Fractional Factorial Experiments in the 2k-p SeriesQuestion 1Answer the following: An article in Industrial and Engineering Chemistry (“More on Planning Experiments...

1. Fractional Factorial Experiments in the 2k-p Series

Answer should be prepared using Minitab.

Question 1

Answer the following: 

An article in Industrial and Engineering Chemistry (“More on Planning Experiments to Increase Research Efficiency”, 1970, pp.60-65) uses a 2^5-2design to investigate the effect of A=condensation temperature, B=amount of materials, C=solvent volume, D=condensation time, and E=amount of material 3 on yield. The results obtained are as follows:

e=23.2           ad=16.9         cd=23.8         bde=16.8

ab=15.5         bc=16.2         ace=23.4       abcde= 18.1

Verify and comment that the design generators used were I=ACE and I=BDE.

Question 2

Answer the following: 

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

Question 3

Answer the following: 

Estimate the main effects.

Question 4

Answer the following: 

Prepare an analysis of variance table and verify that the AB and AD interactions are available to use as error.

Question 5

Answer the following: 

Plot the residuals versus the fitted values. Also construct a normal probability plot of the residuals. Comment on the results. Consider the 2^7-2 design by choosing two four-factor interactions as the independent generators.

Question 6

Answer the following: 

Write down the complete alias structures for this design.

Question 7

Answer the following: 

Outline the analysis of variance table.

Question 8

Answer the following: 

What is the resolution of this design?