PROBLEMA AUTOMOTRIZ

Integrantes:

A01424709, Armando Arredondo Valle
A01424732, Emiliano Vivas Rodríguez
A01424731, Aldo Olascoaga Olmedo
A01423655, Diego Efraín Antonio Pérez

Introducción:

En este proyecto, buscamos realizar el análisis de los datos para una empresa la cual presenta un problema de materiales, en la cual existe una tendencia en la falla de creación y desarrollo de los materiales. Con el uso de la estadística podremos presentarle al cliente la razón de las fallas constantes.

Librerias a utilizar

library("skimr")
library("naniar")
library("Hmisc")
library("corrplot")
library("psych")
library("dplyr")
library("GGally")
library("kableExtra")
library("forecast");
library("smooth");

Tablas de análisis

Aquí se muestran dos tablas con la información recabada de la situación problema, es necesario especificar que fué necesario realizar una “limpieza” de datos, esto con el fin de que no existiera problema al realizar los procedimientos de análisis. Así como fué necesario el cambio de nombres de algunas columnas (Cambio en los nombres de piezas defectuosas, así como en la información de las máquinas) junto con la eliminación de otras (Eliminación de forma individual de piezas producidas).

Nota: Solo se muestran los primeros datos, esto para tener una mejor visualización del documento. Así mismo, en lo que abarca el documento, la tabla de “histórico de defectos” será llamada como Tabla 1, y la tabla de “datos de muestreo” será llamada como Tabla 2.

TABLA DE HISTÓRICO DE DEFECTOS:

DEFECTUOSAS A	DEFECTUOSAS B	DEFECTUOSAS C
157800	1100	78050
57400	2100	63350
85800	1200	74900
12400	2200	72450
45600	1900	87150

TABLA DE DATOS DE MUESTREO:

Pressure	PlasticPumpTemperature	PlasticMixerTemperature	ScrewTemperature	ScrewRPM	BarrelTemperature
71	228	208	197	115	180
24	230	194	204	117	120
22	219	238	231	84	143
68	223	250	206	83	175
22	246	252	238	116	121

Análisis de los datos

Para realizar el análisis de los datos se optaron por diversos procedimientos tales como:

Verificación de falta de datos.
Análisis general de verificación de datos. (Data Summary)
Análisis de correlación de cada variable
Gráficas de pares
Gráficas individuales de cada variable

Graficación de pérdidas

Tras haber realizado el análisis general de los datos, pudimos apreciar que el 100% de los datos para cada categoría estaban presentes.

Pérdidas de la Tabla 1:

## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## Please use `gather()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.

Pérdidas Tabla 2:

Data summary

En lo que respecta el data summary, utilizando la libreria skimr, revisamos datos generales de cada variable, esto con el fin de tener una mejor perspectiva de los datos.

Data summary Tabla 1:

skim_type	skim_variable	complete_rate	numeric.mean	numeric.sd	numeric.p0	numeric.p25	numeric.p50	numeric.p75	numeric.p100	numeric.hist
numeric	DEFECTUOSAS A	1	90933.333	61794.179	6400	24350	89950	152475	192800	<U+2587><U+2585><U+2585><U+2585><U+2586>
numeric	DEFECTUOSAS B	1	6229.167	4571.032	1100	2700	4650	8975	15900	<U+2587><U+2586><U+2581><U+2582><U+2583>
numeric	DEFECTUOSAS C	1	73689.583	14691.294	38850	64925	71925	85400	102200	<U+2581><U+2585><U+2587><U+2587><U+2583>

Data summary Tabla 2:

skim_type	skim_variable	complete_rate	numeric.mean	numeric.sd	numeric.p0	numeric.p25	numeric.p50	numeric.p75	numeric.p100	numeric.hist
numeric	Pressure	1	36.980000	23.2191927	16.0000	20.000000	22.00000	67.000000	75.00000	<U+2587><U+2581><U+2581><U+2581><U+2583>
numeric	PlasticPumpTemperature	1	221.660000	21.1216869	167.0000	205.000000	226.50000	237.000000	256.00000	<U+2581><U+2583><U+2583><U+2587><U+2585>
numeric	PlasticMixerTemperature	1	214.530000	20.1225814	184.0000	199.000000	207.00000	235.000000	252.00000	<U+2585><U+2587><U+2582><U+2585><U+2583>
numeric	ScrewTemperature	1	220.340000	22.7210666	186.0000	200.750000	212.50000	243.000000	264.00000	<U+2587><U+2587><U+2583><U+2587><U+2583>
numeric	ScrewRPM	1	98.510000	19.4190862	74.0000	81.000000	87.50000	118.000000	129.00000	<U+2587><U+2582><U+2581><U+2583><U+2583>
numeric	BarrelTemperature	1	146.660000	28.3403628	108.0000	120.000000	144.50000	175.000000	189.00000	<U+2587><U+2582><U+2582><U+2582><U+2587>
numeric	ExtrusionVelocity	1	1.975285	1.4526237	0.2387	0.698675	1.64380	2.793287	5.60625	<U+2587><U+2585><U+2583><U+2582><U+2582>
numeric	CoolerTemperature	1	85.290000	22.3581025	45.0000	67.000000	84.00000	105.000000	125.00000	<U+2586><U+2587><U+2587><U+2586><U+2586>
numeric	RawMaterialType	1	2.040000	0.9419516	1.0000	1.000000	2.00000	3.000000	3.00000	<U+2587><U+2581><U+2582><U+2581><U+2587>
numeric	ErrorPercentage	1	42.287161	12.5109817	15.7133	34.216707	41.65039	49.335154	72.45548	<U+2583><U+2585><U+2587><U+2583><U+2582>

Análisis de correlación de la Extrusión contra la Velocidad

## 
##  Pearson's product-moment correlation
## 
## data:  EXTRUSION and PERCENTAGE
## t = -2.7718, df = 98, p-value = 0.006672
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.44260213 -0.07729936
## sample estimates:
##        cor 
## -0.2696238

Gráficas de pares para las piezas defectuosas

En este apartado podemos apreciar las gráficas de pares para cada variable, obteniendo cada uno de los índices de correlación para cada variable, teniendo una de C con B de índice negativo, así como C con A.

Gráficas de pares (A)

Gráfica de pares (B)

Histogramas múltiples de cada pieza defectuosa

Aquí podemos apreciar los histogramas múltiples de las piezas defectuosas, en el que la gráfica azul es nuestro resultado, sin embargo podemos ver que hay una clara diferencia en las gráficas de pieza defectuosas A y B, pero, podemos ver que la gráfica de pieza C es la que podemos ver que se acerca más al resultado esperado.

Piezas defectuosas A

Piezas defectuosas B

Piezas defectuosas C

Análisis de correlación para piezas defectuosas

Podemos observar de forma más gráfica un análisis de correlación más parcial en lo que respecta a cada una de las piezas defectuosas. En el que podemos ver que es mínima la relación entre las variables.

