Problema 9 (Fuente: http://dx.doi.org/10.1016/j.matpr.2021.01.214)

En el mundo actual, los equipos de manipulación de lodos se enfrentan a muchos problemas de ingeniería, como la erosión. En las centrales hidroeléctricas, la prevención de los lodos juega un papel muy importante. El ángulo de impacto, la velocidad de las partículas, sus propiedades y el sustrato dependen de los estudios de erosión. Para evitar los efectos dañinos de la erosión , se utilizan varios métodos de modificación de la superficie. Por lo tanto, en el presente trabajo, los esfuerzos están hechos para darse cuenta del impacto de los parámetros de la lechada en los revestimientos desarrollado a través de la energía de microondas. Las muestras de revestimiento desarrolladas (25 65 6 mm3 ) fueron fijadas en cada husillo y se sumergieron completamente en la olla de lechada. Agua destilada Se utilizó agua destilada y partículas de arena de sílice en proporción 1:1 para preparar la lechada. Por último, se llevaron a cabo estudios de desgaste erosivo de la lechada bajo tres parámetros, velocidad (S), tiempo (T) y ángulo de impacto (A), junto con sus variaciones en tres niveles. S=(1000, 1250,1500)rpm T=(60,120,180)min A=(15°,30°,45°) Estos experimentos se diseñaron basados en el arreglo ortogonal (OA) estándar de Taguchi L27. Los resultados experimentales obtenidos se tabulan en la siguiente tabla: a) Determine el efecto que cada factor tiene en el desgaste. b) Determine el % de contribución de cada factor. c) Presente el gráfico de efectos de los factores

df<-read.csv("https://raw.githubusercontent.com/Manuela76/Dise-o-Exp/main/Problema%209%20ANOVA%203%20factores.csv")
df$ï..Veloc=factor(df$ï..Veloc)
df$Tiempo=factor(df$Tiempo)
df$Angulo=factor(df$Angulo)
df$Desgaste=as.numeric(df$Desgaste)
df
##    ï..Veloc Tiempo Angulo Desgaste
## 1         1      1      1  0.01865
## 2         1      1      2  0.01639
## 3         1      1      3  0.01203
## 4         1      2      1  0.02455
## 5         1      2      2  0.02036
## 6         1      2      3  0.01451
## 7         1      3      1  0.02866
## 8         1      3      2  0.02133
## 9         1      3      3  0.01693
## 10        2      1      1  0.03078
## 11        2      1      2  0.01908
## 12        2      1      3  0.01696
## 13        2      2      1  0.03370
## 14        2      2      2  0.02408
## 15        2      2      3  0.01920
## 16        2      3      1  0.03326
## 17        2      3      2  0.02700
## 18        2      3      3  0.02304
## 19        3      1      1  0.03099
## 20        3      1      2  0.02333
## 21        3      1      3  0.01916
## 22        3      2      1  0.03605
## 23        3      2      2  0.02873
## 24        3      2      3  0.02362
## 25        3      3      1  0.04550
## 26        3      3      2  0.03368
## 27        3      3      3  0.03015

ANOVA

modelo=lm(Desgaste~ï..Veloc*Tiempo*Angulo,data=df)
anova1=aov(modelo)
summary(anova1)
##                        Df    Sum Sq   Mean Sq
## ï..Veloc                2 0.0005331 0.0002665
## Tiempo                  2 0.0002896 0.0001448
## Angulo                  2 0.0006470 0.0003235
## ï..Veloc:Tiempo         4 0.0000397 0.0000099
## ï..Veloc:Angulo         4 0.0000226 0.0000057
## Tiempo:Angulo           4 0.0000046 0.0000012
## ï..Veloc:Tiempo:Angulo  8 0.0000216 0.0000027
modelo=lm(Desgaste~ï..Veloc+Tiempo+Angulo+ï..Veloc:Tiempo+ï..Veloc:Angulo+Tiempo:Angulo,data=df)
anova=aov(modelo)
summary(anova)
##                 Df    Sum Sq   Mean Sq F value   Pr(>F)    
## ï..Veloc         2 0.0005331 0.0002665  98.761 2.30e-06 ***
## Tiempo           2 0.0002896 0.0001448  53.648 2.32e-05 ***
## Angulo           2 0.0006470 0.0003235 119.870 1.09e-06 ***
## ï..Veloc:Tiempo  4 0.0000397 0.0000099   3.677   0.0553 .  
## ï..Veloc:Angulo  4 0.0000226 0.0000057   2.095   0.1734    
## Tiempo:Angulo    4 0.0000046 0.0000012   0.427   0.7856    
## Residuals        8 0.0000216 0.0000027                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

