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La información aquí contenida es solo para propósitos didácticos, se tomo como referencia la información de ayuda del paquete STATGRAPHICS Centurion, marca registrada de STAT POINT TECHNOLOGIES, Inc Curso de Statgraph ics para Lean Sigma

Curso Stat Graphics Lean Sigma

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Page 1: Curso Stat Graphics Lean Sigma

La información aquí contenida es solo para propósitos didácticos, se tomo como referencia la información de ayuda del paquete STATGRAPHICS Centurion, marca registrada de STAT POINT TECHNOLOGIES, Inc

Curso de Statgraphics para Lean Sigma

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Contenido

EJERCICIOS DE LA FASE DE MEDICIÓN Y CONTROL CON STATGRAPHICS..............................................................3

ENTRADA y FORMAR DOS COLUMNAS DE DATOS NUMÉRICOS Y UNA DE CARACTERES..................................3

1. DIAGRAMA DE PARETO................................................................................................................................. 4

2. DIAGRAMA DE ISHIKAWA..............................................................................................................................5

3. ESTADÍSTICA DESCRIPTIVA............................................................................................................................ 7

4. CARTAS DE CONTROL DE LECTURAS INDIVIDUALES Y RANGO MÓVIL.........................................................13

5. CARTAS DE CONTROL X-R DE MEDIAS RANGOS..........................................................................................16

6. CAPACIDAD DEL PROCESO...........................................................................................................................21

7. CARTAS DE CONTROL P............................................................................................................................... 23

8. CARTAS DE CONTROL np............................................................................................................................. 25

9. CARTAS DE CONTROL C............................................................................................................................... 27

10. CARTAS DE CONTROL u............................................................................................................................. 28

11. ESTUDIO R&R.............................................................................................................................................30

EJERCICIOS DE LA FASE DE ANÁLISIS................................................................................................................... 35

12. REGRESIÓN LINEAL.................................................................................................................................... 35

13. PRUEBA DE HIPÓTESIS DE UNA MEDIA......................................................................................................39

14. PRUEBA DE HIPÓTESIS DE UNA DESVIACIÓN ESTÁNDAR..........................................................................41

15. PRUEBA DE HIPÓTESIS DE UNA PROPORCIÓN (Binomial).........................................................................44

16. PRUEBA DE HIPÓTESIS DE DOS MEDIAS....................................................................................................46

17. PRUEBA DE HIPÓTESIS PAREADAS.............................................................................................................54

18. PRUEBA DE HIPÓTESIS DE DOS PROPORCIONES.......................................................................................61

19. ANOVA DE UNA VÍA...................................................................................................................................63

20. TABLA DE CONTINGENCIA......................................................................................................................... 71

21. CARTAS PARA NEGOCIOS DE BARRAS, DE PASTEL Y DE LÍNEA DE COMPONENTES...................................76

22. DISTRIBUCIONES DE PROBABILIDAD PARA VALORES CRÍTICOS Y NÚMEROS ALEATORIOS.......................79

23. CARTAS DE CONTROL PARA SU PROCESO Y GRAFICADO EN EXCEL...........................................................90

HERRAMIENTAS DE LA FASE DE MEJORA............................................................................................................96

DISEÑO DE EXPERIMENTOS CLASICO.............................................................................................................. 96

Diseño de experimentos de Taguchi............................................................................................................. 121

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EJERCICIOS DE LA FASE DE MEDICIÓN Y CONTROL CON STATGRAPHICS

ENTRADA y FORMAR DOS COLUMNAS DE DATOS NUMÉRICOS Y UNA DE CARACTERES

Colocarse en la columna Col_1 y con botón derecho del ratón, seleccionar la opción de MODIFY COLUMN para indicar si se quieren datos Numéricos o de Texto.

Paso 1 Paso 2 Paso 3

Paso 4 y 5, colocarse en columnas Col_2 y Col_3 y con botón derecho, sel. MODIFY COLUMN

NOTA: Es importante ir pasando los resultados al reporte con Copy Analysis to StatReporter e irlos borrando con clik en la X de la sección de gráficas y resultados, para liberar espacios

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1. DIAGRAMA DE PARETOPaso 1. Cargar datos en las columnas de Defectos y Cantidad. Obtener el Diagrama de Pareto

Paso 2. El reporte se muestra a continuación

Con Botón derecho

4

Defectos CantidadA 23B 12C 67D 98E 3F 120

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Paso 3. Obtener los datos numéricos:

Paso 4. Agregar al reporte, con el cursor en el análisis y botón derecho del ratón

Este reporte se puede abrir con una ceja en la parte inferior de la pantalla

2. DIAGRAMA DE ISHIKAWA

Paso 1. Preparar la columna de CAUSAS en Col_4 u otra libre con ancho de 13 caracteres

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Paso 2. Cargar los datos siguientes en la columna de causas:

a) Al inicio se pone el problema a atacar

b) Cada causa principal se pone normal

c) Cada una de las sub causas correspondientes a las causas principales se escriben debajo de la misma antecedidas de un punto.

d) Cada una de las sub causas correspondientes a las sub causas se escriben debajo de la misma antecedidas de dos puntos

CausasPROBLEMAPersonal.pb.pc..pd..pfMaterial.ma.mb.mc..md..mfAmbiente.aire.agua.tierra..t1..t2

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Paso 3. Ejecutar las siguientesinstrucciones

Paso 4. El diagrama obtenido es el siguiente:

3. ESTADÍSTICA DESCRIPTIVA

Paso 1. Preparar la columna de VISCOCIDAD en Col_1 u otra libre con ancho de 13 numeric

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Paso 2. Cargar datos en columna 1

Viscocidad6.00

5.985.976.016.156.005.976.025.966.005.985.996.016.035.985.986.015.995.995.986.015.995.985.996.005.986.025.996.015.985.995.975.996.015.976.025.996.026.00

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6.026.01

Paso 3. Instrucciones para la estadística descriptiva

Paso 4. Con el segundo ícono del análisis pedir las opciones siguientes:

Paso 5. Los resultados numéricos son los siguientes:

Summary Statistics for Viscocidad

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Paso 5. Obtener las gráficas de los datos con el tercer ícono del menú:

Las gráficas se amplían colocándoles el cursos y dando dos clicks

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CORRIDA EN EXCEL

Paso 1. Usar los datos de viscosidad

Paso 2. Instrucciones

HERRAMIENTAS > ANÁLISIS DE DATOS

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Indicar el rango donde están los datos, indicar que la primera celda el etiqueta, indicar la celda donde se muestran los resultados y resumen de estadística.

Paso 3. Resultados

Viscocidad   Mean 5.998536585Standard Error 0.00464024Median 5.99Mode 5.99Standard Deviation 0.029712033Sample Variance 0.000882805Kurtosis 16.67650192Skewness 3.36583295Range 0.19Minimum 5.96Maximum 6.15Sum 245.94Count 41Confidence Level(95.0%) 0.009378275

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4. CARTAS DE CONTROL DE LECTURAS INDIVIDUALES Y RANGO MÓVIL

Con los datos de viscosidad ejecutar las instrucciones siguientes:

Paso 1. Obtener la carta de control I-MR

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X and MR(2) - Initial Study for Viscocidad

Number of observations = 410 observations excluded

X Chart-------UCL: +3.0 sigma = 6.07899Centerline = 5.99854LCL: -3.0 sigma = 5.91808

1 beyond limits

MR(2) Chart-----------UCL: +3.0 sigma = 0.0988757Centerline = 0.03025LCL: -3.0 sigma = 0.0

2 beyond limits

Estimates---------Process mean = 5.99854Process sigma = 0.0268174Mean MR(2) = 0.03025

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Paso 2. Obtener la carta de Rango móvil MR

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Paso 3. Excluir el punto fuera de control

Colocarse en la gráfica X y con botón derecho seleccionar ANALYSIS OPTIONS y en EXCLUDE Manual, Exclude Subgroup 5 OK

5. CARTAS DE CONTROL X-R DE MEDIAS RANGOS

Con los datos de viscosidad ejecutar las instrucciones siguientes:

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Paso 1. Obtener la carta de control X

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Paso 2. Obtener la carta de control R

Paso 3. Excluir el punto fuera de control

Colocar el cursor en la gráfica, ANALYSIS OPTIONS y EXCLUDE subgroup 1

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CORRIDA EN EXCEL

Paso 1. Arreglo de datos

=Xmedia -+ 2.66*Rmedio

Viscocidad Media LIC LSC =3.267*Rmedio6.00 6.00 5.92 6.08 Rango Rmedio LICr LSCr5.98 6.00 5.92 6.08 0.02 0.03 0 0.0995.97 6.00 5.92 6.08 0.01 0.03 0 0.0996.01 6.00 5.92 6.08 0.04 0.03 0 0.0996.15 6.00 5.92 6.08 0.14 0.03 0 0.0996.00 6.00 5.92 6.08 0.15 0.03 0 0.0995.97 6.00 5.92 6.08 0.03 0.03 0 0.0996.02 6.00 5.92 6.08 0.05 0.03 0 0.0995.96 6.00 5.92 6.08 0.06 0.03 0 0.0996.00 6.00 5.92 6.08 0.04 0.03 0 0.0995.98 6.00 5.92 6.08 0.02 0.03 0 0.0995.99 6.00 5.92 6.08 0.01 0.03 0 0.0996.01 6.00 5.92 6.08 0.02 0.03 0 0.0996.03 6.00 5.92 6.08 0.02 0.03 0 0.0995.98 6.00 5.92 6.08 0.05 0.03 0 0.0995.98 6.00 5.92 6.08 0.00 0.03 0 0.0996.01 6.00 5.92 6.08 0.03 0.03 0 0.0995.99 6.00 5.92 6.08 0.02 0.03 0 0.0995.99 6.00 5.92 6.08 0.00 0.03 0 0.0995.98 6.00 5.92 6.08 0.01 0.03 0 0.0996.01 6.00 5.92 6.08 0.03 0.03 0 0.0995.99 6.00 5.92 6.08 0.02 0.03 0 0.0995.98 6.00 5.92 6.08 0.01 0.03 0 0.0995.99 6.00 5.92 6.08 0.01 0.03 0 0.0996.00 6.00 5.92 6.08 0.01 0.03 0 0.099