Datos limpios

Gráfica de pares en los datos de piezas

En este apartado tenemos las gráficas de pares, en el que la gráfica A es una visión general de todas las variables de la Tabla 2, sin embargo la gráfica B apreciamos una tabla general con los índices de correlación para cada una de las variables, tomando así en variables para remarcar la Velocidad de Extrusión con la Presión; de igual forma es importante señalar el alto índice negativo del Plastic Mixer Temperature con el porcentaje de error del mismo.

Gráfica de pares (A)

Gráfica de pares (B)

Histograma múltiple (PORCENTAJE)

Algoritmo para análisis de regresión

getRegression <- function(x, xLabel, y, yLabel){
  correlation = cor(x, y, method="pearson");
  determinationCoefficient = correlation^2;
  linearRegression = lm(y~x);
  linearRegressionStatus = summary(linearRegression);
  evaluation = anova(linearRegression);
  print("Nuevo análisis de caso.");
  print(paste(yLabel, " = (", round(linearRegressionStatus$coefficients[2, 1], 3), ")*(", xLabel, ") + (", round(linearRegressionStatus$coefficients[1,1], 3), ')', sep = ''));
  print(paste(round(determinationCoefficient, 4)*100, "% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal.", sep = ''));
  if(linearRegressionStatus$coefficients[1,4] > ALPHA){
    print("Ajuste debido a Prueba T");
    linearRegression = lm(y~x-1);
    linearRegressionStatus = summary(linearRegression);
    determinationCoefficient = linearRegressionStatus$r.squared;
    evaluation = anova(linearRegression);
    print(paste(yLabel, " = (", round(linearRegressionStatus$coefficients[1, 1], 3), ")*(", xLabel, ')', sep = ''));
    print(paste(round(determinationCoefficient, 4)*100, "% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal.", sep = ''));
  }
  plot(x, y, xlab=xLabel, ylab=yLabel);
  abline(linearRegression);
  plot(linearRegression);
  return (list(X=x, XLabel=xLabel, Y=y, YLabel=yLabel, LinearRegresion=linearRegression, LinearRegresionStatus=linearRegressionStatus, EstimateCoefficients=linearRegressionStatus$coefficients, Correlation=correlation, DeterminationCoefficient=determinationCoefficient, Evaluation=evaluation));
}

Casos a realizar la regresión

ALPHA = 0.05;
cases = list(
  getRegression(analyze2$Pressure, "Pressure", analyze2$PlasticPumpTemperature, "PlasticPumpTemperature"),
  getRegression(analyze2$Pressure, "Pressure", analyze2$ScrewTemperature, "ScrewTemperature"),
  getRegression(analyze2$Pressure, "Pressure", analyze2$ExtrusionVelocity, "ExtrusionVelocity"),
  getRegression(analyze2$Pressure, "Pressure", analyze2$CoolerTemperature, "CoolerTemperature"),
  getRegression(analyze2$Pressure, "Pressure", analyze2$ErrorPercentage, "ErrorPercentage"),
  
  getRegression(analyze2$PlasticPumpTemperature, "PlasticPumpTemperature", analyze2$ScrewTemperature, "ScrewTemperature"),
  getRegression(analyze2$PlasticPumpTemperature, "PlasticPumpTemperature", analyze2$ExtrusionVelocity, "ExtrusionVelocity"),
  getRegression(analyze2$PlasticPumpTemperature, "PlasticPumpTemperature", analyze2$ErrorPercentage, "ErrorPercentage"),
  
  getRegression(analyze2$PlasticMixerTemperature, "PlasticMixerTemperature", analyze2$ErrorPercentage, "ErrorPercentage"),
  
  getRegression(analyze2$ScrewTemperature, "ScrewTemperature", analyze2$ExtrusionVelocity, "ExtrusionVelocity"),
  getRegression(analyze2$ScrewTemperature, "ScrewTemperature", analyze2$ErrorPercentage, "ErrorPercentage"),
  
  getRegression(analyze2$ScrewRPM, "ScrewRPM", analyze2$ExtrusionVelocity, "ExtrusionVelocity"),
  getRegression(analyze2$ScrewRPM, "ScrewRPM", analyze2$ErrorPercentage, "ErrorPercentage"),
  
  getRegression(analyze2$BarrelTemperature, "BarrelTemperature", analyze2$ErrorPercentage, "ErrorPercentage"),
  
  getRegression(analyze2$ExtrusionVelocity, "ExtrusionVelocity", analyze2$CoolerTemperature, "CoolerTemperature"),
  getRegression(analyze2$ExtrusionVelocity, "ExtrusionVelocity", analyze2$ErrorPercentage, "ErrorPercentage")
);

## [1] "Nuevo análisis de caso."
## [1] "PlasticPumpTemperature = (0.208)*(Pressure) + (213.974)"
## [1] "5.22% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ScrewTemperature = (0.176)*(Pressure) + (213.832)"
## [1] "3.23% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ExtrusionVelocity = (0.054)*(Pressure) + (-0.012)"
## [1] "73.78% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."
## [1] "Ajuste debido a Prueba T"
## [1] "ExtrusionVelocity = (0.054)*(Pressure)"
## [1] "90.86% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "CoolerTemperature = (0.212)*(Pressure) + (77.445)"
## [1] "4.85% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ErrorPercentage = (-0.082)*(Pressure) + (45.314)"
## [1] "2.31% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ScrewTemperature = (0.251)*(PlasticPumpTemperature) + (164.654)"
## [1] "5.45% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ExtrusionVelocity = (0.017)*(PlasticPumpTemperature) + (-1.874)"
## [1] "6.38% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."
## [1] "Ajuste debido a Prueba T"
## [1] "ExtrusionVelocity = (0.009)*(PlasticPumpTemperature)"
## [1] "66.83% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ErrorPercentage = (-0.249)*(PlasticPumpTemperature) + (97.495)"
## [1] "17.68% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ErrorPercentage = (-0.313)*(PlasticMixerTemperature) + (109.437)"
## [1] "25.35% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ExtrusionVelocity = (0.013)*(ScrewTemperature) + (-0.815)"
## [1] "3.92% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."
## [1] "Ajuste debido a Prueba T"
## [1] "ExtrusionVelocity = (0.009)*(ScrewTemperature)"
## [1] "66.38% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ErrorPercentage = (0.082)*(ScrewTemperature) + (24.11)"
## [1] "2.24% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."
## [1] "Ajuste debido a Prueba T"
## [1] "ErrorPercentage = (0.191)*(ScrewTemperature)"
## [1] "91.89% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ExtrusionVelocity = (0.028)*(ScrewRPM) + (-0.789)"
## [1] "14.08% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."
## [1] "Ajuste debido a Prueba T"
## [1] "ExtrusionVelocity = (0.02)*(ScrewRPM)"
## [1] "69.65% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ErrorPercentage = (-0.229)*(ScrewRPM) + (64.842)"
## [1] "12.63% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ErrorPercentage = (-0.175)*(BarrelTemperature) + (67.984)"
## [1] "15.75% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "CoolerTemperature = (2.142)*(ExtrusionVelocity) + (81.058)"
## [1] "1.94% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

## [1] "Nuevo análisis de caso."
## [1] "ErrorPercentage = (-2.322)*(ExtrusionVelocity) + (46.874)"
## [1] "7.27% de los datos especificados son explicados adecuadamente por el modelo de regresión lineal."

