Doe with response surface model
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Doe with response surface model

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Doe with response surface model Doe with response surface model Presentation Transcript

  • Factorial Design Full Factorial Design Factors: 3 Base Design: 3, 8 Runs: 21 Replicates: 2 Blocks: none Center pts (total): 5 Factor Name Low High A Fill Rate (RPM) 20 80 B Ramp Rate 5 75 C Suck Back 2 50 All terms are free from aliasing Data Matrix (randomized) Run A B C 1 0 0 0 2 0 0 0 3 + - - 4 - + + 5 + - - 6 + + - 7 0 0 0 8 0 0 0 9 0 0 0 10 + - + 11 - - + 12 + + + 13 - - - 14 - + + 15 - + - 16 - + - 17 - - +
  • 18 - - - 19 + - + 20 + + - 21 + + + Factorial Fit: Means of rep versus Fill Rate (R, Ramp Rate, Suck Back Estimated Effects and Coefficients for Means of repeats (coded units) Term Effect Coef SE Coef T P Constant 2.7674 0.007729 358.06 0.000 Fill Rate (RPM) -0.0579 -0.0289 0.007729 -3.74 0.003 Ramp Rate -0.0148 -0.0074 0.007729 -0.96 0.358 Suck Back -0.7130 -0.3565 0.007729 -46.13 0.000 Fill Rate (RPM)*Ramp Rate -0.0242 -0.0121 0.007729 -1.56 0.144 Fill Rate (RPM)*Suck Back 0.0345 0.0172 0.007729 2.23 0.046 Ramp Rate*Suck Back -0.0082 -0.0041 0.007729 -0.53 0.604 Fill Rate (RPM)*Ramp Rate*Suck Back 0.0174 0.0087 0.007729 1.12 0.283 Ct Pt -0.0619 0.015840 -3.90 0.002 S = 0.0309159 R-Sq = 99.45% R-Sq(adj) = 99.08% Analysis of Variance for Means of repeats (coded units) Estimated Coefficients for Means of repeats using data in uncoded units Term Coef Constant 3.19539 Fill Rate (RPM) -7.68041E-04 Ramp Rate 0.000939980 Suck Back -0.0151664
  • Fill Rate (RPM)*Ramp Rate -2.04752E-05 Fill Rate (RPM)*Suck Back 1.01513E-05 Ramp Rate*Suck Back -2.21329E-05 Fill Rate (RPM)*Ramp Rate*Suck Back 3.44742E-07 Ct Pt -0.0618525 Effects Pareto for Means of repeats Alias Structure I Fill Rate (RPM) Ramp Rate Suck Back Fill Rate (RPM)*Ramp Rate Fill Rate (RPM)*Suck Back Ramp Rate*Suck Back Fill Rate (RPM)*Ramp Rate*Suck Back Source DF Seq SS Adj SS Adj MS F P Main Effects 3 2.04789 2.04789 0.682630 714.20 0.000 2-Way Interactions 3 0.00736 0.00736 0.002454 2.57 0.103 3-Way Interactions 1 0.00121 0.00121 0.001208 1.26 0.283 Curvature 1 0.01457 0.01457 0.014574 15.25 0.002 Residual Error 12 0.01147 0.01147 0.000956 Pure Error 12 0.01147 0.01147 0.000956 Total 20 2.08250 Unusual Observations for Means of repeats Means of Obs StdOrder repeats Fit SE Fit Residual St Resid 7 20 2.63580 2.70556 0.01383 -0.06976 -2.52R R denotes an observation with a large standardized residual.