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5.98 6.00 5.92 6.08 0.02 0.03 0 0.0996.02 6.00 5.92 6.08 0.04 0.03 0 0.0995.99 6.00 5.92 6.08 0.03 0.03 0 0.0996.01 6.00 5.92 6.08 0.02 0.03 0 0.0995.98 6.00 5.92 6.08 0.03 0.03 0 0.0995.99 6.00 5.92 6.08 0.01 0.03 0 0.0995.97 6.00 5.92 6.08 0.02 0.03 0 0.0995.99 6.00 5.92 6.08 0.02 0.03 0 0.0996.01 6.00 5.92 6.08 0.02 0.03 0 0.0995.97 6.00 5.92 6.08 0.04 0.03 0 0.0996.02 6.00 5.92 6.08 0.05 0.03 0 0.0995.99 6.00 5.92 6.08 0.03 0.03 0 0.0996.02 6.00 5.92 6.08 0.03 0.03 0 0.0996.00 6.00 5.92 6.08 0.02 0.03 0 0.0996.02 6.00 5.92 6.08 0.02 0.03 0 0.0996.01 6.00 5.92 6.08 0.01 0.03 0 0.099

Promedio Rango Promedio

6.00 =PROMEDIO(B6:B46) =ABS(B44-B45) 0.03

Paso 2. Graficar área verde como carta I y área amarillo como rango móvil

INSERTAR GRAFICA DE LÍNEA

1 4 7 10 13 16 19 22 25 28 31 34 37 405.8

5.85

5.9

5.95

6

6.05

6.1

6.15

6.2

ViscocidadMediaLICLSC

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1 4 7 10 13 16 19 22 25 28 31 34 37 400

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

RangoRmedioLICrLSCr

6. CAPACIDAD DEL PROCESO

Paso 1. Con los datos anteriores, determinar la capacidad del proceso, considerando que los límites de especificación son LIE = 5.98 y LSE = 6.06:

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Paso 2. Los resultados son los siguientes:

Analysis Summary

Data variable: Viscocidad

Distribution: Normal sample size = 41 mean = 5.99854 standard deviation = 0.029712

6.0 Sigma Limits +3.0 sigma = 6.08767 mean = 5.99854 -3.0 sigma = 5.9094

Observed EstimatedSpecifications Beyond Spec. Z-Score Beyond Spec.------------------------------------------------------------USL = 6.06 2.4390% 2.07 1.9290%LSL = 5.98 12.1951% -0.62 26.6354%------------------------------------------------------------Total 14.6341% 28.5644%

Aquí el Ppk y el Pp corresponden al Cp y Cpk

CÁLCULO EN EXCELZi, Zs, P(Zi), P(Zs), Pz(Total), Cp y Cpk

Zs = (LSE-Xm)/Sigma = (6.06 – 5.99) / 0.02971 = 2.07

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P(Zs) = DISTR.NORM.ESTAND.INV(-2.07) = 1.92%

Zi = (5.98 – 5998) / 0.02971 = -0.62

P(Zi) = DISTR.NORM.ESTAND.INV(-0.62) = 26.63%

P(Z total) = 28.564%

Cp = (LSE – LIE) / (6*Sigma) = (6.06 – 5.98) / (6*0.0297) = 0.45

Ppk = menor de las Zi y Zs sin signo / 3 = 0.062 / 3 = 0.21

7. CARTAS DE CONTROL P

Preparar las columnas de Serv_No_Confiables y Muestra (colocarse en las columnas vacías y seleccionar MODIFY COLUMN).

Paso 1. Cargar los datos siguientes (Serv_No_Conf es la proporción de los servicios a las muestras):

Serv_no_conf Muestra0.20 980.17 1040.14 970.16 990.13 970.28 1020.20 1040.14 1010.11 550.13 480.14 500.13 530.16 560.10 490.14 560.17 530.17 520.20 510.17 520.21 47

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Paso 2. Obtener la carta de control p

p - Initial Study for Serv_No_Conf

Number of subgroups = 20Average subgroup size = 71.20 subgroups excluded

p Chart-------UCL: +3.0 sigma = 0.299274Centerline = 0.166749LCL: -3.0 sigma = 0.0342228

0 beyond limits

Estimates---------Mean p = 0.166749Sigma = 0.0441753

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8. CARTAS DE CONTROL np

Paso 1. Cargar los datos siguientes:

Prod_Defect

2018141613292114667795899

109

10

Paso 2. Obtener la carta de control np con un tamaño de muestra de n = 200

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Paso 3. Los resultados obtenidos son los siguientes:

np - Initial Study for Prod_Defectuosos

Number of subgroups = 20Subgroup size = 200.00 subgroups excluded

np Chart--------UCL: +3.0 sigma = 22.0757Centerline = 12.0LCL: -3.0 sigma = 1.92429

1 beyond limits

Estimates---------Mean np = 12.0Sigma = 3.35857

The StatAdvisor

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9. CARTAS DE CONTROL C

Paso 1. Con los siguientes datos:

Manchas8

13785

137

122710126

109

13785

Paso 2. Instrucciones

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Paso 3. La carta de control es:

10. CARTAS DE CONTROL u

Paso 1. Con los siguientes datos:

Errores Facturas9 110

11 1012 985 105

15 11013 1008 987 995 1002 1004 1024 982 995 1055 1042 1003 1032 1001 986 102

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Paso 2. Instrucciones

Paso 3. Carta de control u

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11. ESTUDIO R&R

Paso 1. Cargar las columnas de datos:Parte Operador Medición Intento

1 1 157.5 11 1 150 22 1 180 12 1 172.5 23 1 150 13 1 157.5 2

Etcétera……

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Paso 2. Instrucciones

Paso 3. Resultados

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Considerar los límites de especificación: LSE = 487.5 LIE = 37.5 o tolerancia de 450 y 5.15 sigmas

Colocarse en los resultados y con botón derecho en ANALYSIS OPTIONS cargar esta información:

Paso 4. Solicitar los resultados:

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Paso 5. Pedir la gráfica R&R plot

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EJERCICIOS DE LA FASE DE ANÁLISIS

12. REGRESIÓN LINEAL

Paso 1. Cargar los datos siguientes en la hoja de trabajo del paquete:

Y_Resistencia X_%Fibra160 10171 15175 15182 20184 20181 20188 25193 25195 28200 30

Paso 2. Instrucciones

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Paso 3. Resultados

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Paso 4. Seleccionando el área de resultados y botón derecho en ANALYSIS OPTIONS, se puede acceder a otros modelos de regresión:

CÁLCULO EN EXCEL

Paso 1. Usar los datos anteriores

Paso 2. Instrucciones

HERRAMIENTAS > ANÁLISIS DE DATOS

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Indicar el Rango de entrada Y y X , de los datos incluyendo sus etiquetas de columna (seleccionar LABELS), indicar la celda donde se quiere el rango de salida y seleccionar residuos.

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Paso 3. Los resultados de salida son:

Regression StatisticsMultiple R 0.984962R Square 0.970149Adjusted R Square 0.966418Standard Error 2.203201Observations 10

ANOVA

  df SS MS FSignifican

ce F

Regression 1 1262.0671262.06

7260.000

4 2.2E-07

Residual 8 38.832774.85409

7Signif. Si p<0.05

Total 9 1300.9

 Coefficien

tsStandard Error t Stat P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept b 143.8244 2.52152957.0385

79.91E-

12 138.0097 149.639138.009

7 149.639

X_%Fibra m 1.878635 0.11650816.1245

3 2.2E-07 1.6099682.14730

31.60996

82.14730

3

Paso 4. Interpretación

La regresión es significativa (P value < 0.05)El porcentaje de correlación es alto (0.97)

La ecuación de regresión es Y = b + mx = 143.8244 + 1.878635*X_%Fibra_m

13. PRUEBA DE HIPÓTESIS DE UNA MEDIA

(se hace con la prueba t de Student)

Sea Ho: Mu = 40 Ha: Mu <> 40

Paso 1. Determinar los estadísticos de la muestra.

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Se toma una muestra de 50 partes dando una media de 35 y desviación estándar de 4

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Paso 2. Instrucciones

Paso 3. Los resultados son los siguientes:

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Paso 4. Si se quiere una prueba de dos colas (NOT EQUAL), cola izquierda (LESS THAN) o cola derecha (GREATER THAN) se seleccionan los resultados y botón derecho en ANALYSIS OPTIONS

14. PRUEBA DE HIPÓTESIS DE UNA DESVIACIÓN ESTÁNDAR

(se hace con la prueba Chi Cuadrada)

Sea Ho: Sigma = 6 Ha: Sigma <> 6

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Paso 1. Se toma una muestra de 50 piezas, se evalúa la desviación estándar, dando un resultado de 4.8

Paso 2. Instrucciones

Paso 3. Los resultados son los siguientes:

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Paso 4. Si se quiere una prueba de dos colas (NOT EQUAL), cola izquierda (LESS THAN) o cola derecha (GREATER THAN) se seleccionan los resultados y botón derecho en ANALYSIS OPTIONS

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15. PRUEBA DE HIPÓTESIS DE UNA PROPORCIÓN (Binomial)

Sea Ho: p = 0.3 Ha: p <> 0.3

Paso 1. Se toma una muestra de 100 piezas y se obtiene una proporción de 0.25

Paso 2. Instrucciones

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Paso 3. Los resultados son los siguientes

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16. PRUEBA DE HIPÓTESIS DE DOS MEDIAS

Sea Ho: Mu1 – Mu2 = 0 Ha: Mu1 – Mu2 <> 0

Paso 1. Se toman dos muestras de 48 tiempos de servicio de dos departamentos A y B

Servicio A Servicio B6 10

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7 34 5

Etcétera

Paso 2. Instrucciones

Paso 3. Se seleccionan las pruebas deseadas con las instrucciones siguientes en el Menu tabular:

Los resultados son los siguientes

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a) Comparación de desviaciones estándar

b) Comparación de medias

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Paso 4. El análisis gráfico se muestra a continuación

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CALCULO EN EXCEL

a) Probar la igualdad de varianzas (Prueba F)

Paso 1. Usar los datos de arriba

Paso 2. Instrucciones

HERRAMIENTAS > ANÁLISIS DE DATOS

Indicar los rangos de las dos variables incluyendo sus etiquetas (rótulos), seleccionar Labels, indicar donde se obtienen los resultados de salida

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Paso 3. Los resultados son los siguientes

F-Test Two-Sample for Variances

 Servicio 

AServicio 

B

Mean6.35416

7 6.4375

Variance4.82934

45.69813

8Observations 48 48df 47 47F 0.84753

P(F<=f) one-tail0.28646

8

F Critical one-tail0.61585

6

Como el P (F<=f) Es mayora alfa = 0.05, no se rechaza Ho y las varianzas son iguales.