Análisis a fondo de cada caso

Caso 1

## [[1]]
## [[1]]$X
##   [1] 71 24 22 68 22 20 67 68 18 17 23 23 21 16 23 22 24 23 67 20 19 21 73 21 19
##  [26] 20 22 20 22 74 19 73 20 20 16 21 16 21 22 67 17 22 22 19 20 73 21 20 19 23
##  [51] 24 69 74 25 19 21 23 23 71 71 73 69 19 67 20 20 21 67 67 21 67 21 67 75 75
##  [76] 20 21 65 71 73 24 22 66 22 67 21 20 67 24 19 22 68 67 21 22 22 20 71 73 20
## 
## [[1]]$XLabel
## [1] "Pressure"
## 
## [[1]]$Y
##   [1] 228 230 219 223 246 253 233 198 203 230 195 246 182 186 234 193 226 243
##  [19] 256 241 225 188 251 233 200 233 187 235 242 250 227 221 183 237 194 227
##  [37] 242 242 205 185 232 220 228 236 216 233 191 243 211 221 217 254 221 212
##  [55] 195 221 192 245 237 229 212 223 194 227 239 176 204 239 230 221 184 243
##  [73] 245 205 210 199 241 246 219 225 227 236 225 215 217 231 205 243 235 225
##  [91] 232 226 253 167 227 241 185 254 233 181
## 
## [[1]]$YLabel
## [1] "PlasticPumpTemperature"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##    213.9740       0.2078  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -51.339 -14.433   2.661  16.927  34.869 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 213.97402    3.90074  54.855   <2e-16 ***
## x             0.20784    0.08946   2.323   0.0222 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.67 on 98 degrees of freedom
## Multiple R-squared:  0.0522, Adjusted R-squared:  0.04253 
## F-statistic: 5.398 on 1 and 98 DF,  p-value: 0.02223
## 
## 
## [[1]]$EstimateCoefficients
##                Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) 213.9740240 3.90073734 54.854763 2.275542e-75
## x             0.2078414 0.08945939  2.323305 2.222970e-02
## 
## [[1]]$Correlation
## [1] 0.2284813
## 
## [[1]]$DeterminationCoefficient
## [1] 0.0522037
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value  Pr(>F)  
## x          1   2306 2305.65  5.3977 0.02223 *
## Residuals 98  41861  427.15                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso2

## [[1]]
## [[1]]$X
##   [1] 71 24 22 68 22 20 67 68 18 17 23 23 21 16 23 22 24 23 67 20 19 21 73 21 19
##  [26] 20 22 20 22 74 19 73 20 20 16 21 16 21 22 67 17 22 22 19 20 73 21 20 19 23
##  [51] 24 69 74 25 19 21 23 23 71 71 73 69 19 67 20 20 21 67 67 21 67 21 67 75 75
##  [76] 20 21 65 71 73 24 22 66 22 67 21 20 67 24 19 22 68 67 21 22 22 20 71 73 20
## 
## [[1]]$XLabel
## [1] "Pressure"
## 
## [[1]]$Y
##   [1] 197 204 231 206 238 204 248 242 220 197 209 211 233 219 206 195 244 254
##  [19] 210 202 243 221 261 203 227 226 243 206 204 187 218 186 192 230 194 203
##  [37] 245 254 201 245 204 254 207 200 222 244 214 256 192 197 195 245 263 211
##  [55] 199 206 197 254 198 260 189 243 226 248 243 213 211 203 204 247 244 201
##  [73] 246 191 198 189 208 194 208 264 216 198 247 212 200 200 217 239 260 208
##  [91] 241 195 251 200 239 240 200 258 248 218
## 
## [[1]]$YLabel
## [1] "ScrewTemperature"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##     213.832        0.176  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -40.679 -17.690  -5.028  20.607  41.944 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 213.83231    4.23985   50.43   <2e-16 ***
## x             0.17598    0.09724    1.81   0.0734 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.46 on 98 degrees of freedom
## Multiple R-squared:  0.03234,    Adjusted R-squared:  0.02247 
## F-statistic: 3.275 on 1 and 98 DF,  p-value: 0.07339
## 
## 
## [[1]]$EstimateCoefficients
##                Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) 213.8323077 4.23984937 50.433940 6.486283e-72
## x             0.1759787 0.09723658  1.809799 7.339207e-02
## 
## [[1]]$Correlation
## [1] 0.1798368
## 
## [[1]]$DeterminationCoefficient
## [1] 0.03234126
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value  Pr(>F)  
## x          1   1653 1652.91  3.2754 0.07339 .
## Residuals 98  49456  504.65                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 3

## [[1]]
## [[1]]$X
##   [1] 71 24 22 68 22 20 67 68 18 17 23 23 21 16 23 22 24 23 67 20 19 21 73 21 19
##  [26] 20 22 20 22 74 19 73 20 20 16 21 16 21 22 67 17 22 22 19 20 73 21 20 19 23
##  [51] 24 69 74 25 19 21 23 23 71 71 73 69 19 67 20 20 21 67 67 21 67 21 67 75 75
##  [76] 20 21 65 71 73 24 22 66 22 67 21 20 67 24 19 22 68 67 21 22 22 20 71 73 20
## 
## [[1]]$XLabel
## [1] "Pressure"
## 
## [[1]]$Y
##   [1] 5.35665 2.19600 0.61320 2.87470 1.63930 1.67320 4.51030 3.60340 0.30420
##  [10] 1.09755 0.82025 0.64735 0.54990 1.63850 2.47845 0.79060 1.57080 0.43700
##  [19] 2.41345 1.63200 1.79305 1.65135 5.43000 0.55800 1.78825 1.41680 1.87250
##  [28] 0.47000 0.77380 4.41440 0.64200 4.62825 0.35000 0.53100 0.23870 2.04375
##  [37] 1.77500 1.79070 0.91960 2.45590 1.97780 1.64050 1.64710 0.53110 0.63190
##  [46] 2.67415 2.11470 1.29560 1.66605 2.39120 1.59120 5.60625 3.63120 0.53625
##  [55] 0.49385 0.83190 1.09375 1.71010 3.11125 5.34970 2.76615 2.33700 0.55675
##  [64] 4.40130 0.40180 0.58220 1.30800 2.98775 5.48390 1.42140 3.38910 1.40625
##  [73] 3.66600 4.57500 3.66795 0.44880 0.49995 2.67080 3.52755 4.02990 0.78720
##  [82] 0.64640 3.56040 0.47380 4.52075 0.39750 0.71780 3.74650 0.69930 0.63130
##  [91] 0.97750 2.61240 3.30095 0.76140 1.79140 0.69680 1.40060 2.42060 3.58810
## [100] 0.75480
## 
## [[1]]$YLabel
## [1] "ExtrusionVelocity"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Coefficients:
##       x  
## 0.05351  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3783 -0.5676 -0.2645  0.5619  1.9143 
## 
## Coefficients:
##   Estimate Std. Error t value Pr(>|t|)    
## x 0.053506   0.001706   31.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7438 on 99 degrees of freedom
## Multiple R-squared:  0.9086, Adjusted R-squared:  0.9077 
## F-statistic: 983.9 on 1 and 99 DF,  p-value: < 2.2e-16
## 
## 
## [[1]]$EstimateCoefficients
##     Estimate  Std. Error  t value     Pr(>|t|)
## x 0.05350592 0.001705784 31.36735 3.126218e-53
## 
## [[1]]$Correlation
## [1] 0.8589815
## 
## [[1]]$DeterminationCoefficient
## [1] 0.9085797
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x          1 544.31  544.31  983.91 < 2.2e-16 ***
## Residuals 99  54.77    0.55                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 4

