# Anova3_2page - Factorial Experiments and Quality Improvement III 23 experiments introduction 23 experiments have three factors each at two levels

This preview shows pages 1–7. Sign up to view the full content.

Factorial Experiments and Quality Improvement III March 13, 2007 2 3 experiments: introduction 2 3 experiments have three factors, each at two levels. Y ĳk ` = μ ĳ ` + ± ĳk ` = μ + α i + β j + γ k + ( αβ ) ĳ + ( αγ ) ĳ + ( βγ ) jk + ( αβγ ) ĳk + ± ĳk ` Main eﬀects and interactions sum to 0 in any subscript , with other subscripts held ﬁxed.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Overall mean and main eﬀects μ = μ 111 + μ 112 + μ 121 + μ 122 + μ 211 + μ 212 + μ 221 + μ 222 8 α 1 = ( μ 111 + μ 112 + μ 121 + μ 122 ) - ( μ 211 + μ 212 + μ 221 + μ 222 ) 8 β 1 = ( μ 111 + μ 112 + μ 211 + μ 212 ) - ( μ 121 + μ 122 + μ 221 + μ 222 ) 8 and similarly for γ 1 Two-way interactions ( αβ ) 11 = ( μ 111 + μ 112 ) - ( μ 121 + μ 122 ) - ( μ 211 + μ 212 ) + ( μ 221 + μ 222 ) 8 and similarly for ( αγ ) 11 and ( βγ ) 11
Three way interaction ( αβγ ) 111 = ( μ 111 - μ 121 - μ 121 + μ 221 ) - ( μ 112 - μ 122 + μ 122 - μ 222 ) 8 = { ( αβ ) 11 when C=1 } - { ( αβ ) 11 when C=2 } 8 The three-way interaction is I the change in the (AB) interaction as C changes from 1 to 2. I the change in the (AC) interaction as B changes from 1 to 2. I the change in the (BC) interaction as A changes from 1 to 2. Visualizing the eﬀects (Empty slide for drawing)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Visualizing the eﬀects (Empty slide for drawing) Representation of eﬀects run A B C AB AC BC ABC 1 + + + + + + + 2 - + + - - + - 3 + - + - + - - 4 - - + + - - + 5 + + - + - - - 6 - + - - + - + 7 + - - - - + + 8 - - - + + + - Runs would be put in a random order
2 3 experiments: example I Lipton carried out an experiment with 5 factors, each at two levels. I there were 16 “runs” I As we will see later, only three factors had eﬀects I Ignore the factors without eﬀects I 2 3 experiment with two replicates Lipton 2 3 experiment: factors Factors in this analysis: I Temperature (0=water cooled, 1=ambient temperature) I batch weight (1500 lb, 2000 lb) I delay (1 day, 7 day) Response = performance (std. dev.)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
R code lipton.data = read.table(’lipton.txt’,header=TRUE) attach(lipton.data) lmfit = lm(performance ~ temp*wt*delay) pdf(’lipton_boxplot_temp_delay.pdf’) boxplot(performance~temp*delay,xlab=’temp*delay’, ylab=’performance’) pdf(’lipton_boxplot_wt_delay.pdf’) boxplot(performance~wt*delay,xlab=’wt*delay’, ylab=’performance’) graphics.off() detach(lipton.data) ANOVA table anova(lmfit) Analysis of Variance Table Response: performance Df Sum Sq Mean Sq F value Pr(>F) temp 1 0.03062 0.03062
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/09/2009 for the course ORIE 312 taught by Professor D.ruppert,p.jacks during the Spring '08 term at Cornell University (Engineering School).

### Page1 / 20

Anova3_2page - Factorial Experiments and Quality Improvement III 23 experiments introduction 23 experiments have three factors each at two levels

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online