Blocked Two-level Compromise Designs

In practice, there exists one kind of special cases, when the experimenters only want to estimate a part of specified factor effects. Based on this need, Addelman[1]proposed a new class of design in 1962, which is compromise design.Sometimes the experimenters are interested in estimating a part of main effects and second-order effects. In this case,the limitation of designs with resolution Ⅳ or higher will be too strong. For such a situation, Ye, Wang & Zhang[13] promoted the definition of compromise design. And they constructed a large number of such optimal designs by introducing the P-AENP.Since blocking is a necessary and effective method when the experiment units are non-homogeneous, the compromise design can be extended to the case of the blocked design in this paper.(1) Proposing the partial aliased effect number pattern of blocked compromise design, that is, P-B1-AENP.(2) Clarifying the concept of clear blocked compromise design, and then getting some simple nature. And then proving that in some parametric conditions, the form of clear blocked compromise design of class four is proved, as well as the number of factors contained in the largest clear blocked compromise design of class four.(3) Proposing the concept of strongly clear blocked compromise design and a simple inference similar to that of the clearly blocked compromise design of class four.(4) Defining the optimal blocked compromise design in the general case, and proving some properties. Then we focus on the discussion of the optimal blocked com-promise design of class four, also proving the form of the optimal class four blocked compromise design and its P-B1-AENP.