Run order considerations for Plackett and Burman designs

• Theoretical results on the level changes for Plackett and Burman designs are proved.
• Minimum level change designs are produced to minimize experimental cost.
• Maximum level change designs are produced which are trend robust.

Run order considerations for two-level full and fractional factorial designs have been studied in depth, but are lacking for Plackett and Burman designs. We look at the level change problems in Plackett and Burman designs. When a systematic run order is appropriate (as opposed to the conventional random run order), minimizing level changes implies the minimization of experiment costs. We thus aim to find optimal run orders with respect to minimizing level changes. It is shown that level changes are a constant for saturated Plackett and Burman designs. Methods for obtaining the minimum/maximum level changes are given. Tables with example run orders for the cases where N=12N=12 and N=20N=20 are tabulated for practical uses. By finding minimum level change designs, we also produce maximum level change designs and such results can be directly extended to Trend Robust designs.