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  • DOE
    • 1. Introduction to Design of Experiments
      • 1. What is Design of Experiment
      • 2. Step 1 of DOE Introduction Hypothesis Research Question
      • 3. Step 2 of DOE Method
      • 4. Step 3 of DOE Results by Analyzing the Data
      • 5. Step 4 of DOE Contextual Conclusion
      • 6. Reference for Module 1 Intro to DOE
    • 2. Hypothesis Testing/ Inferential Statistics/ Analysis of Variance ANOVA
      • 0. All Data Module 2 Hypothesis Testing
      • 1. What is Hypothesis Testing
      • 2. Single Population Testing
      • 3. Single Sample Z-Test
      • 4. Single Sample T-Test
      • 5. Population Proportion Test Single Sample
      • 6. Comparing Two Populations Hypothesis Testing
      • 7. Two Sample Z-Test
      • 8. Two Sample T-Test Equal Variance
      • 9. Two Sample T-Test Unequal Variance
      • 10. Paired T-Test (Matched Pair/Repeated Measure)
      • 11. Two Sample Population Proportion Test
    • 3. One Way/Single Factor ANOVA
      • 0. All Data Module 3 CRD Single One-Way ANOVA
      • 1. What is One Way/Single Factor ANOVA
      • 2. Fixed Effect Model Analysis Basics for One-Way ANOVA
      • 3. Example One-Way/Single-Factor Fixed Effect Completely Randomized Design
      • 4. Diagnostic, Adequacy & Data Quality Check Fixed Effect One Way ANOVA
      • 5. Random Effect Model Analysis Bacis for One-Way ANOVA
      • 6. Example Problem Random Effect Model
      • 7. Diagnostic, Adequacy, & Data Quality Check Random Effect One Way ANOVA
      • 8. Reference
    • 4. Randomized Complete Block, Latin Square, and Graeco-Latin Design
      • 0. All Data Module 4 RCBD Graeco Latin Square Design
      • 1. What is Randomized Complete Block Design (RCBD)?
      • 2. Randomized Complete Block Design Example Problem
      • 3. Randomized Complete Block Design (RCBD) vs Completely Randomized Design
      • 4. Why Randomized Complete Block Design is so Popular?
      • 5. Latin Square Design of Experiments
      • 6. Latin Square Example Problem
      • 7. Graeco-Latin Square Design of Experiments
      • 8. Graeco-Latin Square Example Problem
      • 9. Reference
    • 5. Factorial Design of Experiments
      • 0. All Data Factorial Design of Experiment
      • 1. What is a Factorial Design of Experiment?
      • 2. Understanding Main Effects?
      • 3. Understanding Interaction Effects?
      • 4. How to Develop the Regression Equation from Effects?
      • 5. How to Fit a Response Surface?
      • 6. How to Construct the ANOVA Table from Effects?
      • 7. Practice Problem
    • 6. 2K Factorial Design of Experiments
      • 1. What is 2K Design
      • 2. Layout/Graphical Representation 22 Design
      • 3. Understanding Factor Effects
      • 4. Contrast, Effect, Estimate, Sum of Square, and ANOVA Table 22
      • 5. Practice Problem 22
      • 6. How to Design 2k Experiment
      • 7. Develop Treatment Combinations 2K Design
      • 8. Develop Generic Formulas 2K Design
      • 9. Manual Analysis Using MS Excel 2K Experiments
      • 10. MS Excel, Minitab, SPSS, and SAS
      • 11. Practice Problem 2k
      • 12. 2K Factorial Design of Experiments References
    • 7. Blocking and Confounding in 2K Design
      • 1. What is Blocking
      • 2. What is Confounding
      • 3. Confound an Effect Using -1/+1 Coding System
      • 4. How to Replicate
      • 5. Confound Two Effects Using -1/+1 Coding System
      • 6. Confound Three Effects Using -1/+1 Coding System
      • 7. Confounding and Blocking Using Linear Combination Method 0/1 Coding
      • 8. Confound Two Effects Using 0/1 Coding System
      • 9. Confound Three Effects with Eight Blocks Using the o/1 Coding System
      • 10. General Blocking and Confounding Scheme for 2k Design in 2p Blocks
      • 11. Complete versus Partial Confounding
      • 12. Reference Blocking and Confounding in 2K Design
    • 8. Fractional Factorial Design of Experiments
      • 1. What is it
      • 2. Primary Basics
      • 3. Design Resolution
      • 4. One-Quarter Fraction Design
      • 5. Alias structure
      • 6. One-Eighth Fraction Design
      • 7. Lowest Runs Design
      • 8. Analysis Example
      • 9. Plackett-Burman Design
      • 10. Reference Fractional Factorial Design of Experiments
    • 9. Applied Regression Analysis
      • 1. What is Regression Analysis
      • 2. Steps in Regression Analysis?
