Change-over designs for factorial experiments with a control treatment

The need for change-over designs is shown. Models used for change-over designs are provided. The optimaHty criteria for good designs are given and examples for optimal designs are provided. The factorial structure for factorial change-over designs is defined and the condition necessary for a factorial change-over design to have factorial structure is given. This condition is also appHcable when the change-over design is extended to have factorial treatments with a control. Change-over designs for 2xk factorial experiments (k = 2,3,4...) and a control treatment are investigated for t treatments, t periods and It experimental units. Designs which give more precise estimates for the main effects of the 2-level factor than Williams squares designs are given and a method of construction of these designs is provided. A change-over design for a 3 by 3 factorial experiment with a conti'ol is given as an example of a design with an even number of treatments. Designs that are best amongst cyclically generated designs are given for t treatments, t periods and t experimental units (where t is odd). Extra period designs are shown to be good for factorial experiments with a control. The idea of natural contrasts is ruled out for factorial experiments with a control. Good cyclic change-over designs for factorial experiments with a control are given for situations where the number of periods, p , is less than the number of treatments, t. Optimal designs for some situations in which p is less than t are provided and the nature of their reduced coefficient matrices for estimating direct effects and residual effects separately is given. Optimal replication is discussed and an example is provided of designs that have optimal replication for the estimation of the main effects of the factors.