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Optimal block designs in small blocks are explored when the treatments have anatural ordering and interest lies in comparing consecutive pairs oftreatments. We first develop an approximate theory which leads to a convenientmultiplicative algorithm for obtaining optimal design measures. This, in turn,yields highly efficient exact designs even when the number of blocks is rathersmall. Moreover, our approach is seen to allow nesting of such efficient exactdesigns which is an advantage when the resources for the experiment areavailable possibly in several stages. Illustrative examples are given. Tablesof optimal design measures are also provided.

Efficient Designs in Small Blocks for Comparing Consecutive Pairs of Treatments