INTERACCIONES

with(df, interaction.plot(x.factor = ï..Veloc, trace.factor = Tiempo,response = Desgaste))

with(df, interaction.plot(x.factor = Angulo, trace.factor = ï..Veloc,response = Desgaste))

with(df, interaction.plot(x.factor = Angulo, trace.factor = Tiempo,response = Desgaste))

Normalidad

qqnorm(anova$residuals)
qqline(anova$residuals)

shapiro.test(anova$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  anova$residuals
## W = 0.9784, p-value = 0.8245

Prueba de varianza

library(car)
## Loading required package: carData
leveneTest(df$Desgaste~df$Tiempo) 
## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  0.2379 0.7901
##       24
leveneTest(df$Desgaste~df$Angulo)
## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  0.2227  0.802
##       24
leveneTest(df$Desgaste~df$ï..Veloc)
## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  0.5052 0.6097
##       24

Pruebas de independencias

plot(anova$residuals,col="blue")
abline(h=0)

Prueba de Tukey

tk=TukeyHSD(anova)
tk
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = modelo)
## 
## $ï..Veloc
##            diff         lwr         upr     p adj
## 2-1 0.005965556 0.003752665 0.008178446 0.0001488
## 3-1 0.010866667 0.008653777 0.013079557 0.0000017
## 3-2 0.004901111 0.002688221 0.007114001 0.0005813
## 
## $Tiempo
##            diff         lwr         upr     p adj
## 2-1 0.004158889 0.001945999 0.006371779 0.0017064
## 3-1 0.008020000 0.005807110 0.010232890 0.0000171
## 3-2 0.003861111 0.001648221 0.006074001 0.0027166
## 
## $Angulo
##             diff          lwr          upr     p adj
## 2-1 -0.007573333 -0.009786223 -0.005360443 0.0000262
## 3-1 -0.011837778 -0.014050668 -0.009624888 0.0000009
## 3-2 -0.004264444 -0.006477335 -0.002051554 0.0014539
## 
## $`ï..Veloc:Tiempo`
##                  diff           lwr           upr     p adj
## 2:1-1:1  6.583333e-03  1.113203e-03  0.0120534639 0.0182577
## 3:1-1:1  8.803333e-03  3.333203e-03  0.0142734639 0.0029898
## 1:2-1:1  4.116667e-03 -1.353464e-03  0.0095867973 0.1772195
## 2:2-1:1  9.970000e-03  4.499869e-03  0.0154401306 0.0012889
## 3:2-1:1  1.377667e-02  8.306536e-03  0.0192467973 0.0001271
## 1:3-1:1  6.616667e-03  1.146536e-03  0.0120867973 0.0177318
## 2:3-1:1  1.207667e-02  6.606536e-03  0.0175467973 0.0003329
## 3:3-1:1  2.075333e-02  1.528320e-02  0.0262234639 0.0000060
## 3:1-2:1  2.220000e-03 -3.250131e-03  0.0076901306 0.7572839
## 1:2-2:1 -2.466667e-03 -7.936797e-03  0.0030034639 0.6632856
## 2:2-2:1  3.386667e-03 -2.083464e-03  0.0088567973 0.3387627
## 3:2-2:1  7.193333e-03  1.723203e-03  0.0126634639 0.0107983
## 1:3-2:1  3.333333e-05 -5.436797e-03  0.0055034639 1.0000000
## 2:3-2:1  5.493333e-03  2.320275e-05  0.0109634639 0.0489352
## 3:3-2:1  1.417000e-02  8.699869e-03  0.0196401306 0.0001031
## 1:2-3:1 -4.686667e-03 -1.015680e-02  0.0007834639 0.1041308
## 2:2-3:1  1.166667e-03 -4.303464e-03  0.0066367973 0.9889308
## 3:2-3:1  4.973333e-03 -4.967973e-04  0.0104434639 0.0795409
## 1:3-3:1 -2.186667e-03 -7.656797e-03  0.0032834639 0.7694470
## 2:3-3:1  3.273333e-03 -2.196797e-03  0.0087434639 0.3721777
## 3:3-3:1  1.195000e-02  6.479869e-03  