On the construction of trend free constant block sum PBIB designs

Agricultural and industrial experimentation may often witness the effect of systematic trend. Trend effects, though remote, may still influence the response under consideration. The incorporation of trend effects in the model thus paves the way for proper model specification. Completely trend robust block designs, which are commonly known as trend-free block designs, are an important class of block designs in such a way that the analysis can be done in the usual manner as it could be done in case of normal block designs due to orthogonal nature of trend effects and treatment effects. This article deals with the construction of some classes of completely trend robust i.e. trend free constant block sum partially balanced incomplete block (TFCBS-PBIB) designs along with characterization properties. SAS macros have also been developed and made available in public domain to provide readymade solutions to the end-users.