## [[1]]
## [[1]]$X
##   [1] 71 24 22 68 22 20 67 68 18 17 23 23 21 16 23 22 24 23 67 20 19 21 73 21 19
##  [26] 20 22 20 22 74 19 73 20 20 16 21 16 21 22 67 17 22 22 19 20 73 21 20 19 23
##  [51] 24 69 74 25 19 21 23 23 71 71 73 69 19 67 20 20 21 67 67 21 67 21 67 75 75
##  [76] 20 21 65 71 73 24 22 66 22 67 21 20 67 24 19 22 68 67 21 22 22 20 71 73 20
## 
## [[1]]$XLabel
## [1] "Pressure"
## 
## [[1]]$Y
##   [1] 125  45 110  77  56  54 110 104 111  62  79  50  85 109  74  52  89 101
##  [19]  84  67  63  74  80  87  58  74  50  85 107  59 100  62  91  66  73 110
##  [37]  89  76  99 113  57 105  54  92  83 116  72  78  67  86  52  49  54  60
##  [55]  98  73  78 124  75 107  92  65  56 122  94  74 103  46 100  67  70  81
##  [73] 107 114  76  84  84 125 111  72 120 104  91  49 113 114 101 111 119 102
##  [91]  63 105 119 105  92  64  97  82 123  72
## 
## [[1]]$YLabel
## [1] "CoolerTemperature"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##     77.4452       0.2121  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -45.658 -17.658   0.433  18.835  41.676 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 77.44518    4.13706  18.720   <2e-16 ***
## x            0.21214    0.09488   2.236   0.0276 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 21.92 on 98 degrees of freedom
## Multiple R-squared:  0.04854,    Adjusted R-squared:  0.03883 
## F-statistic: 4.999 on 1 and 98 DF,  p-value: 0.02763
## 
## 
## [[1]]$EstimateCoefficients
##               Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) 77.4451819 4.13706097 18.719855 3.930586e-34
## x            0.2121368 0.09487923  2.235861 2.762950e-02
## 
## [[1]]$Correlation
## [1] 0.2203069
## 
## [[1]]$DeterminationCoefficient
## [1] 0.04853514
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value  Pr(>F)  
## x          1   2402 2401.94  4.9991 0.02763 *
## Residuals 98  47087  480.48                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 5

## [[1]]
## [[1]]$X
##   [1] 71 24 22 68 22 20 67 68 18 17 23 23 21 16 23 22 24 23 67 20 19 21 73 21 19
##  [26] 20 22 20 22 74 19 73 20 20 16 21 16 21 22 67 17 22 22 19 20 73 21 20 19 23
##  [51] 24 69 74 25 19 21 23 23 71 71 73 69 19 67 20 20 21 67 67 21 67 21 67 75 75
##  [76] 20 21 65 71 73 24 22 66 22 67 21 20 67 24 19 22 68 67 21 22 22 20 71 73 20
## 
## [[1]]$XLabel
## [1] "Pressure"
## 
## [[1]]$Y
##   [1] 29.32304 40.99191 45.87761 15.71330 39.83868 42.00513 21.76614 34.90026
##   [9] 49.97632 32.85096 60.02558 35.15783 56.51168 39.64570 36.65512 49.09259
##  [17] 26.44861 59.94457 26.15434 27.91344 23.94013 46.53838 46.84046 52.78790
##  [25] 45.52684 40.67353 56.22552 35.06948 20.02194 41.28101 43.09747 36.00788
##  [33] 51.81429 43.56376 68.44437 31.94832 49.12143 34.29501 60.11521 65.15244
##  [41] 28.48329 35.58565 35.55663 41.51600 38.85076 68.07452 49.06527 52.12547
##  [49] 33.98180 40.98185 28.59500 32.56293 55.37170 41.21173 68.12488 23.42013
##  [57] 45.61783 37.89023 36.38409 43.94748 41.78477 43.50728 40.84012 46.52753
##  [65] 60.22892 47.93798 46.01500 16.57245 25.44702 48.24823 43.50871 25.09920
##  [73] 43.03068 39.50498 47.35085 57.08497 33.09095 33.69824 35.11669 57.36873
##  [81] 44.58517 38.53610 18.82613 51.61156 26.45527 34.58269 50.16591 54.46714
##  [89] 48.46619 32.46905 72.45548 46.97908 40.92331 70.81549 25.11976 44.18690
##  [97] 61.57475 29.36324 54.13783 50.42630
## 
## [[1]]$YLabel
## [1] "ErrorPercentage"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##    45.31402     -0.08185  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.0348  -8.7087   0.1083   6.8697  28.9422 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 45.31402    2.34575  19.317   <2e-16 ***
## x           -0.08185    0.05380  -1.521    0.131    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.43 on 98 degrees of freedom
## Multiple R-squared:  0.02308,    Adjusted R-squared:  0.01311 
## F-statistic: 2.315 on 1 and 98 DF,  p-value: 0.1314
## 
## 
## [[1]]$EstimateCoefficients
##                Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) 45.31402257 2.34575340 19.317471 3.462074e-35
## x           -0.08185131 0.05379744 -1.521472 1.313615e-01
## 
## [[1]]$Correlation
## [1] -0.1519083
## 
## [[1]]$DeterminationCoefficient
## [1] 0.02307612
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df  Sum Sq Mean Sq F value Pr(>F)
## x          1   357.6  357.59  2.3149 0.1314
## Residuals 98 15138.4  154.47

