Carbon anodes used in a smelting process are baked in a ring furnace. An experiment is run in the furnace to determine which factors influence the weight of packing material that is stuck to the anodes after baking. Six variables are of interest, each at two levels: A = pitch∕fines ratio (0.45, 0.55), B = packing material type (1, 2), C = packing material temperature

(ambient, 325∘C), D = flue location (inside, outside), E = pit temperature(ambient, 195∘C), and F = delay time before packing (zero, 24 hours). A 26−3 design is run, and three replicates are obtained at each of the design points. The weight of packing material stuck to the anodes is measured in grams.

The data in run order are as follows: abd = (984, 826, 936);

abcdef = (1275, 976, 1457); be = (1217, 1201, 890); af =

(1474, 1164, 1541); def = (1320, 1156, 913); cd = (765, 705, 821); ace= (1338, 1254, 1294); and bcf = (1325, 1299, 1253). We wish to minimize the amount of stuck packing material.

(a) Verify that the eight runs correspond to a 26−3 III design.

What is the alias structure?

(b) Use the average weight as a response. What factors appear to be influential?

(c) Use the range of the weights as a response. What factors appear to be influential?

(d) What recommendations would you make to the process engineers?