b) Probar la igualdad de medias con prueba Z

Paso 1. Usar los datos de arriba

Paso 2. Instrucciones

HERRAMIENTAS > ANÁLISIS DE DATOS

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Paso 3. Los resultados se muestran a continuación

z-Test: Two Sample for Means

 Servicio 

AServicio 

B

Mean6.35416

7 6.4375

Known Variance 2.19752.38707

7Observations 48 48Hypothesized Mean Difference 0 z -0.26964

P(Z<=z) one-tail0.39371

7

z Critical one-tail1.64485

4

P(Z<=z) two-tail0.78743

5

z Critical two-tail1.95996

4

Como la P(Z<=z) es de 0.7874 > alfa de 0.2

b) Caso de muestras pequeñas (n <30)

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En el caso de pequeñas muestras, se utiliza la prueba t, hay dos tipos: para cuando las varianzas son iguales y cuando no lo son:

Paso 1. Los datos son los siguientes

Servicio AServicio

B6 107 34 59 34 98 54 39 26 67 68 1

Paso 2. Instrucciones

HERRAMIENTAS > ANÁLISIS DE DATOS

Paso 3. Los resultados se muestran a continuación

t-Test: Two-Sample Assuming Equal Variances

 Servicio 

AServicio 

B Mean 6.54545 4.81818

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5 2

Variance3.67272

77.96363

6 Observations 11 11

Pooled Variance5.81818

2 Hypothesized Mean Difference 0 df 20

t Stat1.67937

9

P(T<=t) one-tail0.05431

7

t Critical one-tail1.72471

8

P(T<=t) two-tail0.10863

4

t Critical two-tail2.08596

3

En la prueba de una cola, el valor P value es mayor a 0.054 por lo que las medias son iguales.

17. PRUEBA DE HIPÓTESIS PAREADAS

(A los mismos sujetos se les evalúa antes y después de un un curso)

Sea Ho: Diferencia de Medias = 0 Ha: Diferencia de medias <> 0

Paso 1. Se toman datos antes y después de un curso como sigue:

Antes Despues6.0 5.45.0 5.27.0 6.56.2 5.96.0 6.06.4 5.8

Paso 2. Instrucciones

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Paso 3. Los resultados se seleccionan el menú tabular como sigue: (dar dos clicks para abrir cada ventana)

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Paso 4. Los resultados gráficos se seleccionan del menú de gráficas

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Paso 5. Para otras opciones de la prueba (una cola, cola izquierda o cola derecha e hipótesis) seleccionar el área de resultados y en PANE OPTIONS seleccionar lo que se desea

Paso 6. El análisis gráfico se muestra a continuación.

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CÁLCULOS EN EXCEL

Paso 1. Con los datos anteriores

Paso 2. InstruccionesHERRAMIENTAS > ANÁLISIS DE DATOS

Paso 3. Los resultados se muestran a continuación

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Paso 3. Los resultados son los siguientes

t-Test: Paired Two Sample for Means

  Antes DespuesMean 6.1 5.8Variance 0.428 0.212Observations 6 6

Pearson Correlation0.87642

4 Hypothesized Mean Difference 0 df 5

t Stat2.19577

5

P(T<=t) one-tail0.03975

8

t Critical one-tail2.01504

8

P(T<=t) two-tail0.07951

6

t Critical two-tail2.57058

2

Como el valor P value de 0.039 es menor a 0.05, se rechaza Ho y se concluye que las medias no son iguales.

18. PRUEBA DE HIPÓTESIS DE DOS PROPORCIONES

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Sea Ho: p1 – p2 = 0 Ha: p1 – p2 <> 0

Paso 1. Se toman muestras de 100 partes y se evalúan sus proporciones de defectuosos, en este caso 30 y 25%, se desea evaluar si son estadísticamente iguales

Paso 2. Instrucciones

Paso 3. Los resultados se muestran a continuación

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19. ANOVA DE UNA VÍA

Sea Ho: Mu1 = Mu2 = Mu3 = …… = Mu n Ha: Alguna de las medias es diferente

Paso 1. Introducir los siguientes datos

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Calificaciones Depto8 Depto_A7 Depto_A8 Depto_A6 Depto_A7 Depto_A8 Depto_A7 Depto_B8 Depto_B7 Depto_B7 Depto_B6 Depto_B8 Depto_B5 Depto_C6 Depto_C6 Depto_C7 Depto_C7 Depto_C6 Depto_C

Paso 2. Instrucciones

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Paso 3. Resultados

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Paso 4. El reporte gráfico se muestra a continuación

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CÁLCULO CON EXCEL

Paso 1. Capturar datos en columnas para cada nivel del factor

Paso 2. Instrucciones

HERRAMIENTAS > ANÁLISIS DE DATOS

Paso 3. Los resultados son los siguientes:

72

Depto_A Depto_B Depto_C8 7 57 8 68 7 66 7 77 6 78 8 6

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Anova: Single Factor

SUMMARYGroups Count Sum Average Variance

Depto_A 6 44 7.333333 0.666667Depto_B 6 43 7.166667 0.566667Depto_C 6 37 6.166667 0.566667

ANOVASource of Variation SS df MS F P-value F crit

Between Groups 4.777777778 2 2.388889 3.981481 0.041018049 3.68232Within Groups 9 15 0.6

Total 13.77777778 17

Como el P value es 0.04 menor a alfa de 0.05, se concluye que hay al menos una media que es diferente (Depto C).

20. TABLA DE CONTINGENCIA

Sea Ho: p1 = p2 = p3 = …… = p n Ha: Alguna de las proporciones es diferente Ho: La variable de renglón es independiente de la variable de columna Ha: La variable de renglón depende de la variable de columna

Paso 1. Introducir los siguientes datos

Los errores presentados en tres tipos de servicios cuando se prestan por tres regiones se muestran a continuación, probar con una tabla de contingencia si los errores dependen del tipo de servicio y región para un 95% de nivel de confianza.

Servicio Region A Region B Region C1 27 12 82 41 22 93 42 14 10

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Paso 2. Instrucciones

Paso 3. Resultados del reporte tabular:

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Paso 4. Resultados del menú de graficos

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Seleccionando las graficas con botón derecho se tiene acceso a su configuración específica

21. CARTAS PARA NEGOCIOS DE BARRAS, DE PASTEL Y DE LÍNEA DE COMPONENTES

Paso 1. Utilizar la columna siguiente

Cantidad

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23126798

3120

Paso 2. Instrucciones para grafica de barras

Paso 3. Resultados

Paso 4. Instrucciones para grafica de Pastel

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Paso 5. Resultados

Paso 6. Grafica de línea de componentes

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Paso 7. Resultados

22. DISTRIBUCIONES DE PROBABILIDAD PARA VALORES CRÍTICOS Y NÚMEROS ALEATORIOS

Caso de la distribución normal

Paso 1. Instrucciones

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Paso 3. Seleccionar la gráfica normal y con botón derecho seleccionar ANALYSIS OPTIONS para cambiar los parámetros de la distribución

Paso 4. Seleccionar el Reporte tabular y seleccionar las siguientes opciones

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En esta sección se pueden evaluar los valores críticos para diversos valores (por ejemplo de Z si la media es cero y la desviación estándar es uno)

Seleccionar esta sección y con botón derecho seleccionar PANE OPTIONS

Los resultados son los siguientes

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En esta sección se pueden evaluar los valores críticos para diversos valores de probabilidad (por ejemplo para encontrar Z si la media es cero y la desviación estándar es uno)

Seleccionar esta sección y con botón derecho seleccionar PANE OPTIONS

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Paso 5. Generar un cierto número de números aleatorios y guardarlos en una columna vacía de la hoja

Seleccionar la ventana de Random numbers mostrada arriba y con botón derecho seleccionar PANE OPTIONS, en esa ventana seleccionar 100 números:

Después pulsar el botón de Almacenado de datos en el menú siguiente:

Seleccionar la distribución y la columna donde se almacenarán los números aleatorios:

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Los datos se almacenan en la columna Datos normales de la hoja de trabajo como sigue:

Datos normales92.9282103.731104.065106.835

GENERACIÓN DE NÚMEROS ALEATORIOS EN EXCEL

Paso 1. Instrucciones (Media = 100, Desviación estándar = 10, N = 10)

HERRAMIENTAS > ANÁLISIS DE DATOS

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Paso 2. Números generados

Datos_Aleatorios

100.5976.10

110.0396.38

102.8097.3087.5293.2385.3884.53

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Paso 5. Seleccionar la grafica deseada con el menú de graficas

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23. CARTAS DE CONTROL PARA SU PROCESO Y GRAFICADO EN EXCEL

a) Carta de control X-R, cálculos y gráficas de línea: zona verde carta X; zona amarilla carta R

Datos de cada uno de los subgrupos Xmedia -+A2*Rm

x1 x2 x3 x4 x5Media

i Media LIC LSCRango i

Rmedio LICr LSCr

15.8 16.3 16.2 16.1 16.6 16.2016.29

216.02

1 16.563 0.80 0.47 0 0.994

16.3 15.9 15.9 16.2 16.4 16.1416.29

216.02

1 16.563 0.50 0.47 0 0.994

16.1 16.2 16.5 16.4 16.3 16.3016.29

216.02

1 16.563 0.40 0.47 0 0.994

16.3 16.2 15.9 16.4 16.2 16.2016.29

216.02

1 16.563 0.50 0.47 0 0.994

16.8 16.9 16.7 16.5 16.6 16.7016.29

216.02

1 16.563 0.40 0.47 0 0.994

16.1 15.8 16.7 16.6 16.4 16.3216.29

216.02

1 16.563 0.90 0.47 0 0.994

16.1 16.3 16.5 16.1 16.5 16.3016.29

216.02

1 16.563 0.40 0.47 0 0.994

16.2 16.1 16.2 16.1 16.3 16.1816.29

216.02

1 16.563 0.20 0.47 0 0.994

16.3 16.2 16.4 16.3 16.5 16.3416.29

216.02

1 16.563 0.30 0.47 0 0.994

16.6 16.3 16.4 16.1 16.5 16.3816.29

216.02

1 16.563 0.50 0.47 0 0.994

16.2 16.4 15.9 16.3 16.4 16.2416.29

216.02

1 16.563 0.50 0.47 0 0.994

15.9 16.6 16.7 16.2 16.5 16.3816.29

216.02

1 16.563 0.80 0.47 0 0.994

16.4 16.1 16.6 16.4 16.1 16.3216.29

216.02

1 16.563 0.50 0.47 0 0.994

16.5 16.3 16.2 16.3 16.4 16.3416.29

216.02

1 16.563 0.30 0.47 0 0.994

16.4 16.1 16.3 16.2 16.2 16.2416.29

216.02

1 16.563 0.30 0.47 0 0.994

16 16.2 16.3 16.3 16.2 16.2016.29

216.02

1 16.563 0.30 0.47 0 0.99416.4 16.2 16.4 16.3 16.2 16.30 16.29 16.02 16.563 0.20 0.47 0 0.994

