Problem 5.6.6

Problem 5.6.7

Problem 5.6.9

6. A 2⁴ factorial design was conducted producing the following test results. Calculate the estimates and derive an empirical model representing the data.

Assumed that all three factor and four factor interactions are negligible, they may be sued to estimate the standard errors.

Based on a 90% confidence interval for five degrees of freedom, the critical t-values are calculated to be 2.015( using a two tailed t-distribution table). The empirical model

7. Use the data provided in Problem 6. Decompose the 16 runs into two data sets. The first data set resembles the results from a fractional factorial design with the generator equal to I=1234. The second data set resembles the results from a fractional factorial design with the generator equal to I=-1234. Write all the confounding patterns associated with each of the two generators.

For I=1234 4I=4(1234)=123 4=123

l₀ estimates mean

l₁ estimates 1 +234

l₂ estimates 2 + 134

l₃ estimates 3 + 124

l₁₂ estimates 12 +34

l₁₃ estimates 13 +24

l₂₃ estimates 23 +14

l₁₂₃ estimates 123 +4

For I=-1234 4I=4(-1234)=-123 4=-123

l₀ estimates mean

l₁ estimates 1 -234

l₂ estimates 2 -134

l₃ estimates 3 - 124

l₁₂ estimates 12 -34

l₁₃ estimates 13 -24

l₂₃ estimates 23 -14

l₁₂₃ estimates -123 +4

(4) Combien Models from I=1234 and I=-1234

9. A 2^4-1 fractional factorial design was conducted on a chemical process by assigning variable 4 to the 123 interaction column.

1. Write down all of the linear combinations of effects that can be estimated form this experiment.

Since 4=123, I=1234

l₀ estimates mean

l₁ estimates 1 + 234

l₂ estimates 2 + 134

l₃ estimates 3 + 124

l₁₂ estimates 12 + 34

l₁₃ estimates 13 + 24

l₂₃ estimates 23 + 14

l123 estimates 123+4

If third order intreactions are negligible.

l₀ estimates mean

l₁ estimates 1

l₂ estimates 2

l₃ estimates 3

l₁₂ estimates 12 and 34

l₁₃ estimates 13 and 24

l₂₃ estimates 23 and 14

l123 estimates 4