D-optimal two-level parallel-flats block designs with partial replication

Under the assumption of random block effects, a new class of two-level factorial block designs with partial replication is proposed for estimating the user-specified requirement sets and variance components. A noteworthy feature of the proposed designs is that the within-block and between-block replicates are both conducted, such that the components of variance can be unbiasedly estimated. Under the framework of parallel-flats block designs, a set of sufficient conditions is presented for design characterization, and an algorithm is developed for systematically constructing the proposed designs. Using the proposed algorithm, a design catalogue is generated as a reference for experimentation. Some examples are given to demonstrate that the proposed designs are promising alternatives for practical applications.