Caso 6

## [[1]]
## [[1]]$X
##   [1] 228 230 219 223 246 253 233 198 203 230 195 246 182 186 234 193 226 243
##  [19] 256 241 225 188 251 233 200 233 187 235 242 250 227 221 183 237 194 227
##  [37] 242 242 205 185 232 220 228 236 216 233 191 243 211 221 217 254 221 212
##  [55] 195 221 192 245 237 229 212 223 194 227 239 176 204 239 230 221 184 243
##  [73] 245 205 210 199 241 246 219 225 227 236 225 215 217 231 205 243 235 225
##  [91] 232 226 253 167 227 241 185 254 233 181
## 
## [[1]]$XLabel
## [1] "PlasticPumpTemperature"
## 
## [[1]]$Y
##   [1] 197 204 231 206 238 204 248 242 220 197 209 211 233 219 206 195 244 254
##  [19] 210 202 243 221 261 203 227 226 243 206 204 187 218 186 192 230 194 203
##  [37] 245 254 201 245 204 254 207 200 222 244 214 256 192 197 195 245 263 211
##  [55] 199 206 197 254 198 260 189 243 226 248 243 213 211 203 204 247 244 201
##  [73] 246 191 198 189 208 194 208 264 216 198 247 212 200 200 217 239 260 208
##  [91] 241 195 251 200 239 240 200 258 248 218
## 
## [[1]]$YLabel
## [1] "ScrewTemperature"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##    164.6542       0.2512  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -40.460 -19.018  -4.773  21.064  42.826 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 164.6542    23.5255   6.999 3.23e-10 ***
## x             0.2512     0.1057   2.378   0.0194 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.21 on 98 degrees of freedom
## Multiple R-squared:  0.05454,    Adjusted R-squared:  0.04489 
## F-statistic: 5.653 on 1 and 98 DF,  p-value: 0.01936
## 
## 
## [[1]]$EstimateCoefficients
##                Estimate Std. Error  t value     Pr(>|t|)
## (Intercept) 164.6542388 23.5255226 6.998962 3.229647e-10
## x             0.2512215  0.1056595 2.377651 1.936399e-02
## 
## [[1]]$Correlation
## [1] 0.2335375
## 
## [[1]]$DeterminationCoefficient
## [1] 0.05453979
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value  Pr(>F)  
## x          1   2787 2787.44  5.6532 0.01936 *
## Residuals 98  48321  493.07                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 7

## [[1]]
## [[1]]$X
##   [1] 228 230 219 223 246 253 233 198 203 230 195 246 182 186 234 193 226 243
##  [19] 256 241 225 188 251 233 200 233 187 235 242 250 227 221 183 237 194 227
##  [37] 242 242 205 185 232 220 228 236 216 233 191 243 211 221 217 254 221 212
##  [55] 195 221 192 245 237 229 212 223 194 227 239 176 204 239 230 221 184 243
##  [73] 245 205 210 199 241 246 219 225 227 236 225 215 217 231 205 243 235 225
##  [91] 232 226 253 167 227 241 185 254 233 181
## 
## [[1]]$XLabel
## [1] "PlasticPumpTemperature"
## 
## [[1]]$Y
##   [1] 5.35665 2.19600 0.61320 2.87470 1.63930 1.67320 4.51030 3.60340 0.30420
##  [10] 1.09755 0.82025 0.64735 0.54990 1.63850 2.47845 0.79060 1.57080 0.43700
##  [19] 2.41345 1.63200 1.79305 1.65135 5.43000 0.55800 1.78825 1.41680 1.87250
##  [28] 0.47000 0.77380 4.41440 0.64200 4.62825 0.35000 0.53100 0.23870 2.04375
##  [37] 1.77500 1.79070 0.91960 2.45590 1.97780 1.64050 1.64710 0.53110 0.63190
##  [46] 2.67415 2.11470 1.29560 1.66605 2.39120 1.59120 5.60625 3.63120 0.53625
##  [55] 0.49385 0.83190 1.09375 1.71010 3.11125 5.34970 2.76615 2.33700 0.55675
##  [64] 4.40130 0.40180 0.58220 1.30800 2.98775 5.48390 1.42140 3.38910 1.40625
##  [73] 3.66600 4.57500 3.66795 0.44880 0.49995 2.67080 3.52755 4.02990 0.78720
##  [82] 0.64640 3.56040 0.47380 4.52075 0.39750 0.71780 3.74650 0.69930 0.63130
##  [91] 0.97750 2.61240 3.30095 0.76140 1.79140 0.69680 1.40060 2.42060 3.58810
## [100] 0.75480
## 
## [[1]]$YLabel
## [1] "ExtrusionVelocity"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Coefficients:
##        x  
## 0.008987  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7468 -1.2032 -0.3919  0.8452  3.4170 
## 
## Coefficients:
##    Estimate Std. Error t value Pr(>|t|)    
## x 0.0089866  0.0006363   14.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.417 on 99 degrees of freedom
## Multiple R-squared:  0.6683, Adjusted R-squared:  0.665 
## F-statistic: 199.5 on 1 and 99 DF,  p-value: < 2.2e-16
## 
## 
## [[1]]$EstimateCoefficients
##      Estimate   Std. Error  t value     Pr(>|t|)
## x 0.008986646 0.0006363013 14.12326 1.840984e-25
## 
## [[1]]$Correlation
## [1] 0.2525035
## 
## [[1]]$DeterminationCoefficient
## [1] 0.6683043
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x          1 400.37  400.37  199.47 < 2.2e-16 ***
## Residuals 99 198.71    2.01                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 8

## [[1]]
## [[1]]$X
##   [1] 228 230 219 223 246 253 233 198 203 230 195 246 182 186 234 193 226 243
##  [19] 256 241 225 188 251 233 200 233 187 235 242 250 227 221 183 237 194 227
##  [37] 242 242 205 185 232 220 228 236 216 233 191 243 211 221 217 254 221 212
##  [55] 195 221 192 245 237 229 212 223 194 227 239 176 204 239 230 221 184 243
##  [73] 245 205 210 199 241 246 219 225 227 236 225 215 217 231 205 243 235 225
##  [91] 232 226 253 167 227 241 185 254 233 181
## 
## [[1]]$XLabel
## [1] "PlasticPumpTemperature"
## 
## [[1]]$Y
##   [1] 29.32304 40.99191 45.87761 15.71330 39.83868 42.00513 21.76614 34.90026
##   [9] 49.97632 32.85096 60.02558 35.15783 56.51168 39.64570 36.65512 49.09259
##  [17] 26.44861 59.94457 26.15434 27.91344 23.94013 46.53838 46.84046 52.78790
##  [25] 45.52684 40.67353 56.22552 35.06948 20.02194 41.28101 43.09747 36.00788
##  [33] 51.81429 43.56376 68.44437 31.94832 49.12143 34.29501 60.11521 65.15244
##  [41] 28.48329 35.58565 35.55663 41.51600 38.85076 68.07452 49.06527 52.12547
##  [49] 33.98180 40.98185 28.59500 32.56293 55.37170 41.21173 68.12488 23.42013
##  [57] 45.61783 37.89023 36.38409 43.94748 41.78477 43.50728 40.84012 46.52753
##  [65] 60.22892 47.93798 46.01500 16.57245 25.44702 48.24823 43.50871 25.09920
##  [73] 43.03068 39.50498 47.35085 57.08497 33.09095 33.69824 35.11669 57.36873
##  [81] 44.58517 38.53610 18.82613 51.61156 26.45527 34.58269 50.16591 54.46714
##  [89] 48.46619 32.46905 72.45548 46.97908 40.92331 70.81549 25.11976 44.18690
##  [97] 61.57475 29.36324 54.13783 50.42630
## 
## [[1]]$YLabel
## [1] "ErrorPercentage"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##     97.4946      -0.2491  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -26.240  -7.414  -0.764   6.471  32.744 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 97.49464   12.08736   8.066 1.84e-12 ***
## x           -0.24906    0.05429  -4.588 1.33e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.41 on 98 degrees of freedom
## Multiple R-squared:  0.1768, Adjusted R-squared:  0.1684 
## F-statistic: 21.05 on 1 and 98 DF,  p-value: 1.327e-05
## 
## 
## [[1]]$EstimateCoefficients
##               Estimate  Std. Error   t value     Pr(>|t|)
## (Intercept) 97.4946380 12.08736334  8.065832 1.835628e-12
## x           -0.2490638  0.05428765 -4.587854 1.326726e-05
## 
## [[1]]$Correlation
## [1] -0.4204824
## 
## [[1]]$DeterminationCoefficient
## [1] 0.1768054
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df  Sum Sq Mean Sq F value    Pr(>F)    
## x          1  2739.8 2739.77  21.048 1.327e-05 ***
## Residuals 98 12756.2  130.17                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 9

