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títuloBibliografía introduccióN
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Linear Model Analysis: Slopes versus A, B, C, D, E, F, G, H

Estimated Model Coefficients for Slopes

Term Coef SE Coef T P

Constant 2.67159 0.03261 81.920 0.000

A 1 -0.00650 0.03261 -0.199 0.860

B 1 -0.08881 0.04612 -1.926 0.194

B 2 0.15085 0.04612 3.271 0.082

C 1 0.11084 0.04612 2.403 0.138

C 2 -0.06683 0.04612 -1.449 0.284

D 1 -0.07792 0.04612 -1.689 0.233

D 2 0.00042 0.04612 0.009 0.994

E 1 -0.04712 0.04612 -1.022 0.414

E 2 0.01610 0.04612 0.349 0.760

F 1 -0.05220 0.04612 -1.132 0.375

F 2 0.01583 0.04612 0.343 0.764

G 1 0.08310 0.04612 1.802 0.213

G 2 -0.11065 0.04612 -2.399 0.139

H 1 0.07595 0.04612 1.647 0.241

H 2 0.12928 0.04612 2.803 0.107
S = 0.1384 R-Sq = 96.1% R-Sq(adj) = 66.9%

Analysis of Variance for Slopes

Source DF Seq SS Adj SS Adj MS F P

A 1 0.000761 0.000761 0.000761 0.04 0.860

B 2 0.206938 0.206938 0.103469 5.40 0.156

C 2 0.112135 0.112135 0.056067 2.93 0.255

D 2 0.072464 0.072464 0.036232 1.89 0.346

E 2 0.020653 0.020653 0.010327 0.54 0.650

F 2 0.025787 0.025787 0.012893 0.67 0.598

G 2 0.119449 0.119449 0.059725 3.12 0.243

H 2 0.387591 0.387591 0.193796 10.12 0.090

Residual Error 2 0.038288 0.038288 0.019144

Total 17 0.984066

Response Table for Signal to Noise Ratios

Dynamic Response
Level A B C D E F G H

1 -15.35 -17.57 -17.77 -16.06 -17.64 -16.96 -16.89 -16.10

2 -18.69 -16.94 -16.55 -17.82 -16.31 -17.39 -16.35 -16.95

3 -16.54 -16.74 -17.18 -17.11 -16.71 -17.82 -18.00

Delta 3.33 1.03 1.21 1.76 1.32 0.69 1.46 1.90

Rank 1 7 6 3 5 8 4 2

Response Table for Slopes

Level A B C D E F G H

1 2.665 2.583 2.782 2.594 2.624 2.619 2.755 2.748

2 2.678 2.822 2.605 2.672 2.688 2.687 2.561 2.801

3 2.610 2.628 2.749 2.703 2.708 2.699 2.466

Delta 0.013 0.240 0.178 0.155 0.078 0.089 0.194 0.335

Rank 8 2 4 5 7 6 3 1


Exp. No.SNRA2SLOPE21-12.962.604151**1**2-12.932.495632**2**3-15.12.434693**3**4-16.772.728994**4**5-14.593.001855**5**6-15.232.794626**6**7-19.042.426587**7**8-15.672.720018**8**9-15.892.779279**9**10-21.272.8545710**10**11-21.12.6553911**11**12-22.092.4522712**12**13-20.663.0499613**13**14-19.892.6603114**14**15-14.512.698915**15**16-15.913.0303416**16**17-15.142.0953517**17**18-17.612.6057718**18**

Las graficas factoriales son las siguientes:





La media de las S/N es – 17.020

La S/N pronosticada con los niveles que maximizan la relación S/N son:

S/N = -16.31-16.35-16.1-5(-17.020) = -11.64
El factor B tiene efecto significativo en la sensibilidad pero no tiene efecto en el S/N por lo que se selecciona en su nivel alto para aumentar la sensibilidad (mayor resolución), por tanto para Beta se tiene:


Beta = 2.66+2.82+2.61+2.60+2.69+2.75 – 6(2.67) = 2.76

Utilizando la Opción de Minitab:

Stat > DOE > Taguchi > Predict Taguchi Results

Predict Slope Signal to noise ratio

Terms A C D E G H

Levels: Select levels from a list 1 2 1 2 2 1

OK
Predicted values

S/N Ratio Slope

  • 11.6363 2.50174


Factor levels for predictions

A C D E G H

1 2 1 2 2 1
Ejemplo 5.2: Mejora del sistema de sello de hule de puerta

Se usa un hule para sellar la puerta de un automóvil, con dos características, esfuerzo para cerrar y ruido del aire ambiente que están en contradicción. La función ideal es como sigue:

