Design and Analysis of Experiments
with R 1st Edition by John Lawson
Complete Chapter Solutions Manual
are included (Ch 1 to 12)
** Immediate Download
** Swift Response
** All Chapters included
,Table of Contents are given below
1. Introduction
2. Completely Randomized Designs with One Factor
3. Factorial Designs
4. Randomized Block Designs
5. Designs to Study Variances
6. Fractional Factorial Designs
7. Incomplete and Confounded Block Designs
8. Split-Plot Designs
9. Crossover and Repeated Measures Designs
10. Response Surface Designs
11. Mixture Experiments
12. Robust Parameter Design Experiments
Experimental Strategies for Increasing Knowledge
,Solutions Manual organized in reverse order, with the last chapter displayed first, to ensure that all
chapters are included in this document. (Complete Chapters included Ch12-1)
Chapter 12 Solutions
John Lawson
2/25/2021
1. Consider the commercial product test of erasers conducted by Sachiyo and Kosaka in 1971 and discussed
by Taguchi (1987). The purpose of the test was to determine the quality of erasure when lines of the
same length drawn on different types of paper were rubbed with different erasers. For the experiment,
lines of the same length were drawn on each type of paper by different pencils. The lines were rubbed
three times back and forth by each eraser and then judged for quality. A response of $0 = $ top means
that no pencil trace was left on the paper. A response of 1 = middle means only a faint pencil trace
was left on the paper, and response of 2 = bottom means it did not erase very well.
Factors and levels for the experiment are shown in Table 1. The hope was to identify the brand and material
that produced the best quality erasure consistently regardless of the type of paper or the hardness of the
pencil lead used.
Table 1: Factors and Levels for Commercial Product Test of Erasers
Levels
Factor 1 2 3 4 5
Control Factors:
A: Manufacturer Rabbit Staedtler
B: Material Rubber Plastic
Noise Factors:
C: Paper Note Paper Tracing Paper
D: Lead Hardness 4H 2H HB 2B 4B
The control-factor array was a 22 factorial. One cell is missing since one manufacturer did not make rubber
erasers, and one cell is duplicated since the other manufacturer made two types of plastic erasers. The noise
factor array was a 2 × 5 full factorial. The product array design and the judged responses are shown in Table
2.
Table 2: Product Array Design and Response for Commercial Product Test
C 1 2
A B D 1 2 3 4 5 1 2 3 4 5
1 1 1 0.5 1 1 1 0 0.5 0.5 2 1.5
1 2 0.5 1 1 1 1 0 0 0 0.5 1.5
2 2 0 0 0 0 0.5 0 0 0 0.5 0
1 2 0 0.5 1 1 0 0 0 0.5 1.5 1.5
(a) Analyze the data using location-dispersion modeling.
# create control array
A<-c(1,1,2,1)
B<-c(1,2,2,2)
Carray<-data.frame(A,B)
#calculate mean and log variance across levels of the noise array
row<-rep(1:4,each=10)
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, y<-c(1,0.5,1,1,1,0,0.5,0.5,2,1.5,0.5,1,1,1,1,0,0,0,0.5,1.5,0,0,0,0,0.5,0,0,0,0.5,
0,0,0.5,1,1,0,0,0,0.5,1.5,1.5)
meany<-tapply(y,row,mean)
logvar<-log(tapply(y,row,var))
# append mean and variance to rows of control array
Carray<-cbind(Carray,meany,logvar)
Carray
## A B meany logvar
## 1 1 1 0.90 -1.1325138
## 2 1 2 0.65 -1.2709835
## 3 2 2 0.10 -3.1135153
## 4 1 2 0.60 -0.9734491
# fit location dispersion models
mody<-lm(meany~A+B, data=Carray)
summary(mody)
##
## Call:
## lm(formula = meany ~ A + B, data = Carray)
##
## Residuals:
## 1 2 3 4
## 0.000e+00 2.500e-02 3.469e-18 -2.500e-02
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.70000 0.07906 21.503 0.0296 *
## A -0.52500 0.04330 -12.124 0.0524 .
## B -0.27500 0.04330 -6.351 0.0994 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03536 on 1 degrees of freedom
## Multiple R-squared: 0.9963, Adjusted R-squared: 0.9889
## F-statistic: 134.3 on 2 and 1 DF, p-value: 0.06091
modv<-lm(logvar~A+B, data=Carray)
summary(modv)
##
## Call:
## lm(formula = logvar ~ A + B, data = Carray)
##
## Residuals:
## 1 2 3 4
## 0.000e+00 -1.488e-01 -2.776e-17 1.488e-01
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8485 0.4704 1.804 0.3223
## A -1.9913 0.2577 -7.728 0.0819 .
## B 0.0103 0.2577 0.040 0.9746
## ---
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