SlideShare une entreprise Scribd logo
1  sur  38
Fractional Factorial Designs (I want acknowledge the teachings on DOE by the subject experts : Mr. Jim Quinlan on Fraction/Full Factorial Designs and Dr. Ranjit K. Roy on Taguchi.)
Fractional Factorial Designs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Fractional Factorial Designs – Learning Objectives ,[object Object],[object Object],[object Object]
Fractional Factorials ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Why Use Fractional Factorials ,[object Object],[object Object],[object Object],[object Object],The full factorial for 1 2-level factor and 7 3-level factors requires…   2 1  x 3 7  = 4374 test combinations. These same factors can be investigated using only 18 of the combinations. Example
Obtaining the Critical Information ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],Fractional Factorials - Confounding The interaction columns are generated, as before, by multiplying appropriate columns, and are used only in  the statistical analysis.
Confounding (continued) Notice the ABC column of all +1’s; the ABC effect can not be evaluated. Notice the A and BC columns are identical as are B and AC, C and AB. This means that when effects are computed the analysis will give: A effect = BC effect B effect = AC effect C effect = AB effect
Confounding (continued) This does not mean that the effects are equal, it means the design cannot separate them.  What is being measured is A + BC, B + AC, C + AB, the combined effects. We say A is confounded with BC and write it as:  A    BC, B    AC,  C    AB.  The actual effects being measured is called the Alias pattern.
Caution When Selecting Type of Experiment ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Hmmm…Is it the  Factor C effect? Or, the A x B Interaction?
Design Resolution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Selecting Design Resolution ,[object Object],[object Object],[object Object],[object Object],The standard approach for selecting which resolution design to use is:
Minitab & Confounding ,[object Object],[object Object],[object Object],[object Object],Click on  Designs Select 1/2 fraction Click OK then OK again. The design will be in columns 5, 6, 7 of the worksheet.  The alias pattern will be in the session window.
Minitab Output – Alias Structure Fractional Factorial Design Factors:  3  Base Design:  3, 4  Resolution: III Runs:  4  Replicates:  1  Fraction:  1/2 Blocks:  none  Center pts (total):  0 Some main effects are confounded with two-way  interactions Design Generators:  C = AB  Alias Structure I + ABC A + BC B + AC C + AB *** NOTE ***
Example – Injection Molding ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Comments About the Output Measure ,[object Object],[object Object],[object Object],[object Object],[object Object],What happens to “part strength” when stresses are uniformly distributed throughout the part? Often, the best way to improve strength and other problem-related measures is  not  to measure the problem directly.  Instead, measure and optimize the process’ intended function. Remember
[object Object],[object Object],[object Object],[object Object],Injection Molding – Selecting the Design Factors:  4  Base Design:  4, 8  Resolution: IV Runs:  16  Replicates:  2  Fraction:  1/2 Blocks:  none  Center pts (total):  0 Design Generators:  D = ABC  Alias Structure I + ABCD A + BCD B + ACD C + ABD D + ABC AB + CD AC + BD AD + BC
Injection Molding – Layout and Data ,[object Object],[object Object],Data is part strength.
Injection Molding – Significant Effects ,[object Object],Fractional Factorial Fit: Data versus Die Temp, Nozzle Temp, ... Estimated Effects and Coefficients for Data (coded units) Term  Effect Coef SE Coef T  P Constant  56.625  0.7235  78.27  0.000 Nozzle T  -1.500  -0.750  0.7235  -1.04  0.330 Die Temp*Nozzle T  5.250  2.625  0.7235  3.63  0.007 -0.750  -0.375  0.7235  -0.52  0.618 Die Temp* Inj. Pre  10.750  5.375  0.7235  -7.43  0.000 Die Temp  -10.000  -5.000  0.7235  -6.91  0.000 -19.500  -9.750  0.7235  -13.48  0.000 Inj. Pre  16.000  8.000  0.7235  11.06  0.000 Die Temp*Shot Siz Shot Siz