  • Term St andardized Effect BC B ABC AB AC A C 50403020100 2.18 Factor Name A Fill Rate (RPM) B Ramp Rate C Suck Back Pareto Chart of the Standardized Effects (response is Means of repeats, Alpha = .05) Reduced Model Factorial Fit: Means of repeats versus Fill Rate (RPM), Suck Back Estimated Effects and Coefficients for Means of repeats (coded units) Term Effect Coef SE Coef T P Constant 2.7674 0.007945 348.33 0.000 Fill Rate (RPM) -0.0579 -0.0289 0.007945 -3.64 0.002 Suck Back -0.7130 -0.3565 0.007945 -44.87 0.000 Fill Rate (RPM)*Suck Back 0.0345 0.0172 0.007945 2.17 0.045 Ct Pt -0.0619 0.016282 -3.80 0.002
  • S = 0.0317791 R-Sq = 99.22% R-Sq(adj) = 99.03% Analysis of Variance for Means of repeats (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 2 2.04702 2.04702 1.02351 1013.46 0.000 2-Way Interactions 1 0.00475 0.00475 0.00475 4.71 0.045 Curvature 1 0.01457 0.01457 0.01457 14.43 0.002 Residual Error 16 0.01616 0.01616 0.00101 Pure Error 16 0.01616 0.01616 0.00101 Total 20 2.08250 Unusual Observations for Means of repeats Means Estimated Coefficients for Means of repeats using data in uncoded units Term Coef Constant 3.23299 Fill Rate (RPM) -0.00158705 Suck Back -0.0160517 Fill Rate (RPM)*Suck Back 2.39410E-05 Ct Pt -0.0618525 Effects Pareto for Means of repeats Alias Structure I Fill Rate (RPM) Suck Back Fill Rate (RPM)*Suck Back of Obs StdOrder repeats Fit SE Fit Residual St Resid 7 20 2.63580 2.70556 0.01421 -0.06976 -2.45R R denotes an observation with a large standardized residual.
  • Term St andardized Effect AC A C 50403020100 2.12 Factor Name A Fill Rate (RPM) C Suck Back Pareto Chart of the Standardized Effects (response is Means of repeats, Alpha = .05)
  • Residual Percent 0.080.040.00-0.04-0.08 99 90 50 10 1 Fitted Value Residual 3.23.02.82.62.4 0.06 0.03 0.00 -0.03 -0.06 Residual Frequency 0.060.040.020.00-0.02-0.04-0.06 6.0 4.5 3.0 1.5 0.0 Obser vation Or der Residual 2018161412108642 0.06 0.03 0.00 -0.03 -0.06 Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values Hist ogram of t he Residuals Residuals Versus t he Order of t he Dat a Residual Plots for Means of repeats
  • MeanofMeansofrepeats 805020 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 50262 Fill Rate (RPM) Suck Back Point Type Corner Center Main Effects Plot (data means) for Means of repeats
  • MeanofMeansofrepeats 805020 3.2 3.0 2.8 2.6 2.4 75405 50262 3.2 3.0 2.8 2.6 2.4 Fill Rate (RPM) Ramp Rate Suck Back Point Type Corner Center Main Effects Plot (data means) for Means of repeats
  • Suck Back Mean 50262 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 Fill 50 Center 80 Corner Rate (RPM) Point Type 20 Corner I nteraction Plot (data means) for Means of repeats
  • Fill Rat e ( RPM ) Ram p Rat e Suck Back 75405 50262 3.00 2.75 2.50 3.00 2.75 2.50 Fill 50 Center 80 Corner Rate (RPM) Point Type 20 Corner Ramp 40 Center 75 Corner Rate Point Type 5 Corner I nteraction Plot (data means) for Means of repeats
