A general minimum lower-order confounding criterion for s -level blocked designs

Blocked designs are widely used in practical experiments with heterogeneous experimental units. The blocked general minimum lower-order confounding (B1-GMC) criterion is appropriate for selecting optimal blocked designs. This article extends B1-GMC criterion to s-level blocked designs. First, we introduce a blocked aliased component-number pattern (B1-ACNP) to reflect the confounding information among various component effects s. Further, the existing optimal criteria can be expressed by some functions of elements in the B1-ACNP. Finally, we not only give the formulas of lower-order confounding information by the complementary method, but also provide an algorithm to calculate the lower-order confounding in blocked designs. Some examples are given to illustrate our theoretical results.