Injection Molding – Response Table ,[object Object],Least Squares Means for Data  -1  -1  48.25  1.447 1  -1  49.00  1.447 -1  1  75.00  1.447 1  1  54.25  1.447 Mean  SE Mean Die Temp (A) -1  61.63  1.023 1  51.63  1.023 Nozzle T (B) -1  57.38  1.023 1  55.88  1.023 Shot Siz (C) -1  66.38  1.023 1  46.88  1.023 Inj . Pre (D) -1  48.63  1.023 1  64.63  1.023 Die Temp* Inj . Pre Die Temp*Nozzle T -1  -1  65.00  1.447 1  -1  49.75  1.447 -1  1  58.25  1.447 1  1  53.50  1.447 Die Temp*Shot Siz -1  -1  71.00  1.447 1  -1  61.75  1.447 -1  1  52.25  1.447 1  1  41.50  1.447 Mean  SE Mean
Main Effects Graphs Data 1 - 1 1 - 1 1 - 1 1 - 1 6 6 6 1 5 6 5 1 4 6 Die Temp Nozzle Temp Shot Size Inj. Press Main Effects Plot (data means) for Data
Interaction Graphs Nozzle Temp A, B A, D 1 1 - 1 - 1 6 5 6 0 5 5 5 0 Mean Interaction Plot (data means) for Data Die Temp -1 1 1 1 - 1 - 1 7 0 6 0 5 0 I n j . P r e s s Interaction Plot (data means) for Data Mean Die Temp -1 1
Best Levels ,[object Object],[object Object],[object Object],To  maximize strength  the levels to be used are: The analysis picks A -1   B -1   C -1   D +1  to be the  combination to maximize strength.  Notice, it  was not one of the tested combinations.
Prediction ,[object Object],Regression Analysis: Data versus Die Temp, Shot Size, ... The regression equation is Data = 56.6 - 5.00 Die Temp - 9.75 Shot Size + 8.00 Inj . Press + 2.62 DTemp * NTemp - 5.38 DTemp * IPress Predicted Values for New Observations New  Obs Fit  SE Fit  95.0% CI  95.0% PI 1  87.375  1.713  (  83.558,  91.192)  (  80.066,  94.684) Values of Predictors for New Observations New  Obs Die Temp  Shot Siz  Inj . Pre DTemp *NT DTemp *IP 1  -1.00  -1.00  1.00  1.00  -1.00 The predicted average strength, 87.375, exceeds any in our test matrix.
Factors that Affect Variation ,[object Object],[object Object],[object Object]
Blocking ,[object Object],[object Object],What is the purpose of running the tests in this manner? Question For example, we may decide to run the ABC –   tests in the morning and the ABC +  tests in the afternoon. The highest order interaction column is used to create the block. 1 5 6 2 7 3 4 8 Run order A B C AB AC BC ABC 1 – – – + + + – 2 + – – – – + + 3 – + – – + – + 4 + + – + – – – 5 – – + + – – + 6 + – + – + – – 7 – + + – – + – 8 + + + + + + +
Fractional Factorials: 3-level factors ,[object Object],The factors will be confounded with interactions as in the 2-level fractionals, but in a more complex fashion.
Other Designs ,[object Object],[object Object],[object Object],Note All of these designs are available in Minitab.
Plackett-Burman Designs ,[object Object],[object Object],[object Object]
Plackett-Burman Designs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Central Composite Designs (C.C.D.) ,[object Object],[object Object]
Taguchi Designs ,[object Object],[object Object],Dr. Taguchi uses the L 12  and L 18  arrays to conduct optimization experiments.  Classical Design of Experiment techniques utilize these same arrays for screening. Note
L 12  O.A. Can handle up to eleven 2-level factors.
L 18  O.A Can handle one 2-level factor, and up to seven 3-level factors.
Variability Reduction Strategies ,[object Object],[object Object],1. Achieving robustness against noise using noise factor and Signal-to-Noise ratio. 2. Optimizing Ideal Function:  achieving maximum sensitivity to an input signal and robustness against noise.  (M is the input signal factor). A number of additional strategies accompany these experiments.  Since, however, Dr. Taguchi’s techniques are beyond the scope of this course, we limit our discussion to the classical techniques described in the next slide. Note ABDC… Orthogonal  Array ABCDE… Noise Level 1 Noise Level 2 S/N Orthogonal Array M 1 M 2 M 3 S/N N 1 N 2 N 1 N 2 N 1 N 2
Variability Reduction Strategies (continued) ,[object Object],1. Find factors that affect variation by analyzing standard deviations computed from replications or repetitions. 2. Same as #1 except take natural log of standard deviation. 3. Use a noise factor to induce variation, but still analyze with s or In s. A B   AxB Replications S Factorial Design A B   AxB Replications In S Factorial Design A B   AxB N 1 N 2 S Factorial Design
Strategy for Design Selection ,[object Object],Full factorials 1/2 fraction of a 2 5  full factorial (16 runs) Screening design (12 runs) Number of  factors K 2 K  design 1/2 • 2 5  design L 12 K  4 K=5 6  K  11
Strategy for Design Selection ,[object Object],All factors at 3-levels - some are qualitative Central composite design for model building Screening design Full factorials Screening design Number of factors K C.C.D. L 18 K  5 6  K  7 Number of factors K 3 K  design L 18 K  3 4  K  7

