Second and third Order Rotatable Designs with Minimum Number of Levels and Some Further Methods for Constructing Third Order Designs

Abstract

A method for obtaining second order rotatable designs in three levels has been described. Through this method the existing second order rotatable designs can be converted to designs with three levels of each of the factors. A number of examples have been given to illustrate this method. The investigation has been extended to obtain third order rotatable designs, both non-sequential and sequential, with five levels of each of the factors. Two tables giving third order rotatable designs in five levels have been given along with a detailed example for 4 factors. A series of five levelled second order rotatable designs, obtainable through the omission of treatments in a design has been presented. A more useful series of three levelled second order rotatable designs has been obtained through the omission of treatments. Particularly, the series obtained through the B.I.B. designs with 8seems to be of paramount importance. This series helps us in getting three levelled designs with smaller number of design points. A number of much useful designs have been given in section 8. We have also obtained a series of five levelled third order rotatable designs by uniting some treatments in a doubly B.I.B design. The utility is that the numbers of design points in these third order rotatable designs are reduced to large extent. A use of rotatable arrangements to obtain third order rotatable designs is quite interesting. Third order rotatable designs up to10 factors, both non-sequential and sequential have been obtained through the B.I.B. designs with blocks of unequal sizes. A series of seven levelled third order rotatable designs obtained through the omission of treatments in a doubly B.I.B. design has also been given. This series also, helps in reducing the number of design points to a large extent.