Y = Presión/carga



Función ideal
M1 M2 Mk M = Factor de Señal

Desplazamiento hacia adentro del hule
Los factores de ruido son:

N1Ambiente húmedoN2Ambiente secoQ1Flujo lento de aireQ2Flujo medio de aireQ3Flujo alto de aire

Los factores de control son los siguientes:

Factores de controlNivel 1Nivel 2Nivel 3Nivel 4Nivel 5Nivel 6A MaterialEsponja bajaEsponja mediaEsponja altaDensa bajaDensa mediaDensa altaB RecubrimientoNingunoTipo 1Tipo 2   C Forma de esquinaRadio pequeñoRadio grandePlano   D VentilaciónNingunoGrandePequeña   E Forma bulboRedondeadoCuadradoTriangular   F AccesoriosCintaPinCarrillera   

El arreglo a usar es el L18 mostrado a continuación:
L18Factores de controlExp. ABCDEF111111121222223133333421122352223316233112731213383232119331322104133211142113212432213135123121452312315531231166132321762131318632121

El arreglo externo y los datos obtenidos se muestran en la tabla siguiente:
L18M1M2M3Exp. Q1Q2Q3Q1Q2Q3Q1Q2Q3No.N1N2N1N2N1N2N1N2N1N2N1N2N1N2N1N2N1N211.789.151.789.862.3712.682.523.634.726.656.298.164.45.846.486.636.259.6420000003.624.593.624.593.824.593.384.723.384.723.384.7234.117.323.3810.93.6210.347.077.436.3410.316.8811.754.144.264.535.914.926.7344.675.044.679.245.619.2410.6826.5311.1728.5711.6529.596.659.747.2510.497.2510.86500.441.360.442.170.882.650.964.131.353.544.433.582.853.934.074.294.6161.6901.4101.690.742.081.152.341.912.732.674.743.424.743.854.93.8572.333.62.624.43.215.22.624.253.424.693.34.833.524.813.524.683.444.582.4710.753.579.813.029.356.611.726.612.68812.928.3525.278.1328.698.4630.62902.2703.7903.79010.36011.71013.5105.7906.841.349.47101.0201.2802.30.244.3506.7207.5106.228.778.119.478.3811.23111.683.21.682.491.683.556.0620.158.1321.178.2921.175.9613.066.5412.846.6914.221203.703.703.71.372.563.666.255.265.974.619.786.6610.378.711.74131.284.191.264.631.264.339.3812.169.8113.419.2913.8312.5113.9513.771514.5314.911400000000000.1200.693.251.433.771.84.2915000.7401.2302.7954.184.293.767.864.588.117.210.076.4610.07160000000.41.171.113.162.114.091.19.422.99.83.3110.79174.983.556.164.485.644.786.823.077.646.398.476.653.281.815.523.396.384.071801.9402.903.231.214.842.525.464.036.42.993.383.124.963.035.75

Las instrucciones en Minitab son las siguientes:
Stat > DOE > Taguchi > Create Taguchi design

Number of factors 6

Design L18 1 column 6 levels, 5 columns 3 levels

(display available designs Mixed 3 – 6 levels)

Seleccionar: Add a signal factor for dynamic characteristics

Factors Signal Factor Name M Levels 0.05 0.25 0.45

OK
Los datos se arreglan como sigue:

L18Q1N1Q1N2Q2N1Q2N2Q3N1Q3N211.789.151.789.862.3712.6812.523.634.726.656.298.1614.45.846.486.636.259.64200000023.624.593.624.593.824.5923.384.723.384.723.384.7234.117.323.3810.93.6210.3437.077.436.3410.316.8811.7534.144.264.535.914.926.7344.675.044.679.245.619.24410.6826.5311.1728.5711.6529.5946.659.747.2510.497.2510.86500.441.360.442.170.8852.650.964.131.353.544.4353.582.853.934.074.294.6161.6901.4101.690.7462.081.152.341.912.732.6764.743.424.743.854.93.8572.333.62.624.43.215.272.624.253.424.693.34.8373.524.813.524.683.444.582.4710.753.579.813.029.3586.611.726.612.68812.9288.3525.278.1328.698.4630.62902.2703.7903.799010.36011.71013.51905.7906.841.349.47101.0201.2802.30.24104.3506.7207.510106.228.778.119.478.3811.23111.683.21.682.491.683.55116.0620.158.1321.178.2921.17115.9613.066.5412.846.6914.221203.703.703.7121.372.563.666.255.265.97124.619.786.6610.378.711.74131.284.191.264.631.264.33139.3812.169.8113.419.2913.831312.5113.9513.771514.5314.91140000001400000.120140.693.251.433.771.84.2915000.7401.230152.7954.184.293.767.86154.588.117.210.076.4610.0716000000160.41.171.113.162.114.09161.19.422.99.83.3110.79174.983.556.164.485.644.78176.823.077.646.398.476.65173.281.815.523.396.384.071801.9402.903.23181.214.842.525.464.036.4182.993.383.124.963.035.75