      • 3. Perform Regression Analysis
      • 4. Results Explained Regression Analysis
      • 4.1. Significance Test Regression Analysis
      • 4.2. Practical Test r-square: The Coefficient of Determination
      • 4.3. Functional Relationships Explained
      • 4.4. Diagnostics Regression Analysis
      • 4.4.1. Linearity Assumption Check
      • 4.4.2. Outlier, Leverage, and Influential Points Unusual Observations Check
      • 4.4.3. Residuals Analysis
      • 5. Lack-of-fit Test
      • 6. Practice Problem Regression
      • 7. Reference Regression
    • 10. Response Surface Methodology
      • 1. What is Response Surface Methodology
      • 2. Design Response Surface Methodology
      • 3. Analyze and Explain Response Surface Methodology
      • 4. Box-Behnken Response Surface Methodology
      • 5. Multiple Response Surface Design and Analysis
      • 6. Reference Response Surface Modeling
    • 11. Expected Mean Square EMS Basics to Advanced Design of Experiments
      • 11.1 Are You Performing the Correct ANOVA?
      • 11.2 EMS for All Fixed Factors Design
      • 11.3 EMS for All Random Factors Design
      • 11.4 Approximate or Pseudo F-Statistics/Tests
      • 11.5 EMS for Two Fixed and One Random Factors Design
      • 11.6 EMS for Fixed, Random and Nested Factors Design
      • 11.7 Expected Mean Square Using an Alternative Shortcut Method
      • 11.8 Restricted vs Unrestricted Models, Which is the Best One?
      • 11.9 References for EMS Module
    • 12. Mixed Factors Design of Experiments Nested Repeated Measure Split Plot
      • 12.1. Nested Hierarchical Design
      • 12.2. Repeated Measure Design
      • 12.3. Split-Plot Design
      • 12.4. Are Partially Nested, Repeated Measure and Split-Plot Designs differ
      • 12.5. Reference for Mixed Model Designs
    • 13. Taguchi Robust Parameter Design of Experiments
  • Econ
    • Econ Ch2
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    • Ergonomic Toolbox
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    • Fluid Power Lab Demo
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  • Assessment
    • Assessment of Student Learning Certificate
    • Program-Level Student Learning Assessment Certificate Training
  • CV/Resume
The Open Educator
  • Home
  • DOE
    • 1. Introduction to Design of Experiments
      • 1. What is Design of Experiment
      • 2. Step 1 of DOE Introduction Hypothesis Research Question
      • 3. Step 2 of DOE Method
      • 4. Step 3 of DOE Results by Analyzing the Data
      • 5. Step 4 of DOE Contextual Conclusion
      • 6. Reference for Module 1 Intro to DOE
    • 2. Hypothesis Testing/ Inferential Statistics/ Analysis of Variance ANOVA
      • 0. All Data Module 2 Hypothesis Testing
      • 1. What is Hypothesis Testing
      • 2. Single Population Testing
      • 3. Single Sample Z-Test
      • 4. Single Sample T-Test
      • 5. Population Proportion Test Single Sample
      • 6. Comparing Two Populations Hypothesis Testing
      • 7. Two Sample Z-Test
      • 8. Two Sample T-Test Equal Variance
      • 9. Two Sample T-Test Unequal Variance
      • 10. Paired T-Test (Matched Pair/Repeated Measure)
      • 11. Two Sample Population Proportion Test
    • 3. One Way/Single Factor ANOVA
      • 0. All Data Module 3 CRD Single One-Way ANOVA
      • 1. What is One Way/Single Factor ANOVA
      • 2. Fixed Effect Model Analysis Basics for One-Way ANOVA
      • 3. Example One-Way/Single-Factor Fixed Effect Completely Randomized Design
      • 4. Diagnostic, Adequacy & Data Quality Check Fixed Effect One Way ANOVA
      • 5. Random Effect Model Analysis Bacis for One-Way ANOVA
      • 6. Example Problem Random Effect Model
      • 7. Diagnostic, Adequacy, & Data Quality Check Random Effect One Way ANOVA
      • 8. Reference
    • 4. Randomized Complete Block, Latin Square, and Graeco-Latin Design
      • 0. All Data Module 4 RCBD Graeco Latin Square Design
      • 1. What is Randomized Complete Block Design (RCBD)?