  • 50 2 8020 Suck Back Fill Rate (RPM) 2.70556 2.39920 3.077753.17010 2.42260 Centerpoint Factorial Point Cube Plot (data means) for Means of repeats
  • 50 2 75 5 8020 Suck Back Ramp Rate Fill Rate (RPM) 2.70556 2.38430 2.414102.43070 2.41450 3.05370 3.101803.15260 3.18760 Centerpoint Factorial Point Cube Plot (data means) for Means of repeats Response Surface Regression: Means of rep versus Fill Rate (R, Ramp Rate, ... The following terms cannot be estimated, and were removed. Ramp Rate*Ramp Rate Suck Back*Suck Back The analysis was done using coded units. Estimated Regression Coefficients for Means of repeats Term Coef SE Coef T P Constant 2.70556 0.013965 193.733 0.000 Fill Rate (RPM) -0.02894 0.007807 -3.707 0.003 Ramp Rate -0.00739 0.007807 -0.946 0.361
  • Suck Back -0.35651 0.007807 -45.666 0.000 Fill Rate (RPM)*Fill Rate (RPM) 0.06185 0.015999 3.866 0.002 Fill Rate (RPM)*Ramp Rate -0.01209 0.007807 -1.548 0.146 Fill Rate (RPM)*Suck Back 0.01724 0.007807 2.208 0.046 Ramp Rate*Suck Back -0.00411 0.007807 -0.527 0.607 S = 0.03123 R-Sq = 99.4% R-Sq(adj) = 99.1% Analysis of Variance for Means of repeats Source DF Seq SS Adj SS Adj MS F P Regression 7 2.06983 2.06983 0.295690 303.22 0.000 Linear 3 2.04789 2.04789 0.682630 700.02 0.000 Square 1 0.01457 0.01457 0.014574 14.95 0.002 Interaction 3 0.00736 0.00736 0.002454 2.52 0.104 Residual Error 13 0.01268 0.01268 0.000975 Lack-of-Fit 1 0.00121 0.00121 0.001208 1.26 0.283 Pure Error 12 0.01147 0.01147 0.000956 Total 20 2.08250 Unusual Observations for Means of repeats Estimated Regression Coefficients for Means of repeats using data in uncoded units Term Coef Constant 3.32327 Fill Rate (RPM) -0.00799907 Ramp Rate 0.000491815 Suck Back -0.0158559 Fill Rate (RPM)*Fill Rate (RPM) 6.87250E-05 Fill Rate (RPM)*Ramp Rate -1.15119E-05 Fill Rate (RPM)*Suck Back 2.39410E-05 Ramp Rate*Suck Back -4.89583E-06 Means of Obs StdOrder repeats Fit SE Fit Residual St Resid 7 20 2.636 2.706 0.014 -0.070 -2.50 R R denotes an observation with a large standardized residual. Reduced Model
  • Response Surface Regression: Means of repeats versus Fill Rate (RPM), Suck Back The following terms cannot be estimated, and were removed. Suck Back*Suck Back The analysis was done using coded units. Estimated Regression Coefficients for Means of repeats Term Coef SE Coef T P Constant 2.70556 0.014212 190.371 0.000 Fill Rate (RPM) -0.02894 0.007945 -3.642 0.002 Suck Back -0.35651 0.007945 -44.874 0.000 Fill Rate (RPM)*Fill Rate (RPM) 0.06185 0.016282 3.799 0.002 Fill Rate (RPM)*Suck Back 0.01724 0.007945 2.170 0.045 S = 0.03178 R-Sq = 99.2% R-Sq(adj) = 99.0% Analysis of Variance for Means of repeats Source DF Seq SS Adj SS Adj MS F P Regression 4 2.06634 2.06634 0.51659 511.52 0.000 Linear 2 2.04702 2.04702 1.02351 1013.46 0.000 Square 1 0.01457 0.01457 0.01457 14.43 0.002 Interaction 1 0.00475 0.00475 0.00475 4.71 0.045 Residual Error 16 0.01616 0.01616 0.00101 Pure Error 16 0.01616 0.01616 0.00101 Total 20 2.08250 Unusual Observations for Means of repeats Means of Obs StdOrder repeats Fit SE Fit Residual St Resid 7 20 2.636 2.706 0.014 -0.070 -2.45 R R denotes an observation with a large standardized residual. Estimated Regression Coefficients for Means of repeats using data in uncoded units Term Coef Constant 3.34295 Fill Rate (RPM) -0.00845955
