Create a blocked response surface design for four factors.

(a) Use the rsm package to create an orthogonally blocked central composite design. How many runs are in this design, and how many runs are in each block?

(b) Use the rsm package to create an orthogonally blocked Box-Behnken design. How many runs are in this design, and how many runs are in each block?

(c) Supposing that only six runs can be made in each block, take the central composite design you created in

(a) and use the optBlock function to block it into ve blocks of six runs each.

(d) Take the Box-Behnken design you created in (b), and add three center points, and then use the optBlock function to block the runs into ve blocks of six runs each.

(e) Create the variance dispersion graphs of the designs you created, and compare them to the variance dispersion graphs of the orthogonally blocked designs you created in

(a) and (b). Do you lose much by re-

ducing the block size?