Contenu connexe

Tendances

Factorial design \Optimization Techniques
Factorial design \Optimization TechniquesFactorial design \Optimization Techniques
Factorial design \Optimization TechniquesPriyanka Tambe
 
Design of Experiments (Pharma)
Design of Experiments (Pharma)Design of Experiments (Pharma)
Design of Experiments (Pharma)VaishnaviBhosale6
 
Central Composite Design
Central Composite DesignCentral Composite Design
Central Composite DesignRuchir Shah
 
Design of experiment
Design of experimentDesign of experiment
Design of experimentbhargavi1603
 
factorial design.pptx
factorial design.pptxfactorial design.pptx
factorial design.pptxSreeLatha98
 
Design of experiments-Box behnken design
Design of experiments-Box behnken designDesign of experiments-Box behnken design
Design of experiments-Box behnken designGulamhushen Sipai
 
Blocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorialsBlocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorialsHimanshu Sharma
 
Response surface method
Response surface methodResponse surface method
Response surface methodIrfan Hussain
 
Applications of sas and minitab in data analysis
Applications of sas and minitab in data analysisApplications of sas and minitab in data analysis
Applications of sas and minitab in data analysisVeenaV29
 
Factorial design
Factorial designFactorial design
Factorial designGaurav Kr
 
QbD by central composite design
QbD by central composite designQbD by central composite design
QbD by central composite designsushmita rana
 
Optimization techniques in formulation Development Response surface methodol...
Optimization techniques in formulation Development  Response surface methodol...Optimization techniques in formulation Development  Response surface methodol...
Optimization techniques in formulation Development Response surface methodol...D.R. Chandravanshi
 
introduction to design of experiments
introduction to design of experimentsintroduction to design of experiments
introduction to design of experimentsKumar Virendra
 
design of experiments
design of experimentsdesign of experiments
design of experimentssigma-tau
 

Tendances (20)

Design of Experiments
Design of ExperimentsDesign of Experiments
Design of Experiments
 
Factorial Design.pptx
Factorial Design.pptxFactorial Design.pptx
Factorial Design.pptx
 
Factorial design \Optimization Techniques
Factorial design \Optimization TechniquesFactorial design \Optimization Techniques
Factorial design \Optimization Techniques
 
Design of Experiments (Pharma)
Design of Experiments (Pharma)Design of Experiments (Pharma)
Design of Experiments (Pharma)
 
factorial design
factorial designfactorial design
factorial design
 
Central Composite Design
Central Composite DesignCentral Composite Design
Central Composite Design
 
Design of experiment
Design of experimentDesign of experiment
Design of experiment
 
factorial design.pptx
factorial design.pptxfactorial design.pptx
factorial design.pptx
 
Design of experiments-Box behnken design
Design of experiments-Box behnken designDesign of experiments-Box behnken design
Design of experiments-Box behnken design
 
Blocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorialsBlocking and Confounding System for Two-level factorials
Blocking and Confounding System for Two-level factorials
 
Response surface method
Response surface methodResponse surface method
Response surface method
 
Applications of sas and minitab in data analysis
Applications of sas and minitab in data analysisApplications of sas and minitab in data analysis
Applications of sas and minitab in data analysis
 
Experimental design techniques
Experimental design techniquesExperimental design techniques
Experimental design techniques
 
Factorial design
Factorial designFactorial design
Factorial design
 
QbD by central composite design
QbD by central composite designQbD by central composite design
QbD by central composite design
 
Optimization techniques in formulation Development Response surface methodol...
Optimization techniques in formulation Development  Response surface methodol...Optimization techniques in formulation Development  Response surface methodol...
Optimization techniques in formulation Development Response surface methodol...
 