0.0174201306 0.0003592
## 2:2-1:2  5.853333e-03  3.832027e-04  0.0113234639 0.0351278
## 3:2-1:2  9.660000e-03  4.189869e-03  0.0151301306 0.0016008
## 1:3-1:2  2.500000e-03 -2.970131e-03  0.0079701306 0.6502919
## 2:3-1:2  7.960000e-03  2.489869e-03  0.0134301306 0.0057511
## 3:3-1:2  1.663667e-02  1.116654e-02  0.0221067973 0.0000308
## 3:2-2:2  3.806667e-03 -1.663464e-03  0.0092767973 0.2349808
## 1:3-2:2 -3.353333e-03 -8.823464e-03  0.0021167973 0.3483508
## 2:3-2:2  2.106667e-03 -3.363464e-03  0.0075767973 0.7978308
## 3:3-2:2  1.078333e-02  5.313203e-03  0.0162534639 0.0007465
## 1:3-3:2 -7.160000e-03 -1.263013e-02 -0.0016898694 0.0111066
## 2:3-3:2 -1.700000e-03 -7.170131e-03  0.0037701306 0.9164584
## 3:3-3:2  6.976667e-03  1.506536e-03  0.0124467973 0.0129817
## 2:3-1:3  5.460000e-03 -1.013059e-05  0.0109301306 0.0504724
## 3:3-1:3  1.413667e-02  8.666536e-03  0.0196067973 0.0001050
## 3:3-2:3  8.676667e-03  3.206536e-03  0.0141467973 0.0032901
## 
## $`ï..Veloc:Angulo`
##                  diff           lwr           upr     p adj
## 2:1-1:1  0.0086266667  0.0031565361  0.0140967973 0.0034176
## 3:1-1:1  0.0135600000  0.0080898694  0.0190301306 0.0001429
## 1:2-1:1 -0.0045933333 -0.0100634639  0.0008767973 0.1136688
## 2:2-1:1 -0.0005666667 -0.0060367973  0.0049034639 0.9999227
## 3:2-1:1  0.0046266667 -0.0008434639  0.0100967973 0.1101673
## 1:3-1:1 -0.0094633333 -0.0149334639 -0.0039932027 0.0018413
## 2:3-1:1 -0.0042200000 -0.0096901306  0.0012501306 0.1610775
## 3:3-1:1  0.0003566667 -0.0051134639  0.0058267973 0.9999977
## 3:1-2:1  0.0049333333 -0.0005367973  0.0104034639 0.0825860
## 1:2-2:1 -0.0132200000 -0.0186901306 -0.0077498694 0.0001723
## 2:2-2:1 -0.0091933333 -0.0146634639 -0.0037232027 0.0022389
## 3:2-2:1 -0.0040000000 -0.0094701306  0.0014701306 0.1972431
## 1:3-2:1 -0.0180900000 -0.0235601306 -0.0126198694 0.0000164
## 2:3-2:1 -0.0128466667 -0.0183167973 -0.0073765361 0.0002125
## 3:3-2:1 -0.0082700000 -0.0137401306 -0.0027998694 0.0045008
## 1:2-3:1 -0.0181533333 -0.0236234639 -0.0126832027 0.0000160
## 2:2-3:1 -0.0141266667 -0.0195967973 -0.0086565361 0.0001055
## 3:2-3:1 -0.0089333333 -0.0144034639 -0.0034632027 0.0027125
## 1:3-3:1 -0.0230233333 -0.0284934639 -0.0175532027 0.0000027
## 2:3-3:1 -0.0177800000 -0.0232501306 -0.0123098694 0.0000187
## 3:3-3:1 -0.0132033333 -0.0186734639 -0.0077332027 0.0001739
## 2:2-1:2  0.0040266667 -0.0014434639  0.0094967973 0.1924912
## 3:2-1:2  0.0092200000  0.0037498694  0.0146901306 0.0021957
## 1:3-1:2 -0.0048700000 -0.0103401306  0.0006001306 0.0876497
## 2:3-1:2  0.0003733333 -0.0050967973  0.0058434639 0.9999968
## 3:3-1:2  0.0049500000 -0.0005201306  0.0104201306 0.0813031
## 3:2-2:2  0.0051933333 -0.0002767973  0.0106634639 0.0647170
## 1:3-2:2 -0.0088966667 -0.0143667973 -0.0034265361 0.0027877
## 2:3-2:2 -0.0036533333 -0.0091234639  0.0018167973 0.2692726
## 3:3-2:2  0.0009233333 -0.0045467973  0.0063934639 0.9975077
## 1:3-3:2 -0.0140900000 -0.0195601306 -0.0086198694 0.0001076
## 2:3-3:2 -0.0088466667 -0.0143167973 -0.0033765361 0.0028940
## 3:3-3:2 -0.0042700000 -0.0097401306  0.0012001306 0.1537734
## 2:3-1:3  0.0052433333 -0.0002267973  0.0107134639 0.0617611
## 3:3-1:3  0.0098200000  0.0043498694  0.0152901306 0.0014305
## 3:3-2:3  0.0045766667 -0.0008934639  0.0100467973 0.1154604
## 
## $`Tiempo:Angulo`
##                 diff           lwr           upr     p adj
## 2:1-1:1  0.004626667 -0.0008434639  0.0100967973 0.1101673
## 3:1-1:1  0.009000000  0.0035298694  0.0144701306 0.0025814
## 1:2-1:1 -0.007206667 -0.0126767973 -0.0017365361 0.0106775
## 2:2-1:1 -0.002416667 -0.0078867973  0.0030534639 0.6827137
## 3:2-1:1  0.000530000 -0.0049401306  0.0060001306 0.9999531
## 1:3-1:1 -0.010756667 -0.0162267973 -0.0052865361 0.0007596
## 2:3-1:1 -0.007696667 -0.0131667973 -0.0022265361 0.0071133
## 3:3-1:1 -0.003433333 -0.0089034639  0.0020367973 0.3256772
## 3:1-2:1  0.004373333 -0.0010967973  0.0098434639 0.1396647
## 1:2-2:1 -0.011833333 -0.0173034639 -0.0063632027 0.0003855
## 2:2-2:1 -0.007043333 -0.0125134639 -0.0015732027 0.0122631
## 3:2-2:1 -0.004096667 -0.0095667973  0.0013734639 0.1805131
## 1:3-2:1 -0.015383333 -0.0208534639 -0.0099132027 0.0000557
## 2:3-2:1 -0.012323333 -0.0177934639 -0.0068532027 0.0002876
## 3:3-2:1 -0.008060000 -0.0135301306 -0.0025898694 0.0053107
## 1:2-3:1 -0.016206667 -0.0216767973 -0.0107365361 0.0000376
## 2:2-3:1 -0.011416667 -0.0168867973 -0.0059465361 0.0004982
## 3:2-3:1 -0.008470000 -0.0139401306 -0.0029998694 0.0038535
## 1:3-3:1 -0.019756667 -0.0252267973 -0.0142865361 0.0000086
## 2:3-3:1 -0.016696667 -0.0221667973 -0.0112265361 0.0000300
## 3:3-3:1 -0.012433333 -0.0179034639 -0.0069632027 0.0002697
## 2:2-1:2  0.004790000 -0.0006801306  0.0102601306 0.0944942
## 3:2-1:2  0.007736667  0.0022665361  0.0132067973 0.0068855
## 1:3-1:2 -0.003550000 -0.0090201306  0.0019201306 0.2946864
## 2:3-1:2 -0.000490000 -0.0059601306  0.0049801306 0.9999741
## 3:3-1:2  0.003773333 -0.0016967973  0.0092434639 0.2420966
## 3:2-2:2  0.002946667 -0.0025234639  0.0084167973 0.4807825
## 1:3-2:2 -0.008340000 -0.0138101306 -0.0028698694 0.0042617
## 2:3-2:2 -0.005280000 -0.0107501306  0.0001901306 0.0596818
## 3:3-2:2 -0.001016667 -0.0064867973  0.0044534639 0.9953137
## 1:3-3:2 -0.011286667 -0.0167567973 -0.0058165361 0.0005406
## 2:3-3:2 -0.008226667 -0.0136967973 -0.0027565361 0.0046562
## 3:3-3:2 -0.003963333 -0.0094334639  0.0015067973 0.2039513
## 2:3-1:3  0.003060000 -0.0024101306  0.0085301306 0.4411622
## 3:3-1:3  0.007323333  0.0018532027  0.0127934639 0.0096811
## 3:3-2:3  0.004263333 -0.0012067973  0.0097334639 0.1547288
plot(tk)

library(agricolae)
LSD<-LSD.test(y=anova,trt="Tiempo",group=T)
bar.group(x=LSD$groups,horiz=TRUE,col="blue",xlim=c(0,0.04),xlab="Desgaste", ylab="Tiempo", main="Desgaste vs tiempo")

LSD<-LSD.test(y=anova,trt="Angulo",group=T)
bar.group(x=LSD$groups,horiz=TRUE,col="blue",xlim=c(0,0.04),xlab="Desgaste", ylab="Angulo", main="Desgaste vs Angulo")

LSD<-LSD.test(y=anova,trt="ï..Veloc",group=T)
bar.group(x=LSD$groups,horiz=TRUE,col="blue",xlim=c(0,0.04),xlab="Desgaste", ylab="ï..Veloc", main="Desgaste vs ï..Veloc")

Pareto

library(pid)
## Registered S3 method overwritten by 'DoE.base':
##   method           from       
##   factorize.factor conf.design
paretoPlot(anova)