Reference no: EM132572827
Design of Experiment (DOE)
In this assignment, student will learn how to use Minitab in solving DOE problems, focusing on two-factor experiments. To understand concepts of DOE and how to download Minitab free version, go to Unit Two/Supplement, folder "Minitab", and read the two handouts.
Design of Experiment (DOE) is a powerful tool that can be used in solving problems in experimental studies. The purpose is to determine whether varying the level of two factors affect the response. DOE can also be used to confirm suspected input/output relationships and to develop a predictive equation suitable for performing what-if analysis. For example, it may be desirable to understand the effect of temperature and pressure on the strength of a glue bond (ASQ-DOE by Dean Christolear).
Problem: a chemical engineer is studying the effects of various reagents and catalysts on the yield of a certain process. Yield is expressed as a percentage of a theoretical maximum. Four runs of the process were made for each combination of three reagents and four catalysts. The results are presented in below table.
|
|
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Reagent
|
|
|
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R1
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R2
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R3
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Catalyst
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A
|
86.8
|
93.4
|
77.9
|
|
|
|
82.4
|
85.2
|
89.6
|
|
|
|
86.7
|
94.8
|
89.9
|
|
|
|
83.5
|
83.1
|
83.7
|
|
|
B
|
71.9
|
74.5
|
87.5
|
|
|
|
72.1
|
87.1
|
82.7
|
|
|
|
80
|
71.9
|
78.3
|
|
|
|
77.4
|
84.1
|
90.1
|
|
|
C
|
65.5
|
66.7
|
72.7
|
|
|
|
72.4
|
77.1
|
77.8
|
|
|
|
76.6
|
76.7
|
83.5
|
|
|
|
66.7
|
86.1
|
78.8
|
|
|
D
|
63.9
|
73.7
|
79.8
|
|
|
|
70.4
|
81.6
|
75.7
|
|
|
|
77.2
|
84.2
|
80.5
|
|
|
|
81.2
|
84.9
|
72.9
|
Using Minitab to perform Two-way ANOVA and answer the following questions:
Question 1. How many degrees of freedom are there for the effect of catalyst type?
Question 2. How many degrees of freedom are there for the effect of reagent type?
Question 3. How many degrees of freedom are there for interactions?
Question 4. How many degrees of freedom are there for error?
Question 5. Construct an ANOVA table, using alpha 0.05 or 95% level of confidence
Question 6. Is the additive model plausible? Provide the value of the test statistic and the P-value.
Question 7. Is it plausible that the main effects of catalyst are all equal to 0? Provide the value of the test statistic and the P-value.
Question 8. Is it plausible that the main effects of reagent are all equal to 0? Provide the value of the test statistic and the P-value.
Question 9. Construct 2 diagrams: 1) main effects plot for yield and 2) Interaction plot for yield.