Y se cargan al arreglo que genera Minitab:
ABCDEFDesplazamientoQ1N1Q1N2Q2N1Q2N2Q3N1Q3N2SNRA4SLOPE4INT41111110.051.789.151.789.862.3712.6811.613417.1501111110.252.523.634.726.656.298.16***1111110.454.45.846.486.636.259.64***1222220.0500000019.448210.6801222220.253.624.593.624.593.824.59***1222220.453.384.723.384.723.384.72***1333330.054.117.323.3810.93.6210.3410.906917.5401333330.257.077.436.3410.316.8811.75***1333330.454.144.264.535.914.926.73***2112230.054.675.044.679.245.619.2410.876134.2502112230.2510.6826.5311.1728.5711.6529.59***2112230.456.659.747.2510.497.2510.86***2223310.0500.441.360.442.170.8819.03929.36302223310.252.650.964.131.353.544.43***2223310.453.582.853.934.074.294.61***2331120.051.6901.4101.690.7422.54419.32802331120.252.081.152.341.912.732.67***2331120.454.743.424.743.854.93.85***3121330.052.333.62.624.43.215.214.308911.1303121330.252.624.253.424.693.34.83***3121330.453.524.813.524.683.444.5***3232110.052.4710.753.579.813.029.3515.287341.0403232110.256.611.726.612.68812.92***3232110.458.3525.278.1328.698.4630.62***3313220.0502.2703.7903.798.332612.4203313220.25010.36011.71013.51***3313220.4505.7906.841.349.47***4133210.051.0201.2802.30.2417.497217.6704133210.254.3506.7207.510***4133210.456.228.778.119.478.3811.23***4211320.051.683.21.682.491.683.5513.499330.3104211320.256.0620.158.1321.178.2921.17***4211320.455.9613.066.5412.846.6914.22***4322130.0503.703.703.718.706618.7904322130.251.372.563.666.255.265.97***4322130.454.619.786.6610.378.711.74***5123120.051.284.191.264.631.264.3323.020334.8405123120.259.3812.169.8113.419.2913.83***5123120.4512.5113.9513.771514.5314.91***5231230.0500000012.06584.28905231230.2500000.120***5231230.450.693.251.433.771.84.29***5312310.05000.7401.23020.935617.4405312310.252.7954.184.293.767.86***5312310.454.588.117.210.076.4610.07***6132320.0500000013.663412.3406132320.250.41.171.113.162.114.09***6132320.451.19.422.99.83.3110.79***6213130.054.983.556.164.485.644.7811.593213.8606213130.256.823.077.646.398.476.65***6213130.453.281.815.523.396.384.07***6321210.0501.9402.903.2315.130510.5706321210.251.214.842.525.464.036.4***6321210.452.993.383.124.963.035.75***

El análisis se realiza con las siguientes instrucciones de Minitab:

Stat > Taguchi > Analyze Taguchi Design Response Data in:

Q1N1Q1N2Q2N1Q2N2Q3N1Q3N2

Graphs: Signal to noise ratios / Slopes

Analysis: Signal to noise ratios / Slopes

Terms: A B C D E F

Analysis graphs: Normal plot of residues

Options: Fit all lines trhough a fixed point 0 0

Storage: Signal to noise ratios / Slopes

OK
La tabla de resultados manual es:

L18Factores de controlExp. ABCDEFSensibilidadS/N111111117.2511.72212222210.61.

19.47313333317.0910.85421122333.2710.6552223319.3219.0062331129.3122.50731213310.9914.20832321140.6815.21933132211.847.921041332117.5717.451142113228.8913.381243221318.7118.651351231234.7823.01145231234.2011.891553123117.3920.891661323212.1813.551762131313.5811.401863212110.4715.05

La salida de Minitab es la siguiente:

