On balanced minimal repeated measurements designs

Abstract

Repeated Measurements designs are concerned with scientific experiments in which each experimental unit is assigned more than once to a treatment either different or identical. This class of designs has the property that the unbiased estimators for elementary contrasts among direct and residual effects are obtainable. Afsarinejad (1983) provided a method of constructing balanced Minimal Repeated Measurements designs p < t , when t is an odd or prime power, one or more than one treatment may occur more than once in some sequences and  designs so constructed no longer remain uniform in periods. In this paper an attempt has been made to provide a new method to overcome this drawback. Specifically, two cases have been considered                RM[t,n=t(t-t)/(p-1),p], λ₂=1 for balanced minimal repeated measurements designs and  RM[t,n=2t(t-t)/(p-1),p], λ₂=2 for balanced  repeated measurements designs. In addition , a method has been provided for constructing              extra-balanced minimal designs for special case RM[t,n=t²/(p-1),p], λ₂=1.