  • Suck Back -0.0160517 Fill Rate (RPM)*Fill Rate (RPM) 6.87250E-05 Fill Rate (RPM)*Suck Back 2.39410E-05 80 60 Means of r epeats 2.50 2.75 3.00 3.25 Fill Rate ( RPM)400 15 2030 45 Suck Back Surface Plot of Means of repeats vs Fill Rate (RPM), Suck Back
  • Suck Back FillRate(RPM) 5040302010 80 70 60 50 40 30 20 Means of 2.55 - 2.70 2.70 - 2.85 2.85 repeats - 3.00 3.00 - 3.15 > 3.15 < 2.40 2.40 - 2.55 Contour Plot of Means of repeats vs Fill Rate (RPM), Suck Back Reduced Model Response Surface Regression: Means of repeats versus Fill Rate (RPM), Suck Back The analysis was done using coded units. Estimated Regression Coefficients for Means of repeats Term Coef SE Coef T P Constant 2.70556 0.014212 190.371 0.000 Fill Rate (RPM) -0.02894 0.007945 -3.642 0.002 Suck Back -0.35651 0.007945 -44.874 0.000 Fill Rate (RPM)*Fill Rate (RPM) 0.06185 0.016282 3.799 0.002
  • Fill Rate (RPM)*Suck Back 0.01724 0.007945 2.170 0.045 S = 0.03178 R-Sq = 99.2% R-Sq(adj) = 99.0% Analysis of Variance for Means of repeats Source DF Seq SS Adj SS Adj MS F P Regression 4 2.06634 2.06634 0.51659 511.52 0.000 Linear 2 2.04702 2.04702 1.02351 1013.46 0.000 Square 1 0.01457 0.01457 0.01457 14.43 0.002 Interaction 1 0.00475 0.00475 0.00475 4.71 0.045 Residual Error 16 0.01616 0.01616 0.00101 Pure Error 16 0.01616 0.01616 0.00101 Total 20 2.08250 Unusual Observations for Means of repeats Means of Obs StdOrder repeats Fit SE Fit Residual St Resid 7 20 2.636 2.706 0.014 -0.070 -2.45 R R denotes an observation with a large standardized residual. Estimated Regression Coefficients for Means of repeats using data in uncoded units Term Coef Constant 3.34295 Fill Rate (RPM) -0.00845955 Suck Back -0.0160517 Fill Rate (RPM)*Fill Rate (RPM) 6.87250E-05 Fill Rate (RPM)*Suck Back 2.39410E-05 Equation for the Model = 3.34295 – 0.00845955 Fill Rate (RPM) – 0.0160517 Suck Back + 6.87250E-05 Fill Rate (RPM)*Fill Rate (RPM) + 2.39410E-05 Fill Rate (RPM)*Suck Back One-way ANOVA: Avg4, Avg3, Avg2, Avg1 Source DF SS MS F P Factor 3 0.0234 0.0078 0.08 0.971 Error 78 7.6049 0.0975 Total 81 7.6283
  • S = 0.3122 R-Sq = 0.31% R-Sq(adj) = 0.00% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ---+---------+---------+---------+------ Avg4 21 2.7256 0.3146 (-------------*------------) Avg3 20 2.7124 0.3064 (-------------*-------------) Avg2 20 2.7384 0.3050 (-------------*-------------) Avg1 21 2.7580 0.3221 (-------------*------------) ---+---------+---------+---------+------ 2.60 2.70 2.80 2.90 Pooled StDev = 0.3122 Dat a Frequency 3.43.23.02.82.62.42.22.0 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Mean 2.738 0.3050 20 2.758 0.3221 21 StDev N 2.726 0.3146 21 2.712 0.3064 20 Variable Avg4 Avg3 Avg2 Avg1 Histogram of Avg4, Avg3, Avg2, Avg1 Normal