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2 1

16 16.2 16.4 16.5 16.1 16.2416.29

216.02

1 16.563 0.50 0.47 0 0.994

16.4 16 16.3 16.4 16.4 16.3016.29

216.02

1 16.563 0.40 0.47 0 0.994

16.4 16.4 16.5 16 15.8 16.2216.29

216.02

1 16.563 0.70 0.47 0 0.994

Media de medias 16.292 A2=0.577Rmedio 0.47

Seleccionar la zona verde, INSERTAR GRÁFICA DE LÍNEA (Carta Xmedia)

Repetir para la zona amarilla (Carta R) OK

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2015.6

15.8

16

16.2

16.4

16.6

16.8

Media iMediaLICLSC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 190

0.2

0.4

0.6

0.8

1

1.2

Rango iRmedioLICrLSCr

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b) Carta de control p, proceso y gráfica de línea de zona verde

Serv_no_confMuestr

a Pi Pprom LIC LSC20 98 0.20 0.17 0.055 0.28218 104 0.17 0.17 0.058 0.27914 97 0.14 0.17 0.055 0.28316 99 0.16 0.17 0.056 0.28113 97 0.13 0.17 0.055 0.28329 102 0.28 0.17 0.057 0.28021 104 0.20 0.17 0.058 0.27914 101 0.14 0.17 0.057 0.2806 55 0.11 0.17 0.017 0.3206 48 0.13 0.17 0.006 0.3317 50 0.14 0.17 0.010 0.3277 53 0.13 0.17 0.014 0.3239 56 0.16 0.17 0.018 0.3195 49 0.10 0.17 0.008 0.3298 56 0.14 0.17 0.018 0.3199 53 0.17 0.17 0.014 0.3239 52 0.17 0.17 0.013 0.324

10 51 0.20 0.17 0.011 0.3269 52 0.17 0.17 0.013 0.324

10 47 0.21 0.17 0.005 0.332

Pprom= 0.17 LC=Pprom+3*(Pprom*(1-Pprom)/ni))

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

PiPpromLICLSC

c) Carta np, proceso y gráfica de todas las columnas

Serv_Error nPprom LIC LSC

8 10.60 1.09520.10

5

13 10.60 1.09520.10

5

7 10.60 1.09520.10

5

8 10.60 1.09520.10

5

5 10.60 1.09520.10

5

13 10.60 1.09520.10

5

7 10.60 1.09520.10

5

12 10.60 1.09520.10

5

27 10.60 1.09520.10

5

10 10.60 1.09520.10

5

12 10.60 1.09520.10

56 10.60 1.095 20.10

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5

10 10.60 1.09520.10

5

9 10.60 1.09520.10

5

13 10.60 1.09520.10

5

7 10.60 1.09520.10

5

8 10.60 1.09520.10

5

5 10.60 1.09520.10

5

15 10.60 1.09520.10

5

25 10.60 1.09520.10

5

7 10.60 1.09520.10

5

10 10.6 1.09520.10

5

5 10.6 1.09520.10

5

12 10.6 1.09520.10

5

6 10.6 1.09520.10

5

6 10.6 1.09520.10

5

10 10.6 1.09520.10

5

17 10.6 1.09520.10

5

14 10.6 1.09520.10

5

11 10.6 1.09520.10

5Prom.= 10.6 P prom= 0.053

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 290

5

10

15

20

25

30

Serv_ErrornPpromLICLSC

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d) Carta de control C, graficar todas las columnas

CLC = C+- 3raiz*(C )

Errores Cmedia LIC LSC9 5.55 0 12.62

11 5.55 0 12.622 5.55 0 12.625 5.55 0 12.62

15 5.55 0 12.6213 5.55 0 12.628 5.55 0 12.627 5.55 0 12.625 5.55 0 12.622 5.55 0 12.624 5.55 0 12.624 5.55 0 12.622 5.55 0 12.625 5.55 0 12.625 5.55 0 12.622 5.55 0 12.623 5.55 0 12.622 5.55 0 12.621 5.55 0 12.626 5.55 0 12.62

Prom= 5.55

e) Carta de control u, proceso y gráfica de la zona verde

ULC=U-+3*raiz(U/ni)

Defectos

Facturas Ui

Umedia LIC LSC

9 110 0.082 0.055 0 0.1211 101 0.109 0.055 0 0.12

2 98 0.020 0.055 0 0.135 105 0.048 0.055 0 0.12

15 110 0.136 0.055 0 0.1213 100 0.130 0.055 0 0.12

8 98 0.082 0.055 0 0.13

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7 99 0.071 0.055 0 0.135 100 0.050 0.055 0 0.122 100 0.020 0.055 0 0.124 102 0.039 0.055 0 0.124 98 0.041 0.055 0 0.132 99 0.020 0.055 0 0.135 105 0.048 0.055 0 0.125 104 0.048 0.055 0 0.122 100 0.020 0.055 0 0.123 103 0.029 0.055 0 0.122 100 0.020 0.055 0 0.121 98 0.010 0.055 0 0.136 102 0.059 0.055 0 0.12

Umedia 0.055Grafica de línea de la zona verde

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

UiUmediaLICLSC

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HERRAMIENTAS DE LA FASE DE MEJORA

DISEÑO DE EXPERIMENTOS CLASICO

PROBLEMA 1. Diseño de experimentos de dos niveles: En un proceso de mantenimiento de Generador de Vapor se desea mejorar el proceso de soldadura en un componente de acero inoxidable. Para lo cual se realiza un diseño de experimentos de 3 factores y 2 niveles.

Factor Nivel bajo Nivel AltoA. Caudal de gas (l/min.) 8 12B. Intensidad de Corriente (A) 230 240C. Vel. de Cadena (m/min.) 0.6 1

Como respuesta se toma la calidad del componente en una escala de 0 a 30 entre mayor sea mejor es la calidad

Paso 1. Generar el diseño

Paso 2. Ingresar los datos de los factores y sus niveles (en la misma pantalla escribir los factores)

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Paso 3. Iniciar datos de la variable de respuesta

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Paso 4. Indicar las réplicas del experimento (quitar la bandera de Randomize)

Paso 5. Los resultados del diseño son:

Block Caudal Intensidad Velocidad1 8 230 0.61 12 230 0.61 8 240 0.61 12 240 0.61 8 230 11 12 230 11 8 240 11 12 240 1

El reporte indica lo siguiente:

Screening Design Attributes

Design Summary--------------Design class: ScreeningDesign name: Factorial 2^3 File name: <Untitled>

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Base Design-----------Number of experimental factors: 3 Number of blocks: 1Number of responses: 1Number of runs: 8 Error degrees of freedom: 1Randomized: No

Factors Low High Units Continuous------------------------------------------------------------------------Caudal 8 12 YesIntensidad 230 240 YesVelocidad 0.6 1.0 Yes

Responses Units-----------------------------------Y m

The StatAdvisor--------------- You have created a Factorial design which will study the effects of3 factors in 8 runs. The design is to be run in a single block. Theorder of the experiments has not been randomized. If lurkingvariables are present, they may distort the results. Only 1 degree offreedom is available to estimate the experimental error. Therefore,the statistical tests on the results will be very weak. It isrecommended that you add enough centerpoints to give you at least 3degrees of freedom for the error.

Colocarse en la pantalla de Resultados y con botón derecho accesar

Seleccionar Copy Analysis to StatReporter

Paso 6. Copiar los datos de la columna de respuesta Y a la Worksheet

Y10

26.515

17.511.526

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17.520

Paso 7. Analizar el diseño

Paso 8. Seleccionar las opciones de reporte tabular

Analyze Experiment - Y

Analysis Summary----------------File name: <Untitled>

Estimated effects for Y----------------------------------------------------------------------average = 18.0 +/- 0.25

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A:Caudal = 9.0 +/- 0.5B:Intensidad = -1.0 +/- 0.5C:Velocidad = 1.5 +/- 0.5AB = -6.5 +/- 0.5AC = -0.5 +/- 0.5BC = 1.0 +/- 0.5----------------------------------------------------------------------Standard errors are based on total error with 1 d.f.

The StatAdvisor--------------- This table shows each of the estimated effects and interactions. Also shown is the standard error of each of the effects, whichmeasures their sampling error. To plot the estimates in decreasingorder of importance, select Pareto Charts from the list of GraphicalOptions. To test the statistical significance of the effects, selectANOVA Table from the list of Tabular Options. You can then removeinsignificant effects by pressing the alternate mouse button,selecting Analysis Options, and pressing the Exclude button.

Standardized Pareto Chart for Y

0 3 6 9 12 15 18

Standardized effect

AC

B:Intensidad

BC

C:Velocidad

AB

A:Caudal

Analysis of Variance for Y--------------------------------------------------------------------------------Source Sum of Squares Df Mean Square F-Ratio P-Value--------------------------------------------------------------------------------A:Caudal SIGNIFICATIVO 162.0 1 162.0 324.00 0.0353B:Intensidad 2.0 1 2.0 4.00 0.2952C:Velocidad 4.5 1 4.5 9.00 0.2048AB SIGNIFICATIVO 84.5 1 84.5 169.00 0.0489AC 0.5 1 0.5 1.00 0.5000BC 2.0 1 2.0 4.00 0.2952Total error 0.5 1 0.5--------------------------------------------------------------------------------Total (corr.) 256.0 7

R-squared = 99.8047 percentR-squared (adjusted for d.f.) = 98.6328 percent

The StatAdvisor--------------- The ANOVA table partitions the variability in Y into separatepieces for each of the effects. It then tests the statisticalsignificance of each effect by comparing the mean square against anestimate of the experimental error. In this case, 2 effects haveP-values less than 0.05, indicating that they are significantlydifferent from zero at the 95.0% confidence level. The R-Squared statistic indicates that the model as fitted explains99.8047% of the variability in Y. The adjusted R-squared statistic,which is more suitable for comparing models with different numbers ofindependent variables, is 98.6328%. The standard error of theestimate shows the standard deviation of the residuals to be 0.707107.The mean absolute error (MAE) of 0.25 is the average value of theresiduals. The Durbin-Watson (DW) statistic tests the residuals to

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determine if there is any significant correlation based on the orderin which they occur in your data file. Since the DW value is greaterthan 1.4, there is probably not any serious autocorrelation in theresiduals.

