Write down the complete defining relation and the aliases for this design. Estimate the main effects.

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Question 1. (Problem 8.11) 

8.11. An article in Industrial and Engineering Chemistry (“More on Planning Experiments to Increase Research Efficiency.” 1970. pp. 60—65) uses a 25—2 design to investigate the effect of A = condensation temperature.B=amount of material 1, C = solvent volume, D = condensation time, and E = amount of material 2 on yield. The results obtained are as follows: e=23.2ad= 16.9 cd=23.8 bde= 16.8 ab= 15.5 bc= 16.2ace= 23.4 abcde = 18.1

(a) Verify that the design generators used were ¡ = ACE and I = BDE.

(b) Write down the complete defining relation and the aliases for this design. Estimate the main effects. Prepare an analysis of variance table. Verify that the AB and AD interactions are available to use as error.

(e) Plot the residuals versus the fitted values. Also construct a normal probability plot of the residuals. Comment on the results.

8.27. 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 = pìtchlflnes ratio (0.45, 0.55). B = packing material type (1, 2), C = packing material tempera-turc (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  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?

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