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The percentage of hardwood concentration in raw pulp, the vat pressure, and the cooking time of...

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Mechanical Engineering

The percentage of hardwood concentration in raw pulp, the vatpressure, and the cooking time of the pulp are being investigatedfor their effects on the strength of paper. Three levels ofhardwood concentration, three levels of pressure, and two cookingtimes are selected. A factorial experiment with two replicates isconducted, and the following data are obtained:


Percentage of Hardwood Concentration

Cooking Time 3.0 HoursCooking Time 4.0 Hours
PressurePressure
400500650400500650
2196.6197.7199.8198.4199.6200.6
196196199.4198.6200.4200.9
4198.5196198.4197.5198.7199.6
197.2196.9197.6198.1198199
8197.5195.6197.4197.6197198.5
196.6196.2198.1198.4197.8199.8  

(a) Analyze the data and draw conclusions. Use ? =0.05.

(b) Prepare appropriate residual plots and comment on themodel’s adequacy.

(c) Under what set of conditions would you run the process?Why?

Answer & Explanation Solved by verified expert
4.2 Ratings (555 Votes)

THE ANOVA for the fractional experiment is performed in the R stastistial software.

>tt<-read.Csv(\"clipboard\",sep=\"\t\")

>head(ttt)

Hardwood Cooking Pressure Strength

1 2 3 400 196.6

2 2 3 400 196.0

3 2 3 500 197.7

4 2 3 500 196.0

5 2 3 600 199.8

6 2 3 600 199.4

>tt$Hardwood <-as.factor(tt$ Hardwood)

>tt$Cooking <-as.factor(tt$Cooking)

>tt$Pressure <-as.factor(tt$Pressure)

>Strenght_aov <-aov(Strength~.,tt)

>summary(Strength_aov)

Df Sum Sq Mean Sq F value pr(>f)

Hardwood 28.84724.42366.91430.003392**

Cooking 121.777821.777834.03962.217e-06***

Presure 220.373910.186915.92261.937e-05***

Residucals 3019.19330.6398

-----

Signif.codes:0'****'0.001'**'0.01'*'0.05'.'0.1''1

Each of the factors is significant
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