Regression coeffs. for Y----------------------------------------------------------------------constant = -658.75A:Caudal = 79.125B:Intensidad = 2.75C:Velocidad = -107.5AB = -0.325AC = -0.625BC = 0.5----------------------------------------------------------------------

The StatAdvisor--------------- This pane displays the regression equation which has been fitted tothe data. The equation of the fitted model is

Y = -658.75 + 79.125*Caudal + 2.75*Intensidad - 107.5*Velocidad -0.325*Caudal*Intensidad - 0.625*Caudal*Velocidad +0.5*Intensidad*Velocidad

where the values of the variables are specified in their originalunits. To have STATGRAPHICS evaluate this function, selectPredictions from the list of Tabular Options. To plot the function,select Response Plots from the list of Graphical Options.

Correlation Matrix for Estimated Effects

(1) (2) (3) (4) (5) (6) (7)---------------------------------------------------------------------(1)average 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000(2)A:Caudal 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000(3)B:Intensidad 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000(4)C:Velocidad 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000(5)AB 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000(6)AC 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000(7)BC 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000---------------------------------------------------------------------

The StatAdvisor--------------- The correlation matrix shows the extent of the confounding amongstthe effects. A perfectly orthogonal design will show a diagonalmatrix with 1's on the diagonal and 0's off the diagonal. Anynon-zero terms off the diagonal imply that the estimates of theeffects corresponding to that row and column will be correlated. Inthis case, there is no correlation amongst any of the effects. Thismeans that you will get clear estimates of all those effects.

Estimation Results for Y---------------------------------------------------------------------- Observed Fitted Lower 95.0% CL Upper 95.0% CLRow Value Value for Mean for Mean---------------------------------------------------------------------- 1 10.0 10.25 1.84564 18.6544 2 26.5 26.25 17.8456 34.6544 3 15.0 14.75 6.34564 23.1544 4 17.5 17.75 9.34564 26.1544 5 11.5 11.25 2.84564 19.6544

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6 26.0 26.25 17.8456 34.6544 7 17.5 17.75 9.34564 26.1544 8 20.0 19.75 11.3456 28.1544----------------------------------------------------------------------

The StatAdvisor--------------- This table contains information about values of Y generated usingthe fitted model. The table includes: (1) the observed value of Y (if any) (2) the predicted value of Y using the fitted model (3) 95.0% confidence limits for the mean responseEach item corresponds to the values of the experimental factors in aspecific row of your data file. To generate forecasts for additionalcombinations of the factors, add additional rows to the bottom of yourdata file. In each new row, enter values for the experimental factorsbut leave the cell for the response empty. When you return to thispane, forecasts will be added to the table for the new rows, but themodel will be unaffected.

Path of Steepest Ascent for Y

PredictedCaudal Intensidad Velocidad Y (m)---------- ---------- ---------- ------------10.0 235.0 0.8 18.0 11.0 234.332 0.814337 20.5738 12.0 232.994 0.822727 24.0386 13.0 231.229 0.825327 28.8038 14.0 229.212 0.823318 35.0649 15.0 227.045 0.817849 42.9128

The StatAdvisor--------------- This pane displays the path of steepest ascent (or descent). Thisis the path from the center of the current experimental region alongwhich the estimated response changes most quickly for the smallestchange in the experimental factors. It indicates good locations torun additional experiments if your goal is to increase or decrease Y. Currently, 6 points have been generated by changing Caudal inincrements of 1.0. You can specify the amount to change any onefactor by pressing the alternate mouse button and selecting PaneOptions. STATGRAPHICS will then determine how much all the otherfactors have to change to stay on the path of steepest ascent. Theprogram also computes the estimated Y at each of the points along thepath, which you can compare to your results if you run those points.

Optimize Response-----------------Goal: maximize Y

Optimum value = 26.25

Factor Low High Optimum-----------------------------------------------------------------------Caudal 8.0 12.0 12.0 Intensidad 230.0 240.0 230.0 Velocidad 0.6 1.0 0.6

The StatAdvisor--------------- This table shows the combination of factor levels which maximizes Yover the indicated region. Use the Analysis Options dialog box to

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indicate the region over which the optimization is to be performed. You may set the value of one or more factors to a constant by settingthe low and high limits to that value.

Colocarse en la pantalla de Resultados y con botón derecho accesar

Seleccionar Copy Analysis to StatReporter

Paso 9. Obtener el reporte grafico

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Main Effects Plot for Y

13

15

17

19

21

23

Y

Caudal8 12

Intensidad230 240

Velocidad0.6 1.0

Regression coeffs. for Y----------------------------------------------------------------------constant = -658.75A:Caudal = 79.125B:Intensidad = 2.75C:Velocidad = -107.5AB = -0.325AC = -0.625BC = 0.5----------------------------------------------------------------------

The StatAdvisor--------------- This pane displays the regression equation which has been fitted tothe data. The equation of the fitted model is

Y = -658.75 + 79.125*Caudal + 2.75*Intensidad - 107.5*Velocidad -0.325*Caudal*Intensidad - 0.625*Caudal*Velocidad +0.5*Intensidad*Velocidad

where the values of the variables are specified in their originalunits. To have STATGRAPHICS evaluate this function, selectPredictions from the list of Tabular Options. To plot the function,select Response Plots from the list of Graphical Options.

Interaction Plot for Y

10

13

16

19

22

25

28

Y

AB8 12

-

-

+

+

AC8 12

-

-

+

+

BC230 240

--

+ +

Correlation Matrix for Estimated Effects

(1) (2) (3) (4) (5) (6) (7)---------------------------------------------------------------------(1)average 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000(2)A:Caudal 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000

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(3)B:Intensidad 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000(4)C:Velocidad 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000(5)AB 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000(6)AC 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000(7)BC 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000---------------------------------------------------------------------

The StatAdvisor--------------- The correlation matrix shows the extent of the confounding amongstthe effects. A perfectly orthogonal design will show a diagonalmatrix with 1's on the diagonal and 0's off the diagonal. Anynon-zero terms off the diagonal imply that the estimates of theeffects corresponding to that row and column will be correlated. Inthis case, there is no correlation amongst any of the effects. Thismeans that you will get clear estimates of all those effects.

Normal Probability Plot for Y

-13 -3 7 17 27

Standardized effects

0.115

2050809599

99.9

perc

enta

ge

Estimation Results for Y---------------------------------------------------------------------- Observed Fitted Lower 95.0% CL Upper 95.0% CLRow Value Value for Mean for Mean---------------------------------------------------------------------- 1 10.0 10.25 1.84564 18.6544 2 26.5 26.25 17.8456 34.6544 3 15.0 14.75 6.34564 23.1544 4 17.5 17.75 9.34564 26.1544 5 11.5 11.25 2.84564 19.6544 6 26.0 26.25 17.8456 34.6544 7 17.5 17.75 9.34564 26.1544 8 20.0 19.75 11.3456 28.1544----------------------------------------------------------------------

The StatAdvisor--------------- This table contains information about values of Y generated usingthe fitted model. The table includes: (1) the observed value of Y (if any) (2) the predicted value of Y using the fitted model (3) 95.0% confidence limits for the mean responseEach item corresponds to the values of the experimental factors in aspecific row of your data file. To generate forecasts for additionalcombinations of the factors, add additional rows to the bottom of yourdata file. In each new row, enter values for the experimental factorsbut leave the cell for the response empty. When you return to thispane, forecasts will be added to the table for the new rows, but themodel will be unaffected.

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Estimated Response SurfaceVelocidad=0.8

8 9 10 11 12Caudal

230232234236238240

Intensidad10131619222528

Y

Path of Steepest Ascent for Y

PredictedCaudal Intensidad Velocidad Y (m)---------- ---------- ---------- ------------10.0 235.0 0.8 18.0 11.0 234.332 0.814337 20.5738 12.0 232.994 0.822727 24.0386 13.0 231.229 0.825327 28.8038 14.0 229.212 0.823318 35.0649 15.0 227.045 0.817849 42.9128

The StatAdvisor--------------- This pane displays the path of steepest ascent (or descent). Thisis the path from the center of the current experimental region alongwhich the estimated response changes most quickly for the smallestchange in the experimental factors. It indicates good locations torun additional experiments if your goal is to increase or decrease Y. Currently, 6 points have been generated by changing Caudal inincrements of 1.0. You can specify the amount to change any onefactor by pressing the alternate mouse button and selecting PaneOptions. STATGRAPHICS will then determine how much all the otherfactors have to change to stay on the path of steepest ascent. Theprogram also computes the estimated Y at each of the points along thepath, which you can compare to your results if you run those points.

Contours of Estimated Response SurfaceVelocidad=0.8

8 9 10 11 12

Caudal

230

232

234

236

238

240

Inte

nsid

ad

Y10.011.813.615.417.219.020.822.624.426.228.0

Optimize Response-----------------

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Goal: maximize Y

Optimum value = 26.25

Factor Low High Optimum-----------------------------------------------------------------------Caudal 8.0 12.0 12.0 Intensidad 230.0 240.0 230.0 Velocidad 0.6 1.0 0.6

The StatAdvisor--------------- This table shows the combination of factor levels which maximizes Yover the indicated region. Use the Analysis Options dialog box toindicate the region over which the optimization is to be performed. You may set the value of one or more factors to a constant by settingthe low and high limits to that value.

Residual Plot for Y

10 13 16 19 22 25 28

predicted

-0.25

-0.15

-0.05

0.05

0.15

0.25

resi

dual

Colocarse en la pantalla de Resultados y con botón derecho accesar

Seleccionar Copy Analysis to StatReporter

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PROBLEMA 2. Diseño de dos niveles: Se usa un Router para hacer los barrenos de localización de una placa de circuito impreso. La vibración es fuente principal de variación. La vibración de la placa a ser cortada depende del tamaño de los barrenos (A1 = 1/16" y A2 = 1/8") y de la velocidad de corte (B1 = 40 RPMs y B2 = 90 RPMs).

La variable de respuesta se mide en tres acelerómetros A,Y,Z en cada uno de los circuitos impresos.