## [[1]]
## [[1]]$X
##   [1] 71 24 22 68 22 20 67 68 18 17 23 23 21 16 23 22 24 23 67 20 19 21 73 21 19
##  [26] 20 22 20 22 74 19 73 20 20 16 21 16 21 22 67 17 22 22 19 20 73 21 20 19 23
##  [51] 24 69 74 25 19 21 23 23 71 71 73 69 19 67 20 20 21 67 67 21 67 21 67 75 75
##  [76] 20 21 65 71 73 24 22 66 22 67 21 20 67 24 19 22 68 67 21 22 22 20 71 73 20
## 
## [[1]]$XLabel
## [1] "Pressure"
## 
## [[1]]$Y
##   [1] 5.35665 2.19600 0.61320 2.87470 1.63930 1.67320 4.51030 3.60340 0.30420
##  [10] 1.09755 0.82025 0.64735 0.54990 1.63850 2.47845 0.79060 1.57080 0.43700
##  [19] 2.41345 1.63200 1.79305 1.65135 5.43000 0.55800 1.78825 1.41680 1.87250
##  [28] 0.47000 0.77380 4.41440 0.64200 4.62825 0.35000 0.53100 0.23870 2.04375
##  [37] 1.77500 1.79070 0.91960 2.45590 1.97780 1.64050 1.64710 0.53110 0.63190
##  [46] 2.67415 2.11470 1.29560 1.66605 2.39120 1.59120 5.60625 3.63120 0.53625
##  [55] 0.49385 0.83190 1.09375 1.71010 3.11125 5.34970 2.76615 2.33700 0.55675
##  [64] 4.40130 0.40180 0.58220 1.30800 2.98775 5.48390 1.42140 3.38910 1.40625
##  [73] 3.66600 4.57500 3.66795 0.44880 0.49995 2.67080 3.52755 4.02990 0.78720
##  [82] 0.64640 3.56040 0.47380 4.52075 0.39750 0.71780 3.74650 0.69930 0.63130
##  [91] 0.97750 2.61240 3.30095 0.76140 1.79140 0.69680 1.40060 2.42060 3.58810
## [100] 0.75480
## 
## [[1]]$YLabel
## [1] "ExtrusionVelocity"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Coefficients:
##       x  
## 0.05351  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3783 -0.5676 -0.2645  0.5619  1.9143 
## 
## Coefficients:
##   Estimate Std. Error t value Pr(>|t|)    
## x 0.053506   0.001706   31.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7438 on 99 degrees of freedom
## Multiple R-squared:  0.9086, Adjusted R-squared:  0.9077 
## F-statistic: 983.9 on 1 and 99 DF,  p-value: < 2.2e-16
## 
## 
## [[1]]$EstimateCoefficients
##     Estimate  Std. Error  t value     Pr(>|t|)
## x 0.05350592 0.001705784 31.36735 3.126218e-53
## 
## [[1]]$Correlation
## [1] 0.8589815
## 
## [[1]]$DeterminationCoefficient
## [1] 0.9085797
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x          1 544.31  544.31  983.91 < 2.2e-16 ***
## Residuals 99  54.77    0.55                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 10

## [[1]]
## [[1]]$X
##   [1] 197 204 231 206 238 204 248 242 220 197 209 211 233 219 206 195 244 254
##  [19] 210 202 243 221 261 203 227 226 243 206 204 187 218 186 192 230 194 203
##  [37] 245 254 201 245 204 254 207 200 222 244 214 256 192 197 195 245 263 211
##  [55] 199 206 197 254 198 260 189 243 226 248 243 213 211 203 204 247 244 201
##  [73] 246 191 198 189 208 194 208 264 216 198 247 212 200 200 217 239 260 208
##  [91] 241 195 251 200 239 240 200 258 248 218
## 
## [[1]]$XLabel
## [1] "ScrewTemperature"
## 
## [[1]]$Y
##   [1] 5.35665 2.19600 0.61320 2.87470 1.63930 1.67320 4.51030 3.60340 0.30420
##  [10] 1.09755 0.82025 0.64735 0.54990 1.63850 2.47845 0.79060 1.57080 0.43700
##  [19] 2.41345 1.63200 1.79305 1.65135 5.43000 0.55800 1.78825 1.41680 1.87250
##  [28] 0.47000 0.77380 4.41440 0.64200 4.62825 0.35000 0.53100 0.23870 2.04375
##  [37] 1.77500 1.79070 0.91960 2.45590 1.97780 1.64050 1.64710 0.53110 0.63190
##  [46] 2.67415 2.11470 1.29560 1.66605 2.39120 1.59120 5.60625 3.63120 0.53625
##  [55] 0.49385 0.83190 1.09375 1.71010 3.11125 5.34970 2.76615 2.33700 0.55675
##  [64] 4.40130 0.40180 0.58220 1.30800 2.98775 5.48390 1.42140 3.38910 1.40625
##  [73] 3.66600 4.57500 3.66795 0.44880 0.49995 2.67080 3.52755 4.02990 0.78720
##  [82] 0.64640 3.56040 0.47380 4.52075 0.39750 0.71780 3.74650 0.69930 0.63130
##  [91] 0.97750 2.61240 3.30095 0.76140 1.79140 0.69680 1.40060 2.42060 3.58810
## [100] 0.75480
## 
## [[1]]$YLabel
## [1] "ExtrusionVelocity"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Coefficients:
##        x  
## 0.009003  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8498 -1.2373 -0.3974  1.0253  3.6472 
## 
## Coefficients:
##    Estimate Std. Error t value Pr(>|t|)    
## x 0.0090032  0.0006439   13.98   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.426 on 99 degrees of freedom
## Multiple R-squared:  0.6638, Adjusted R-squared:  0.6604 
## F-statistic: 195.5 on 1 and 99 DF,  p-value: < 2.2e-16
## 
## 
## [[1]]$EstimateCoefficients
##      Estimate   Std. Error  t value     Pr(>|t|)
## x 0.009003241 0.0006439353 13.98159 3.590639e-25
## 
## [[1]]$Correlation
## [1] 0.1980713
## 
## [[1]]$DeterminationCoefficient
## [1] 0.6638198
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x          1 397.68  397.68  195.48 < 2.2e-16 ***
## Residuals 99 201.40    2.03                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Caso 11