Optimization techniques
Optimization techniquesOptimization techniques
Optimization techniques
 
introduction to design of experiments
introduction to design of experimentsintroduction to design of experiments
introduction to design of experiments
 
design of experiments
design of experimentsdesign of experiments
design of experiments
 
2^3 factorial design in SPSS
2^3 factorial design in SPSS2^3 factorial design in SPSS
2^3 factorial design in SPSS
 

Similaire à Fractional Factorial Designs

Introduction To Taguchi Method
Introduction To Taguchi MethodIntroduction To Taguchi Method
Introduction To Taguchi MethodRamon Balisnomo
 
Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.
Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.
Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.SALMA RASHID SHAIKH
 
General Factor Factorial Design
General Factor Factorial DesignGeneral Factor Factorial Design
General Factor Factorial DesignNoraziah Ismail
 
Evaluation and optimization of variables using response surface methodology
Evaluation and optimization of variables using response surface methodologyEvaluation and optimization of variables using response surface methodology
Evaluation and optimization of variables using response surface methodologyMohammed Abdullah Issa
 
DOE in Pharmaceutical and Analytical QbD.
DOE in  Pharmaceutical and Analytical QbD.DOE in  Pharmaceutical and Analytical QbD.
DOE in Pharmaceutical and Analytical QbD.SALMA RASHID SHAIKH
 
Design of Experiments & Regression Analysis
Design of Experiments & Regression AnalysisDesign of Experiments & Regression Analysis
Design of Experiments & Regression AnalysisSagar Sable
 
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W3 Solver
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W3 SolverJavier Garcia - Verdugo Sanchez - Six Sigma Training - W3 Solver
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W3 SolverJ. García - Verdugo
 
qc-tools.ppt
qc-tools.pptqc-tools.ppt
qc-tools.pptAlpharoot
 
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points...
 Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points... Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points...
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points...J. García - Verdugo
 
DS-004-Robust Design
DS-004-Robust DesignDS-004-Robust Design
DS-004-Robust Designhandbook
 
Module 5 lecture_4_final
Module 5 lecture_4_finalModule 5 lecture_4_final
Module 5 lecture_4_finalAmol Wadghule
 
How to do ahp analysis in excel
How to do ahp analysis in excelHow to do ahp analysis in excel
How to do ahp analysis in excelJ.Roberto S.F
 
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docxSWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docxssuserf9c51d
 
Optimization technology and screening design sathish h t
Optimization technology and screening design sathish h tOptimization technology and screening design sathish h t
Optimization technology and screening design sathish h tSatishHT1
 
New 7QC tools for the quality person during RCa
New 7QC tools for the quality person during RCaNew 7QC tools for the quality person during RCa
New 7QC tools for the quality person during RCaAravindhNagaraj1
 

Similaire à Fractional Factorial Designs (20)

How to use statistica for rsm study
How to use statistica for rsm studyHow to use statistica for rsm study
How to use statistica for rsm study
 
DoE Project
DoE ProjectDoE Project
DoE Project
 
Introduction To Taguchi Method
Introduction To Taguchi MethodIntroduction To Taguchi Method
Introduction To Taguchi Method
 
Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.
Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.
Design Of Experiments (DOE) Applied To Pharmaceutical and Analytical QbD.
 
General Factor Factorial Design
General Factor Factorial DesignGeneral Factor Factorial Design
General Factor Factorial Design
 
Evaluation and optimization of variables using response surface methodology
Evaluation and optimization of variables using response surface methodologyEvaluation and optimization of variables using response surface methodology
Evaluation and optimization of variables using response surface methodology
 
DOE in Pharmaceutical and Analytical QbD.
DOE in  Pharmaceutical and Analytical QbD.DOE in  Pharmaceutical and Analytical QbD.
DOE in Pharmaceutical and Analytical QbD.
 
Design of Experiments & Regression Analysis
Design of Experiments & Regression AnalysisDesign of Experiments & Regression Analysis
Design of Experiments & Regression Analysis
 
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W3 Solver
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W3 SolverJavier Garcia - Verdugo Sanchez - Six Sigma Training - W3 Solver
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W3 Solver
 
qc-tools.ppt
qc-tools.pptqc-tools.ppt
qc-tools.ppt
 
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points...
 Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points... Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points...
Javier Garcia - Verdugo Sanchez - Six Sigma Training - W32 DOE Center Points...
 