Los resultados se muestran a continuación.

Niveles reales RéplicaA B I II III IV

0.063 40 18.2 18.9 12.9 14.40.125 40 27.2 24.0 22.4 22.50.063 90 15.9 14.5 15.1 14.20.125 90 41.0 43.9 36.3 39.9

Paso 1. Generar el diseño

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Paso 2. Ingresar los datos de los factores y sus niveles (en la misma pantalla seleccionar los factores)

Paso 3. Datos de la variable de respuesta

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Paso 4. Indicar las réplicas del experimento

Paso 5. Los resultados del diseño son los siguientes:

BlockDiametro Velocidad

1 0.063 401 0.125 401 0.063 901 0.125 902 0.063 402 0.125 402 0.063 902 0.125 903 0.063 403 0.125 403 0.063 903 0.125 904 0.063 404 0.125 404 0.063 904 0.125 90

Screening Design Attributes

Design Summary--------------Design class: ScreeningDesign name: Factorial 2^2 File name: <Untitled>

Base Design-----------Number of experimental factors: 2 Number of blocks: 4Number of responses: 1Number of runs: 16 Error degrees of freedom: 9Randomized: No

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Factors Low High Units Continuous------------------------------------------------------------------------Diametro 0.063 0.125 YesVelocidad 40 90 Yes

Responses Units-----------------------------------Vibracion

The StatAdvisor--------------- You have created a Factorial design which will study the effects of2 factors in 16 runs. The design is to be run in a single block. Theorder of the experiments has not been randomized. If lurkingvariables are present, they may distort the results.

Colocarse en la pantalla de Resultados y con botón derecho accesar

Seleccionar Copy Analysis to StatReporter

Paso 5. Copiar los datos de la variable de respuesta, resultado de los experimentos físicos a la hoja de cálculo en el Statgraphics

VIBRACIÓN18.227.215.941

18.924

14.543.912.922.415.136.314.422.514.2

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39.9

Paso 6. Analizar el diseño

Paso 7. Seleccionar las opciones de reporte tabular

Analyze Experiment - Vibracion

Analysis Summary----------------File name: <Untitled>

Estimated effects for Vibracion----------------------------------------------------------------------average = 23.8312 +/- 0.435895A:Diametro = 16.6375 +/- 0.87179B:Velocidad = 7.5375 +/- 0.87179AB = 8.7125 +/- 0.87179block = 2.9875 +/- 1.50998block = -4.3125 +/- 1.50998block = -2.1625 +/- 1.50998----------------------------------------------------------------------Standard errors are based on total error with 9 d.f.

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The StatAdvisor--------------- This table shows each of the estimated effects and interactions. Also shown is the standard error of each of the effects, whichmeasures their sampling error. To plot the estimates in decreasingorder of importance, select Pareto Charts from the list of GraphicalOptions. To test the statistical significance of the effects, selectANOVA Table from the list of Tabular Options. You can then removeinsignificant effects by pressing the alternate mouse button,selecting Analysis Options, and pressing the Exclude button.

Standardized Pareto Chart for Vibracion

0 4 8 12 16 20

Standardized effect

B:Velocidad

AB

A:Diametro

Analysis of Variance for Vibracion--------------------------------------------------------------------------------Source Sum of Squares Df Mean Square F-Ratio P-Value--------------------------------------------------------------------------------A:Diametro SIGNIFICATIVOS 1107.23 1 1107.23 364.21 0.0000B:Velocidad 227.256 1 227.256 74.75 0.0000AB 303.631 1 303.631 99.88 0.0000blocks 44.3619 3 14.7873 4.86 0.0280Total error 27.3606 9 3.04007--------------------------------------------------------------------------------Total (corr.) 1709.83 15

R-squared = 98.3998 percentR-squared (adjusted for d.f.) = 97.9998 percent

The StatAdvisor--------------- The ANOVA table partitions the variability in Vibracion intoseparate pieces for each of the effects. It then tests thestatistical significance of each effect by comparing the mean squareagainst an estimate of the experimental error. In this case, 4effects have P-values less than 0.05, indicating that they aresignificantly different from zero at the 95.0% confidence level. The R-Squared statistic indicates that the model as fitted explains98.3998% of the variability in Vibracion. The adjusted R-squaredstatistic, which is more suitable for comparing models with differentnumbers of independent variables, is 97.9998%. The standard error ofthe estimate shows the standard deviation of the residuals to be1.74358. The mean absolute error (MAE) of 1.14375 is the averagevalue of the residuals. The Durbin-Watson (DW) statistic tests theresiduals to determine if there is any significant correlation basedon the order in which they occur in your data file. Since the DWvalue is greater than 1.4, there is probably not any seriousautocorrelation in the residuals.

Regression coeffs. for Vibracion----------------------------------------------------------------------constant = 23.152A:Diametro = -97.0161

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B:Velocidad = -0.377621AB = 5.62097----------------------------------------------------------------------

The StatAdvisor--------------- This pane displays the regression equation which has been fitted tothe data. The equation of the fitted model is

Vibracion = 23.152 - 97.0161*Diametro - 0.377621*Velocidad +5.62097*Diametro*Velocidad

where the values of the variables are specified in their originalunits. To have STATGRAPHICS evaluate this function, selectPredictions from the list of Tabular Options. To plot the function,select Response Plots from the list of Graphical Options.

Correlation Matrix for Estimated Effects

(1) (2) (3) (4) (5) (6) (7)---------------------------------------------------------------------(1)average 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000(2)A:Diametro 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000(3)B:Velocidad 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000(4)AB 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000(5)block 0.0000 0.0000 0.0000 0.0000 1.0000-0.3333-0.3333(6)block 0.0000 0.0000 0.0000 0.0000-0.3333 1.0000-0.3333(7)block 0.0000 0.0000 0.0000 0.0000-0.3333-0.3333 1.0000---------------------------------------------------------------------

The StatAdvisor--------------- The correlation matrix shows the extent of the confounding amongstthe effects. A perfectly orthogonal design will show a diagonalmatrix with 1's on the diagonal and 0's off the diagonal. Anynon-zero terms off the diagonal imply that the estimates of theeffects corresponding to that row and column will be correlated. Inthis case, there are 3 pairs of effects with non-zero correlations. However, since none are greater than or equal to 0.5, you willprobably be able to interpret the results without much difficulty.

Estimation Results for Vibracion---------------------------------------------------------------------- Observed Fitted Lower 95.0% CL Upper 95.0% CLRow Value Value for Mean for Mean---------------------------------------------------------------------- 1 18.2 17.8437 15.2349 20.4526 2 27.2 25.7687 23.1599 28.3776 3 15.9 16.6687 14.0599 19.2776 4 41.0 42.0187 39.4099 44.6276 5 18.9 17.5937 14.9849 20.2026 6 24.0 25.5187 22.9099 28.1276 7 14.5 16.4187 13.8099 19.0276 8 43.9 41.7687 39.1599 44.3776 9 12.9 13.9437 11.3349 16.5526 10 22.4 21.8687 19.2599 24.4776 11 15.1 12.7688 10.1599 15.3776 12 36.3 38.1187 35.5099 40.7276 13 14.4 15.0188 12.4099 17.6276 14 22.5 22.9437 20.3349 25.5526 15 14.2 13.8438 11.2349 16.4526 16 39.9 39.1937 36.5849 41.8026----------------------------------------------------------------------

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The StatAdvisor--------------- This table contains information about values of Vibracion generatedusing the fitted model. The table includes: (1) the observed value of Vibracion (if any) (2) the predicted value of Vibracion using the fitted model (3) 95.0% confidence limits for the mean responseEach item corresponds to the values of the experimental factors in aspecific row of your data file. To generate forecasts for additionalcombinations of the factors, add additional rows to the bottom of yourdata file. In each new row, enter values for the experimental factorsbut leave the cell for the response empty. When you return to thispane, forecasts will be added to the table for the new rows, but themodel will be unaffected.

Path of Steepest Ascent for Vibracion

PredictedDiametro Velocidad Vibracion---------- ---------- ------------0.094 65.0 23.8312 1.094 845.466 4796.81 2.094 1651.85 18639.0 3.094 2458.28 41547.4 4.094 3264.73 73521.8 5.094 4071.17 114562.0

The StatAdvisor--------------- This pane displays the path of steepest ascent (or descent). Thisis the path from the center of the current experimental region alongwhich the estimated response changes most quickly for the smallestchange in the experimental factors. It indicates good locations torun additional experiments if your goal is to increase or decreaseVibracion. Currently, 6 points have been generated by changingDiametro in increments of 1.0. You can specify the amount to changeany one factor by pressing the alternate mouse button and selectingPane Options. STATGRAPHICS will then determine how much all the otherfactors have to change to stay on the path of steepest ascent. Theprogram also computes the estimated Vibracion at each of the pointsalong the path, which you can compare to your results if you run thosepoints.

Optimize Response-----------------Goal: maximize Vibracion

Optimum value = 40.275

Factor Low High Optimum-----------------------------------------------------------------------Diametro 0.063 0.125 0.125 Velocidad 40.0 90.0 90.0

The StatAdvisor--------------- This table shows the combination of factor levels which maximizesVibracion over the indicated region. Use the Analysis Options dialogbox to indicate the region over which the optimization is to beperformed. You may set the value of one or more factors to a constantby setting the low and high limits to that value.

Colocarse en la pantalla de Resultados y con botón derecho accesar

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Seleccionar Copy Analysis to StatReporter

Paso 8. Obtener el reporte grafico

Analyze Experiment - Vibracion

Analysis Summary----------------File name: <Untitled>

Estimated effects for Vibracion----------------------------------------------------------------------average = 23.8312 +/- 0.435895A:Diametro = 16.6375 +/- 0.87179B:Velocidad = 7.5375 +/- 0.87179AB = 8.7125 +/- 0.87179block = 2.9875 +/- 1.50998block = -4.3125 +/- 1.50998block = -2.1625 +/- 1.50998----------------------------------------------------------------------Standard errors are based on total error with 9 d.f.

The StatAdvisor--------------- This table shows each of the estimated effects and interactions. Also shown is the standard error of each of the effects, whichmeasures their sampling error. To plot the estimates in decreasing

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order of importance, select Pareto Charts from the list of GraphicalOptions. To test the statistical significance of the effects, selectANOVA Table from the list of Tabular Options. You can then removeinsignificant effects by pressing the alternate mouse button,selecting Analysis Options, and pressing the Exclude button.

