Problem 6-4.
Solution:

(1) Calculate the main effects and the effects of two-factor interactions

(2) estimate the standard error of an effect.

(3) The significant effects are depth of cut and feed.

(4) Derive an empirical model which describes the functional relationship between the cutting force and the three cutting parameters.

Problem 6-6.
Solution:

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

Problem 6-6.
Solution:

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) Combine Models from I=1234 and I=-1234