CS代考 MATH1302 Assignment 4.docx Page 1 of 4

Assignment 4
Design and Analysis of Experiments
Submission due day as shown on canvas
RMIT Classification: Trusted

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The following list of questions are based on the material covered in the lectures and the lab sessions. Please work through all problems using a statistical package where and if required. You will need to create a Word document to copy your outputs into (or use R markdown to prepare your solution) and prepare your written answers to the questions below.
Please submit online by the due day.
Question 1.
A 25-2 design was used 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 = 16.2 ace = 23.4 abcde = 18.1
(a) Generate the design and the data by hand using the given labels.
(b)Verify that the design generators used were I = ACE and I = BDE.
(c) Write down the complete defining relations and a l l the aliases for this design.
(d)Estimate the main effects.
(e)Prepare an analysis of variance table. Verify that the AB and AD interactions are available to use as error.
(f) Plot the residuals versus the fitted values. Also construct a normal probability plot of the residuals. Comment on the results.
Question 2.
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¡ãC), D = flue location (inside, outside), E = pit temperature (ambient, 195¡ãC), 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) Generate the design and the data by hand using the given labels.
(b)Verify that the eight runs correspond to a 26-3III design. What is the alias structure?
(c) Use the average weight as a response. What factors appear to be influential?
(d)Use the range of the weights as a response. What factors appear to be influential?
Document: MATH1302 Assignment 4.docx Page 1 of 4

RMIT Classification: Trusted
(e) What recommendations would you make to the process engineers?
Question 3.
Consider the following data:
Run A B C D E y
1 2 3 4 5 6 7 8
-1 -1 -1 1 -1 50
1 -1 -1 -1 -1 20
-1 1 -1 -1 1 40
1 1 -1 1 1 25 -1 -1 1 -1 1 45
1 -1 1 1 1 30 -1 1 1 1 -1 40 1 1 1 -1 -1 30
(a) What is the generator for column D in the design? (b)What is the generator for column E in the design?
(c) Find the full alias structure of this design and the resolution of the design
(d)If this design was run in two blocks with the AB interaction confounded with blocks, the run d
would be in the block where the sign on AB is – or +? Explain.
(e) If this design is folded over what would be the resolution of the generated design (the
combined design)
(f) Estimate the main effects of this experiment.
(g)Prepare an analysis of variance table with the best model you can find with no blocking. (Hint: proceed sequentially: 1. find main significant effects, 2. keep only those effects try to include their interactions).
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