## [[1]]
## [[1]]$X
##   [1] 197 204 231 206 238 204 248 242 220 197 209 211 233 219 206 195 244 254
##  [19] 210 202 243 221 261 203 227 226 243 206 204 187 218 186 192 230 194 203
##  [37] 245 254 201 245 204 254 207 200 222 244 214 256 192 197 195 245 263 211
##  [55] 199 206 197 254 198 260 189 243 226 248 243 213 211 203 204 247 244 201
##  [73] 246 191 198 189 208 194 208 264 216 198 247 212 200 200 217 239 260 208
##  [91] 241 195 251 200 239 240 200 258 248 218
## 
## [[1]]$XLabel
## [1] "ScrewTemperature"
## 
## [[1]]$Y
##   [1] 29.32304 40.99191 45.87761 15.71330 39.83868 42.00513 21.76614 34.90026
##   [9] 49.97632 32.85096 60.02558 35.15783 56.51168 39.64570 36.65512 49.09259
##  [17] 26.44861 59.94457 26.15434 27.91344 23.94013 46.53838 46.84046 52.78790
##  [25] 45.52684 40.67353 56.22552 35.06948 20.02194 41.28101 43.09747 36.00788
##  [33] 51.81429 43.56376 68.44437 31.94832 49.12143 34.29501 60.11521 65.15244
##  [41] 28.48329 35.58565 35.55663 41.51600 38.85076 68.07452 49.06527 52.12547
##  [49] 33.98180 40.98185 28.59500 32.56293 55.37170 41.21173 68.12488 23.42013
##  [57] 45.61783 37.89023 36.38409 43.94748 41.78477 43.50728 40.84012 46.52753
##  [65] 60.22892 47.93798 46.01500 16.57245 25.44702 48.24823 43.50871 25.09920
##  [73] 43.03068 39.50498 47.35085 57.08497 33.09095 33.69824 35.11669 57.36873
##  [81] 44.58517 38.53610 18.82613 51.61156 26.45527 34.58269 50.16591 54.46714
##  [89] 48.46619 32.46905 72.45548 46.97908 40.92331 70.81549 25.11976 44.18690
##  [97] 61.57475 29.36324 54.13783 50.42630
## 
## [[1]]$YLabel
## [1] "ErrorPercentage"
## 
## [[1]]$LinearRegresion
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Coefficients:
##      x  
## 0.1908  
## 
## 
## [[1]]$LinearRegresionStatus
## 
## Call:
## lm(formula = y ~ x - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.296  -6.825  -0.550   8.013  32.660 
## 
## Coefficients:
##   Estimate Std. Error t value Pr(>|t|)    
## x 0.190778   0.005695    33.5   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.61 on 99 degrees of freedom
## Multiple R-squared:  0.9189, Adjusted R-squared:  0.9181 
## F-statistic:  1122 on 1 and 99 DF,  p-value: < 2.2e-16
## 
## 
## [[1]]$EstimateCoefficients
##    Estimate  Std. Error  t value     Pr(>|t|)
## x 0.1907779 0.005695158 33.49826 8.131611e-56
## 
## [[1]]$Correlation
## [1] 0.1498213
## 
## [[1]]$DeterminationCoefficient
## [1] 0.9189278
## 
## [[1]]$Evaluation
## Analysis of Variance Table
## 
## Response: y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## x          1 178563  178563  1122.1 < 2.2e-16 ***
## Residuals 99  15754     159                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Series de tiempo

Producto A

Producto B

Producto C

Suavizado para cada producto

Producto A (suavizado)

Producto B (Suavizado)

Producto C (suavizado)

Pronostico para cada producto

Producto A (Pronostico)

	Point Forecast	Lo 0.95	Hi 0.95
Jan 2022	102400.0	-55593.92	260393.9
Feb 2022	132766.7	-33773.55	299306.9
Mar 2022	125622.2	-55116.33	306360.8

Producto B (Pronostico)

	Point Forecast	Lo 0.95	Hi 0.95
Jan 2022	14533.33	10276.162	18790.50
Feb 2022	14811.11	10323.659	19298.56
Mar 2022	14448.15	9578.119	19318.18

Producto C (Pronostico)

	Point Forecast	Lo 0.95	Hi 0.95
Jan 2022	59850.00	28253.95	91446.05
Feb 2022	56933.33	23628.17	90238.50
Mar 2022	56544.44	20399.86	92689.03

Arima & Modelo de prediccion

X izquierda representa $pred, X derecha representa $se

Producto A

## $pred
##            Jan       Feb       Mar       Apr       May
## 2022 111055.35  56498.48  63292.28  89502.85  89502.85
## 
## $se
##           Jan      Feb      Mar      Apr      May
## 2022 53215.16 53948.30 55221.08 61796.99 61796.99

x
111055.35
56498.48
63292.28
89502.85
89502.85

x
53215.16
53948.30
55221.08
61796.99
61796.99

Producto B

## $pred
##            Jan       Feb       Mar       Apr       May
## 2022 12190.243  9177.619  6823.038  6283.275  6283.275
## 
## $se
##           Jan      Feb      Mar      Apr      May
## 2022 1967.729 2523.858 3287.772 3430.701 3430.701

x
12190.243
9177.619
6823.038
6283.275
6283.275

x
1967.729
2523.858
3287.772
3430.701
3430.701

Producto C

## $pred
##           Jan      Feb      Mar      Apr      May
## 2022 72230.40 69318.39 68923.80 74039.03 74039.03
## 
## $se
##           Jan      Feb      Mar      Apr      May
## 2022 10255.51 10782.88 11988.46 14339.70 14339.70

x
72230.40
69318.39
68923.80
74039.03
74039.03

x
10255.51
10782.88
11988.46
14339.70
14339.70

Autoarima

Producto A (Arima)

## 
##  ARIMA(2,0,2)            with non-zero mean : Inf
##  ARIMA(0,0,0)            with non-zero mean : 601.1741
##  ARIMA(1,0,0)            with non-zero mean : 603.5883
##  ARIMA(0,0,1)            with non-zero mean : 603.5594
##  ARIMA(0,0,0)            with zero mean     : 627.1432
##  ARIMA(1,0,1)            with non-zero mean : 606.4575
## 
##  Best model: ARIMA(0,0,0)            with non-zero mean