Standardized Pareto Chart for Vibracion

0 4 8 12 16 20

Standardized effect

B:Velocidad

AB

A:Diametro

Main Effects Plot for Vibracion

15

18

21

24

27

30

33

Vib

raci

on

Diametro0.063 0.125

Velocidad40 90

Interaction Plot for Vibracion

14

19

24

29

34

39

44

Vib

raci

on

Diametro0.063 0.125

Velocidad=40

Velocidad=40

Velocidad=90

Velocidad=90

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Normal Probability Plot for Vibracion

-3 1 5 9 13 17 21

Standardized effects

0.115

2050809599

99.9

perc

enta

ge

Estimated Response Surface

63 83 103 123 143(X 0.001)Diametro

40 50 60 70 80 90

Velocidad14

24

34

44

54

Vib

raci

on

Contours of Estimated Response Surface

63 83 103 123 143(X 0.001)

Diametro

40

50

60

70

80

90

Velo

cida

d

Vibracion14.018.022.026.030.034.038.042.046.050.0

Residual Plot for Vibracion

12 22 32 42 52

predicted

-2.4

-1.4

-0.4

0.6

1.6

2.6

resi

dual

Colocarse en la pantalla de Resultados y con botón derecho accesar

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Seleccionar Copy Analysis to StatReporter

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Problema 4.

Diseño de experimentos de Taguchi

Taguchi ha desarrollado una serie de arreglos para experimentos con factores a dos niveles, los más utilizados y difundidos según el número de factores a analizar son:

Si el número de factores queArreglo a utilizar

Nº de condiciones

se desean analizar es a probar

Entre 1 y 3 L4 4

Entre 4 y 7 L8 8

Entre 8 y 11 L12 12

Entre 12 y 15 L16 16Entre 16 y 31 L32 32

Entre 32 y 63 L64 64

Taguchi sugiere utilizar un estadístico que proporcione información acerca de la media y de la variancia denominado Relación Señal a Ruido (SNR), como la variable de respuesta, se consideran tres tipos principales. Las fórmulas para cada esquema son las siguientes:

1. Menor es mejor (Smaller is better - s)

2. Mayor es mejor Larger is better - l)

3. Nominal es mejor - (Target is better - t)

Donde la SNR se expresa en decibeles y debe ser maximizada

Una vez insertados los componentes en una placa de circuito impreso, esta se pasa a una máquina de soldar donde por medio de un transportador pasa por un baño de flux para eliminar oxido, se precalienta para reducir la torcedura y se suelda. Se diseña un experimento para determinar las condiciones que dan el número mínimo de defectos de soldadura por millón de uniones. Los factores de control y niveles se muestran a continuación:

ARREGLO INTERNO

125

SNRs=−10 log∑i=1

nYi2

n

SNRl=−10 log∑i=1

n 1 /Yi2 ¿n

¿

SNRt=−10 log s2

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Factor Descripción (-1) (+1)A Temperatura de soldado ºF 480 510B Velocidad del transportador (ft/min) 7.2 10.C Densidad del flux remover oxido 0.9 1.0D Temperatura de precalentado ºF 150 200E Altura de ola de soldadura(pulg.) 0.5 0.6

Además se tienen otros factores denominados factores de ruido que no se pueden o no se quieren controlar como el tipo de producto. También se pueden considerar factores de ruido las tolerancias de algunos de los factores críticos en este proceso, en este caso la temperatura de la soldadura varia entre ±5ºF y la velocidad del transportador entre ± 0.2 ft/min. Esta variabilidad también tiene influencia en la respuesta.

ARREGLO INTERNOFactor Descripción (-1) (+1)

F Temperatura de soldadura (ºF) -5 5G Velocidad del transportador (ft/min) -0.2 +0.2H Tipo de producto en la placa 2 1

El arreglo cruzado de ambos y los valores de las respuestas se muestran a continuación:En este caso se busca la respuesta Menor es mejor para los defectos de soldadura.

F -1 1 1 -1

Arreglo interno G -1 1 -1 1

H -1 -1 1 1

A B C D E SNR

-1 -1 -1 -1 -1 186 187 105 104 -43.59

-1 -1 1 1 1 328 326 247 322 -49.76

-1 1 -1 -1 1 234 159 231 157 -45.97

-1 1 1 1 -1 295 216 204 293 -48.15

1 -1 -1 1 -1 47 125 127 42 -39.51

1 -1 1 -1 1 185 261 264 264 -47.81

1 1 -1 1 1 136 136 132 136 -42.61

1 1 1 -1 -1 194 197 193 275 -46.75

Paso 1. Generar el diseño

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Paso 2. Variable de respuesta (quitar banderas de Randomize)

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Paso 3. Seleccionar el arreglo orthogonal (default) quitar banderas de RandomizeSeleccionar el arreglo L8 (8 corridas experimentales) con L4 en los factores de ruido (4 réplicas de los resultados de cada bloque de 8 experimentos)

Paso 4. Asignación de columnas

NOTA: Dejar la columna 3 libre ya que de acuerdo a las gráficas lineales de Taguchi, ahí se presenta la interacción de los factores A y B que es de interés.

Paso 5. Dar nombres a los factores e indicar sus unidades (en este caso no se consideraron). Todos los factores se inicializan en la misma pantalla.

Continuar con los otros factores hasta el factor H

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El arreglo resultante es:

Block A B C D E F G H Defectos1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 2 2 1 2 1 1 2 2 2 1 1 1 2 1 1 2 2 2 1 2 2 2 1 1 2 2 2 2 1 2 2 1 1 2 2 2 2 2 1 3 1 2 1 2 2 1 1 1 3 1 2 1 2 2 1 2 2 3 1 2 1 2 2 2 1 2 3 1 2 1 2 2 2 2 1 4 1 2 2 1 1 1 1 1 4 1 2 2 1 1 1 2 2 4 1 2 2 1 1 2 1 2 4 1 2 2 1 1 2 2 1 5 2 1 1 2 1 1 1 1 5 2 1 1 2 1 1 2 2 5 2 1 1 2 1 2 1 2 5 2 1 1 2 1 2 2 1 6 2 1 2 1 2 1 1 1 6 2 1 2 1 2 1 2 2 6 2 1 2 1 2 2 1 2 6 2 1 2 1 2 2 2 1 7 2 2 1 1 2 1 1 1 7 2 2 1 1 2 1 2 2 7 2 2 1 1 2 2 1 2 7 2 2 1 1 2 2 2 1

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8 2 2 2 2 1 1 1 1 8 2 2 2 2 1 1 2 2 8 2 2 2 2 1 2 1 2 8 2 2 2 2 1 2 2 1

Inner/Outer Arrays Design AttributesDesign Summary--------------Design class: Inner/Outer ArraysFile name: <Untitled>

Base Design-----------Number of control factors: 5 Number of noise factors: 3Number of responses: 1Number of runs in inner array: 8 Number of runs in outer array: 4Randomized: No

Factors Levels Units-----------------------------------------------A 2 B 2 C 2 D 2 E 2 F 2 G 2 H 2

Responses Units-----------------------------------Defectos

The StatAdvisor--------------- You have created an experimental design which will estimate theeffects of 5 control factors and 3 noise factors. The inner array, inwhich the control factors are varied, contains 8 runs. The outerarray, in which the noise factors are varied, contains 4 runs. Thisresults in a total of 32 runs.

Colocarse en la pantalla de Resultados y con botón derecho accesar

Seleccionar Copy Analysis to StatReporterPaso 6. Cargar los resultados de los experimentos a la columna de Defectos

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Defectos186328234295

47185136194187326159216125261136197105247231204127264132193104322157293

42264136275

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Paso 7. Analizar el diseño de experimentos

Se pueden analizar las medias de las respuestas o las relaciones Señal / Ruido, seleccionar estas últimas con la opción Menor es mejor

Paso 8. Obtener el reporte tabular del diseño de experimentos

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Analysis Summary----------------File name: <Untitled>

Estimated effects for Defectos (SN: smaller)----------------------------------------------------------------------average = -46.2787 +/- 0.423871A:A = -0.109419 +/- 0.847742B:B = -0.647976 +/- 0.847742C:C = 2.18606 +/- 0.847742D:D = 0.913815 +/- 0.847742E:E = 0.623349 +/- 0.847742----------------------------------------------------------------------Standard errors are based on total error with 2 d.f.

The StatAdvisor--------------- This table shows each of the estimated effects and interactions. Also shown is the standard error of each of the effects, whichmeasures their sampling error. To plot the estimates in decreasingorder of importance, select Pareto Charts from the list of GraphicalOptions. To test the statistical significance of the effects, selectANOVA Table from the list of Tabular Options. You can then removeinsignificant effects by pressing the alternate mouse button,selecting Analysis Options, and pressing the Exclude button.

Standardized Pareto Chart for Defectos (SN: smaller)

0 1 2 3 4 5

Standardized effect

A:A

E:E

B:B

D:D

C:C

Analysis of Variance for Defectos (SN: smaller)--------------------------------------------------------------------------------Source Sum of Squares Df Mean Square F-Ratio P-Value--------------------------------------------------------------------------------A:A 0.0239449 1 0.0239449 0.02 0.9091B:B 0.839746 1 0.839746 0.58 0.5245C:C 9.55773 1 9.55773 6.65 0.1232D:D 1.67012 1 1.67012 1.16 0.3938E:E 0.777128 1 0.777128 0.54 0.5387Total error 2.87467 2 1.43733--------------------------------------------------------------------------------Total (corr.) 15.7433 7

R-squared = 81.7404 percentR-squared (adjusted for d.f.) = 36.0915 percent

The StatAdvisor--------------- The ANOVA table partitions the variability in Defectos into

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separate pieces for each of the effects. It then tests thestatistical significance of each effect by comparing the mean squareagainst an estimate of the experimental error. In this case, 0effects have P-values less than 0.05, indicating that they aresignificantly different from zero at the 95.0% confidence level. The R-Squared statistic indicates that the model as fitted explains81.7404% of the variability in Defectos. The adjusted R-squaredstatistic, which is more suitable for comparing models with differentnumbers of independent variables, is 36.0915%. The standard error ofthe estimate shows the standard deviation of the residuals to be1.19889. The mean absolute error (MAE) of 0.572423 is the averagevalue of the residuals. The Durbin-Watson (DW) statistic tests theresiduals to determine if there is any significant correlation basedon the order in which they occur in your data file. Since the DWvalue is greater than 1.4, there is probably not any seriousautocorrelation in the residuals.