Taguchi Analysis: Q1N1, Q1N2, Q2N1, Q2N2, Q3N1, Q3N2 versus A, B, C, D, E, F

Linear Model Analysis: SN ratios versus A, B, C, D, E, F

Taguchi Analysis: Q1N1, Q1N2, Q2N1, Q2N2, Q3N1, Q3N2 versus A, B, C, D, E, F

Linear Model Analysis: SN ratios versus A, B, C, D, E, F

Estimated Model Coefficients for SN ratios

Term Coef SE Coef T P

Constant 15.4705 1.154 13.407 0.006

A 1 -1.4809 2.580 -0.574 0.624

A 2 2.0160 2.580 0.781 0.516

A 3 -2.8275 2.580 -1.096 0.387

A 4 1.0972 2.580 0.425 0.712

A 5 3.2034 2.580 1.242 0.340

B 1 -0.3073 1.632 -0.188 0.868

B 2 -0.3150 1.632 -0.193 0.865

C 1 -2.6621 1.632 -1.631 0.244

C 2 2.8051 1.632 1.719 0.228

D 1 -0.6102 1.632 -0.374 0.744

D 2 1.0157 1.632 0.622 0.597

E 1 1.6570 1.632 1.015 0.417

E 2 -1.5787 1.632 -0.967 0.435

F 1 1.1134 1.632 0.682 0.565

F 2 1.2808 1.632 0.785 0.515
S = 4.896 R-Sq = 85.2% R-Sq(adj) = 0.0%

Analysis of Variance for SN ratios

Source DF Seq SS Adj SS Adj MS F P Porc. De contribución

A 5 89.252 89.252 17.850 0.74 0.659 27.6

B 2 3.485 3.485 1.742 0.07 0.932

C 2 89.856 89.856 44.928 1.87 0.348 27.63

D 2 9.411 9.411 4.705 0.20 0.836

E 2 31.465 31.465 15.733 0.66 0.604 9.6

F 2 51.676 51.676 25.838 1.08 0.481 16.0

Residual Error 2 47.932 47.932 23.966

Total 17 323.076
Linear Model Analysis: Slopes versus A, B, C, D, E, F

Estimated Model Coefficients for Slopes

Term Coef SE Coef T P

Constant 17.9453 5.081 3.532 0.072

A 1 -2.8211 11.361 -0.248 0.827

A 2 -0.2966 11.361 -0.026 0.982

A 3 3.5822 11.361 0.315 0.782

A 4 4.3130 11.361 0.380 0.741

A 5 0.9107 11.361 0.080 0.943

B 1 3.2861 7.186 0.457 0.692

B 2 0.3106 7.186 0.043 0.969

C 1 2.9605 7.186 0.412 0.720

C 2 -2.0493 7.186 -0.285 0.802

D 1 -4.1487 7.186 -0.577 0.622

D 2 4.4780 7.186 0.623 0.597

E 1 4.5558 7.186 0.634 0.591

E 2 -2.9629 7.186 -0.412 0.720

F 1 0.9281 7.186 0.129 0.909

F 2 0.3744 7.186 0.052 0.963
S = 21.56 R-Sq = 48.5% R-Sq(adj) = 0.0%

Analysis of Variance for Slopes

Source DF Seq SS Adj SS Adj MS F P

A 5 218.00 218.00 43.599 0.09 0.984

B 2 142.99 142.99 71.495 0.15 0.867

C 2 82.77 82.77 41.384 0.09 0.918

D 2 224.24 224.24 112.118 0.24 0.806

E 2 192.43 192.43 96.216 0.21 0.828

F 2 16.19 16.19 8.094 0.02 0.983

Residual Error 2 929.39 929.39 464.693

Total 17 1806.00

Response Table for Signal to Noise Ratios

Dynamic Response
Level A B C D E F

1 13.99 15.16 12.81 14.86 17.13 16.58

2 17.49 15.16 18.28 16.49 13.89 16.75

3 12.64 16.09 15.33 15.06 15.39 13.08

4 16.57

5 18.67

6 13.46

Delta 6.03 0.94 5.47 1.63 3.24 3.68

Rank 1 6 2 5 4 3

Response Table for Slopes

Level A B C D E F

1 15.12 21.23 20.91 13.80 22.50 18.87

2 17.65 18.26 15.90 22.42 14.98 18.32

3 21.53 14.35 17.03 17.62 16.35 16.64

4 22.26

5 18.86

6 12.26

Delta 10.00 6.88 5.01 8.63 7.52 2.23

Rank 1 4 5 2 3 6


Las graficas factoriales se muestran a continuación:



La S/N estimada seleccionando los factores significativos que maximizan la respuesta S/N es la siguiente:

S/N = 18.6+15.1+18.31+16.4+17.08+16.63-5(15.4) = 25.12

La Beta 1 estimada es:

Beta 1 = 18.79+21.04+15.81+22.16+22.4+18.8-5(17.69) = 30.55

Con la opción de Predicción de Minitab

Stat > DOE > Taguchi > Predict Taguchi Results

Predict Slope Signal to noise ratio

Terms A B C D E F

Levels: Select levels from a list 5 1 2 2 1

OK
Los resultados son los siguientes:
1   ...   8   9   10   11   12   13   14   15   16

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