## Series: productA.ts 
## ARIMA(0,0,0) with non-zero mean 
## 
## Coefficients:
##           mean
##       90933.33
## s.e.  12348.23
## 
## sigma^2 = 3.819e+09:  log likelihood = -298.3
## AIC=600.6   AICc=601.17   BIC=602.96

## $pred
##           Jan      Feb      Mar      Apr      May
## 2022 90933.33 90933.33 90933.33 90933.33 90933.33
## 
## $se
##          Jan     Feb     Mar     Apr     May
## 2022 60493.1 60493.1 60493.1 60493.1 60493.1

Producto B (Arima)

## 
##  ARIMA(2,1,2)            with drift         : Inf
##  ARIMA(0,1,0)            with drift         : 419.1688
##  ARIMA(1,1,0)            with drift         : 410.2179
##  ARIMA(0,1,1)            with drift         : 414.171
##  ARIMA(0,1,0)                               : 418.5257
##  ARIMA(2,1,0)            with drift         : 413.127
##  ARIMA(1,1,1)            with drift         : 413.1542
##  ARIMA(2,1,1)            with drift         : 416.3143
##  ARIMA(1,1,0)                               : 414.5579
## 
##  Best model: ARIMA(1,1,0)            with drift

## Series: productB.ts 
## ARIMA(1,1,0) with drift 
## 
## Coefficients:
##           ar1     drift
##       -0.6355  596.2183
## s.e.   0.1581  197.8724
## 
## sigma^2 = 2546880:  log likelihood = -201.48
## AIC=408.95   AICc=410.22   BIC=412.36

## $pred
##           Jan      Feb      Mar      Apr      May
## 2022 14934.38 14474.87 14700.85 14589.72 14644.37
## 
## $se
##           Jan      Feb      Mar      Apr      May
## 2022 1784.994 2002.289 2408.677 2659.112 2930.216

Producto C (Arima)

## 
##  ARIMA(2,0,2)            with non-zero mean : Inf
##  ARIMA(0,0,0)            with non-zero mean : 532.2195
##  ARIMA(1,0,0)            with non-zero mean : 526.4324
##  ARIMA(0,0,1)            with non-zero mean : 529.174
##  ARIMA(0,0,0)            with zero mean     : 609.1537
##  ARIMA(2,0,0)            with non-zero mean : 529.2105
##  ARIMA(1,0,1)            with non-zero mean : 529.2842
##  ARIMA(2,0,1)            with non-zero mean : 532.1736
##  ARIMA(1,0,0)            with zero mean     : 532.4383
## 
##  Best model: ARIMA(1,0,0)            with non-zero mean

## Series: productC.ts 
## ARIMA(1,0,0) with non-zero mean 
## 
## Coefficients:
##          ar1       mean
##       0.5562  72910.486
## s.e.  0.1711   5264.889
## 
## sigma^2 = 156472987:  log likelihood = -259.62
## AIC=525.23   AICc=526.43   BIC=528.77

## $pred
##           Jan      Feb      Mar      Apr      May
## 2022 61751.86 66703.51 69457.86 70989.97 71842.20
## 
## $se
##           Jan      Feb      Mar      Apr      May
## 2022 11976.38 13704.52 14196.68 14345.54 14391.28

Forecast para cada producto

Producto A (Forecast)

## $pred
##           Jan      Feb      Mar      Apr      May
## 2022 90933.33 90933.33 90933.33 90933.33 90933.33
## 
## $se
##          Jan     Feb     Mar     Apr     May
## 2022 60493.1 60493.1 60493.1 60493.1 60493.1

Producto B (Forecast)

## $pred
##           Jan      Feb      Mar      Apr      May
## 2022 14934.38 14474.87 14700.85 14589.72 14644.37
## 
## $se
##           Jan      Feb      Mar      Apr      May
## 2022 1784.994 2002.289 2408.677 2659.112 2930.216

Producto C (Forecast)

## $pred
##           Jan      Feb      Mar      Apr      May
## 2022 61751.86 66703.51 69457.86 70989.97 71842.20
## 
## $se
##           Jan      Feb      Mar      Apr      May
## 2022 11976.38 13704.52 14196.68 14345.54 14391.28

Pressure	PlasticPumpTemperature	PlasticMixerTemperature	ScrewTemperature	ScrewRPM	BarrelTemperature
71	228	208	197	115	180
24	230	194	204	117	120
22	219	238	231	84	143
68	223	250	206	83	175
22	246	252	238	116	121

Pressure	PlasticPumpTemperature	PlasticMixerTemperature	ScrewTemperature	ScrewRPM	BarrelTemperature
71	228	208	197	115	180
24	230	194	204	117	120
22	219	238	231	84	143
68	223	250	206	83	175
22	246	252	238	116	121

PROBLEMA AUTOMOTRIZ

Análisis estadístico

23/5/2022

Integrantes:

Introducción:

Librerias a utilizar

Tablas de análisis

TABLA DE HISTÓRICO DE DEFECTOS:

TABLA DE DATOS DE MUESTREO:

Análisis de los datos

Graficación de pérdidas

Pérdidas de la Tabla 1:

Pérdidas Tabla 2:

Data summary

Data summary Tabla 1:

Data summary Tabla 2:

Análisis de correlación de la Extrusión contra la Velocidad

Gráficas de pares para las piezas defectuosas

Gráficas de pares (A)

Gráfica de pares (B)

Histogramas múltiples de cada pieza defectuosa

Piezas defectuosas A

Piezas defectuosas B

Piezas defectuosas C

Análisis de correlación para piezas defectuosas

Datos limpios

Gráfica de pares en los datos de piezas

Gráfica de pares (A)

Gráfica de pares (B)

Histograma múltiple (PORCENTAJE)

Algoritmo para análisis de regresión

Casos a realizar la regresión

Análisis a fondo de cada caso

Caso 1

Caso2

Caso 3

Caso 4

Caso 5

Caso 6

Caso 7

Caso 8

Caso 9

Caso 10

Caso 11

Series de tiempo

Producto A

Producto B

Producto C

Suavizado para cada producto

Producto A (suavizado)

Producto B (Suavizado)

Producto C (suavizado)

Pronostico para cada producto

Producto A (Pronostico)

Producto B (Pronostico)

Producto C (Pronostico)

Arima & Modelo de prediccion

Producto A

Producto B

Producto C

Autoarima

Producto A (Arima)

Producto B (Arima)

Producto C (Arima)

Forecast para cada producto

Producto A (Forecast)

Producto B (Forecast)

Producto C (Forecast)

Pressure	PlasticPumpTemperature	PlasticMixerTemperature	ScrewTemperature	ScrewRPM	BarrelTemperature
71	228	208	197	115	180
24	230	194	204	117	120
22	219	238	231	84	143
68	223	250	206	83	175
22	246	252	238	116	121