Construction of Fractional Factorial Designs with Some Linear Trend Free Effects Through Finite Field

By : Puja Thapliyal, Poonam Singh, Veena Budhraja

Page No: 57-76

Abstract
Sometimes in experimental situations, experimental units exhibit a smooth trend over time or space. In that situation randomization may lead to an undesirable run order in the sense that observations obtained may be affected by uncontrollable variables which are correlated with the time or position in which they occur. Instead systematic run order may have to be used to eliminate the effects of such a trend. Such type of ordering of treatments is referred to as trend free designs. This article presents a simple methodology to construct the fractional factorial designs with s, s ? 2 levels, having some effects (main and two factor interactions) linear trend free using finite field. Further this method is used to generate the blocked fractional factorial designs and mixed fractional factorial designs with some linear trend free effects.

Authors :
Poonam Singh : Associate Professor in Department of Statistics, University of Delhi.
Puja Thapliyal : Research scholar in Department of Statistics, University of Delhi.
Veena Budhraja : Associate Professor in Department of Statistics, Sri Venkateswara College, University of Delhi.