Definitions and Properties for M-Concurrence Designs

Summary Incomplete block designs can be regarded as being in some sense approximately partially balanced. In this paper, we show that parameters pjki corresponding to those used for partially balanced designs can be defined for certain designs with m distinct concurrences. These parameters have properties analogous to those for m associate-class partially balanced incomplete block (PBIB(m)) designs and have proved useful in searching for optimal designs. This leads to a new upper bound for the efficiency factor which, for given pjki values, is attained if a PBIB(2) design exists. Some results on complement and dual designs are also given.