The specification of rank reducing observation sets in experimental design

If observations are lost from an experiment involving one or more forms of blocking, it can happen that the resultant design is treatment disconnected which has serious implications for the experiment. A method is described in this paper for specifying each set of observations which has the property that a treatment disconnected design will result if this observation set is missing. Some implications for two-replicate designs are described and four applications that portray the value of the method are discussed.