A Balanced Incomplete Block Design (BIBD) can be used when it is not possible to include all treatments or factor combinations in every block. Use BIBDs for testing a treatments in b blocks when only k treatments can be run in any one block (and k < a). For example, you might have a situation where there are limitations on the number of treatments that can be tested at the same time. The BIBD design is constructed such that each treatment and each pair of treatments occurs together in blocks an equal number of times. This makes the design balanced. Not including all treatments in every block makes the design incomplete.
Figure 23.1 BIBD for 4 Treatments in 4 Blocks of Size 3

Help created on 7/12/2018