Regression coeffs. for Defectos (SN: smaller)----------------------------------------------------------------------constant = -50.7274A:A = -0.109419B:B = -0.647976C:C = 2.18606D:D = 0.913815E:E = 0.623349----------------------------------------------------------------------

The StatAdvisor--------------- This pane displays the regression equation which has been fitted tothe data. The equation of the fitted model is

Defectos = -50.7274 - 0.109419*A - 0.647976*B + 2.18606*C + 0.913815*D+ 0.623349*E

where the values of the variables are specified in their originalunits. To have STATGRAPHICS evaluate this function, selectPredictions from the list of Tabular Options. To plot the function,select Response Plots from the list of Graphical Options.

Correlation Matrix for Estimated Effects

(1) (2) (3) (4) (5) (6)--------------------------------------------------------------(1)average 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000(2)A:A 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000(3)B:B 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000(4)C:C 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000(5)D:D 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000(6)E:E 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000--------------------------------------------------------------

The StatAdvisor--------------- The correlation matrix shows the extent of the confounding amongstthe effects. A perfectly orthogonal design will show a diagonalmatrix with 1's on the diagonal and 0's off the diagonal. Anynon-zero terms off the diagonal imply that the estimates of theeffects corresponding to that row and column will be correlated. Inthis case, there is no correlation amongst any of the effects. Thismeans that you will get clear estimates of all those effects.

Estimation Results for Defectos (SN: smaller)

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---------------------------------------------------------------------- Observed Fitted Lower 95.0% CL Upper 95.0% CLRow Value Value for Mean for Mean---------------------------------------------------------------------- 1 -48.512 -47.7616 -52.2289 -43.2943 2 -43.6439 -44.0384 -48.5057 -39.5711 3 -47.2669 -46.8724 -51.3397 -42.4051 4 -45.4732 -46.2235 -50.6908 -41.7562 5 -46.2069 -46.9572 -51.4245 -42.4899 6 -45.4561 -45.0616 -49.5289 -40.5943 7 -47.5012 -47.8957 -52.363 -43.4284 8 -46.1695 -45.4191 -49.8864 -40.9518----------------------------------------------------------------------

The StatAdvisor--------------- This table contains information about values of Defectos generatedusing the fitted model. The table includes: (1) the observed value of Defectos (if any) (2) the predicted value of Defectos using the fitted model (3) 95.0% confidence limits for the mean responseEach item corresponds to the values of the experimental factors in aspecific row of your data file. To generate forecasts for additionalcombinations of the factors, add additional rows to the bottom of yourdata file. In each new row, enter values for the experimental factorsbut leave the cell for the response empty. When you return to thispane, forecasts will be added to the table for the new rows, but themodel will be unaffected.

Path of Steepest Ascent for Defectos (SN: smaller)

PredictedA B C D E Defectos (SN: smaller)---------- ---------- ---------- ---------- ---------- ------------1.5 1.5 1.5 1.5 1.5 -46.2787 2.5 7.42199 -18.4789 -6.85154 -4.19691 -105.083 3.5 13.344 -38.4577 -15.2031 -9.89383 -163.888 4.5 19.266 -58.4366 -23.5546 -15.5907 -222.693 5.5 25.1879 -78.4155 -31.9062 -21.2877 -281.497 6.5 31.1099 -98.3943 -40.2577 -26.9846 -340.302

The StatAdvisor--------------- This pane displays the path of steepest ascent (or descent). Thisis the path from the center of the current experimental region alongwhich the estimated response changes most quickly for the smallestchange in the experimental factors. It indicates good locations torun additional experiments if your goal is to increase or decreaseDefectos. Currently, 6 points have been generated by changing A inincrements of 1.0. You can specify the amount to change any onefactor by pressing the alternate mouse button and selecting PaneOptions. STATGRAPHICS will then determine how much all the otherfactors have to change to stay on the path of steepest ascent. Theprogram also computes the estimated Defectos at each of the pointsalong the path, which you can compare to your results if you run thosepoints.

Optimize Response-----------------Goal: maximize Defectos

Optimum value = -44.0384

Factor Low High Optimum-----------------------------------------------------------------------

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A 1.0 2.0 1.0 B 1.0 2.0 1.0 C 1.0 2.0 2.0 D 1.0 2.0 2.0 E 1.0 2.0 2.0

The StatAdvisor--------------- This table shows the combination of factor levels which maximizesDefectos over the indicated region. Use the Analysis Options dialogbox to indicate the region over which the optimization is to beperformed. You may set the value of one or more factors to a constantby setting the low and high limits to that value.

Colocarse en la pantalla de Resultados y con botón derecho accesar

Seleccionar Copy Analysis to StatReporter

Paso 9. Obtener el reporte gráfico del diseño de experimentos

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Main Effects Plot for Defectos (SN: smaller)

-48

-47.5

-47

-46.5

-46

-45.5

-45

Def

ecto

s (S

N: s

mal

ler)

AB

CD

E

Regression coeffs. for Defectos (SN: smaller)----------------------------------------------------------------------constant = -50.7274A:A = -0.109419B:B = -0.647976C:C = 2.18606D:D = 0.913815E:E = 0.623349----------------------------------------------------------------------

The StatAdvisor--------------- This pane displays the regression equation which has been fitted tothe data. The equation of the fitted model is

Defectos = -50.7274 - 0.109419*A - 0.647976*B + 2.18606*C + 0.913815*D+ 0.623349*E

where the values of the variables are specified in their originalunits. To have STATGRAPHICS evaluate this function, selectPredictions from the list of Tabular Options. To plot the function,select Response Plots from the list of Graphical Options.

No valid interaction specified.

Correlation Matrix for Estimated Effects

(1) (2) (3) (4) (5) (6)--------------------------------------------------------------(1)average 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000

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(2)A:A 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000(3)B:B 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000(4)C:C 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000(5)D:D 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000(6)E:E 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000--------------------------------------------------------------

The StatAdvisor--------------- The correlation matrix shows the extent of the confounding amongstthe effects. A perfectly orthogonal design will show a diagonalmatrix with 1's on the diagonal and 0's off the diagonal. Anynon-zero terms off the diagonal imply that the estimates of theeffects corresponding to that row and column will be correlated. Inthis case, there is no correlation amongst any of the effects. Thismeans that you will get clear estimates of all those effects.

Normal Probability Plot for Defectos (SN: smaller)

-0.8 0.2 1.2 2.2 3.2

Standardized effects

0.115

2050809599

99.9

perc

enta

ge

Estimation Results for Defectos (SN: smaller)---------------------------------------------------------------------- Observed Fitted Lower 95.0% CL Upper 95.0% CLRow Value Value for Mean for Mean---------------------------------------------------------------------- 1 -48.512 -47.7616 -52.2289 -43.2943 2 -43.6439 -44.0384 -48.5057 -39.5711 3 -47.2669 -46.8724 -51.3397 -42.4051 4 -45.4732 -46.2235 -50.6908 -41.7562 5 -46.2069 -46.9572 -51.4245 -42.4899 6 -45.4561 -45.0616 -49.5289 -40.5943 7 -47.5012 -47.8957 -52.363 -43.4284 8 -46.1695 -45.4191 -49.8864 -40.9518----------------------------------------------------------------------

The StatAdvisor--------------- This table contains information about values of Defectos generatedusing the fitted model. The table includes: (1) the observed value of Defectos (if any) (2) the predicted value of Defectos using the fitted model (3) 95.0% confidence limits for the mean responseEach item corresponds to the values of the experimental factors in aspecific row of your data file. To generate forecasts for additionalcombinations of the factors, add additional rows to the bottom of yourdata file. In each new row, enter values for the experimental factorsbut leave the cell for the response empty. When you return to thispane, forecasts will be added to the table for the new rows, but themodel will be unaffected.

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Estimated Response SurfaceC=1.5,D=1.5,E=1.5

1 1.2 1.4 1.6 1.8 2A

1 1.21.41.61.82

B-46.7

-46.5

-46.3

-46.1

-45.9

Def

ecto

s (S

N: s

mal

ler)

Path of Steepest Ascent for Defectos (SN: smaller)

PredictedA B C D E Defectos (SN: smaller)---------- ---------- ---------- ---------- ---------- ------------1.5 1.5 1.5 1.5 1.5 -46.2787 2.5 7.42199 -18.4789 -6.85154 -4.19691 -105.083 3.5 13.344 -38.4577 -15.2031 -9.89383 -163.888 4.5 19.266 -58.4366 -23.5546 -15.5907 -222.693 5.5 25.1879 -78.4155 -31.9062 -21.2877 -281.497 6.5 31.1099 -98.3943 -40.2577 -26.9846 -340.302

The StatAdvisor--------------- This pane displays the path of steepest ascent (or descent). Thisis the path from the center of the current experimental region alongwhich the estimated response changes most quickly for the smallestchange in the experimental factors. It indicates good locations torun additional experiments if your goal is to increase or decreaseDefectos. Currently, 6 points have been generated by changing A inincrements of 1.0. You can specify the amount to change any onefactor by pressing the alternate mouse button and selecting PaneOptions. STATGRAPHICS will then determine how much all the otherfactors have to change to stay on the path of steepest ascent. Theprogram also computes the estimated Defectos at each of the pointsalong the path, which you can compare to your results if you run thosepoints.

Contours of Estimated Response SurfaceC=1.5,D=1.5,E=1.5

1 1.2 1.4 1.6 1.8 2

A

1

1.2

1.4

1.6

1.8

2

B

Defectos (SN: smaller)-46.7-46.62-46.54-46.46-46.38-46.3-46.22-46.14-46.06-45.98-45.9

Optimize Response

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-----------------Goal: maximize Defectos

Optimum value = -44.0384

Factor Low High Optimum-----------------------------------------------------------------------A 1.0 2.0 1.0 B 1.0 2.0 1.0 C 1.0 2.0 2.0 D 1.0 2.0 2.0 E 1.0 2.0 2.0

The StatAdvisor--------------- This table shows the combination of factor levels which maximizesDefectos over the indicated region. Use the Analysis Options dialogbox to indicate the region over which the optimization is to beperformed. You may set the value of one or more factors to a constantby setting the low and high limits to that value.

Residual Plot for Defectos (SN: smaller)

0 100 200 300 400

predicted

-0.8

-0.4

0

0.4

0.8

resi

dual

Colocarse en la pantalla de Resultados y con botón derecho accesar

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Seleccionar Copy Analysis to StatReporter

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