality of the orthogonal design with any order interaction effects is established.Because B-optimality implies A-, D-, E-optimality, our theorem includes the results in [1], [2] as a special case.更多还原