DS-004-Robust Design
DS-004-Robust DesignDS-004-Robust Design
DS-004-Robust Design
 
Module 5 lecture_4_final
Module 5 lecture_4_finalModule 5 lecture_4_final
Module 5 lecture_4_final
 
How to do ahp analysis in excel
How to do ahp analysis in excelHow to do ahp analysis in excel
How to do ahp analysis in excel
 
Response Surface.pptx
Response Surface.pptxResponse Surface.pptx
Response Surface.pptx
 
Chap10 anova
Chap10 anovaChap10 anova
Chap10 anova
 
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docxSWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
 
Optimization technology and screening design sathish h t
Optimization technology and screening design sathish h tOptimization technology and screening design sathish h t
Optimization technology and screening design sathish h t
 
ansys tutorial
ansys tutorialansys tutorial
ansys tutorial
 
New 7QC tools for the quality person during RCa
New 7QC tools for the quality person during RCaNew 7QC tools for the quality person during RCa
New 7QC tools for the quality person during RCa
 

Fractional Factorial Designs

  • 1. Fractional Factorial Designs (I want acknowledge the teachings on DOE by the subject experts : Mr. Jim Quinlan on Fraction/Full Factorial Designs and Dr. Ranjit K. Roy on Taguchi.)
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8. Confounding (continued) Notice the ABC column of all +1’s; the ABC effect can not be evaluated. Notice the A and BC columns are identical as are B and AC, C and AB. This means that when effects are computed the analysis will give: A effect = BC effect B effect = AC effect C effect = AB effect
  • 9. Confounding (continued) This does not mean that the effects are equal, it means the design cannot separate them. What is being measured is A + BC, B + AC, C + AB, the combined effects. We say A is confounded with BC and write it as: A  BC, B  AC, C  AB. The actual effects being measured is called the Alias pattern.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14. Minitab Output – Alias Structure Fractional Factorial Design Factors: 3 Base Design: 3, 4 Resolution: III Runs: 4 Replicates: 1 Fraction: 1/2 Blocks: none Center pts (total): 0 Some main effects are confounded with two-way interactions Design Generators: C = AB Alias Structure I + ABC A + BC B + AC C + AB *** NOTE ***
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21. Main Effects Graphs Data 1 - 1 1 - 1 1 - 1 1 - 1 6 6 6 1 5 6 5 1 4 6 Die Temp Nozzle Temp Shot Size Inj. Press Main Effects Plot (data means) for Data
  • 22. Interaction Graphs Nozzle Temp A, B A, D 1 1 - 1 - 1 6 5 6 0 5 5 5 0 Mean Interaction Plot (data means) for Data Die Temp -1 1 1 1 - 1 - 1 7 0 6 0 5 0 I n j . P r e s s Interaction Plot (data means) for Data Mean Die Temp -1 1
  • 23.
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33. L 12 O.A. Can handle up to eleven 2-level factors.
  • 34. L 18 O.A Can handle one 2-level factor, and up to seven 3-level factors.
  • 35.
  • 36.
  • 37.
  • 38.

Notes de l'éditeur

  1. The purpose of injection molding is not to get part strength. Part strength is determined by raw material. The only thing that injection molding can do is hurt part strength. Therefore, I want to maximize/optimize the function of injection molding …. SHAPE. The strength will be improved when the function is improved. There is a big difference between theoretical experimenters and practical experimenters. Theoretical experimenters don’t care about the output measure, they are interested in all the affects/interactions with the output measure … all theory stuff. Practical experimenters want to optimize a process … they don’t want interactions and they want their output measure to be the function of the process (so that they can optimize it).
  2. Purpose of blocking, so that the block does not affect factor output. I can determine affect of the block and the affect of the factors independently.
  3. Interactions are spread throughout the matrix. Therefore, if a factor is significant it overpowers the interactions. For example, if you look at AB interaction, there are no other factors that confound with it (same with any other interaction).
  4. Ln(s) is actually a better measure than s because the distribution of variance is skewed (cant go below 0). If you use s you can actually have confidence intervals that give you negative s, which you cant get.