      • 2. Randomized Complete Block Design Example Problem
      • 3. Randomized Complete Block Design (RCBD) vs Completely Randomized Design
      • 4. Why Randomized Complete Block Design is so Popular?
      • 5. Latin Square Design of Experiments
      • 6. Latin Square Example Problem
      • 7. Graeco-Latin Square Design of Experiments
      • 8. Graeco-Latin Square Example Problem
      • 9. Reference
    • 5. Factorial Design of Experiments
      • 0. All Data Factorial Design of Experiment
      • 1. What is a Factorial Design of Experiment?
      • 2. Understanding Main Effects?
      • 3. Understanding Interaction Effects?
      • 4. How to Develop the Regression Equation from Effects?
      • 5. How to Fit a Response Surface?
      • 6. How to Construct the ANOVA Table from Effects?
      • 7. Practice Problem
    • 6. 2K Factorial Design of Experiments
      • 1. What is 2K Design
      • 2. Layout/Graphical Representation 22 Design
      • 3. Understanding Factor Effects
      • 4. Contrast, Effect, Estimate, Sum of Square, and ANOVA Table 22
      • 5. Practice Problem 22
      • 6. How to Design 2k Experiment
      • 7. Develop Treatment Combinations 2K Design
      • 8. Develop Generic Formulas 2K Design
      • 9. Manual Analysis Using MS Excel 2K Experiments
      • 10. MS Excel, Minitab, SPSS, and SAS
      • 11. Practice Problem 2k
      • 12. 2K Factorial Design of Experiments References
    • 7. Blocking and Confounding in 2K Design
      • 1. What is Blocking
      • 2. What is Confounding
      • 3. Confound an Effect Using -1/+1 Coding System
      • 4. How to Replicate
      • 5. Confound Two Effects Using -1/+1 Coding System
      • 6. Confound Three Effects Using -1/+1 Coding System
      • 7. Confounding and Blocking Using Linear Combination Method 0/1 Coding
      • 8. Confound Two Effects Using 0/1 Coding System
      • 9. Confound Three Effects with Eight Blocks Using the o/1 Coding System
      • 10. General Blocking and Confounding Scheme for 2k Design in 2p Blocks
      • 11. Complete versus Partial Confounding
      • 12. Reference Blocking and Confounding in 2K Design
    • 8. Fractional Factorial Design of Experiments
      • 1. What is it
      • 2. Primary Basics
      • 3. Design Resolution
      • 4. One-Quarter Fraction Design
      • 5. Alias structure
      • 6. One-Eighth Fraction Design
      • 7. Lowest Runs Design
      • 8. Analysis Example
      • 9. Plackett-Burman Design
      • 10. Reference Fractional Factorial Design of Experiments
    • 9. Applied Regression Analysis
      • 1. What is Regression Analysis
      • 2. Steps in Regression Analysis?
      • 3. Perform Regression Analysis
      • 4. Results Explained Regression Analysis
      • 4.1. Significance Test Regression Analysis
      • 4.2. Practical Test r-square: The Coefficient of Determination
      • 4.3. Functional Relationships Explained
      • 4.4. Diagnostics Regression Analysis
      • 4.4.1. Linearity Assumption Check
      • 4.4.2. Outlier, Leverage, and Influential Points Unusual Observations Check
      • 4.4.3. Residuals Analysis
      • 5. Lack-of-fit Test
      • 6. Practice Problem Regression
      • 7. Reference Regression
    • 10. Response Surface Methodology
      • 1. What is Response Surface Methodology
      • 2. Design Response Surface Methodology
      • 3. Analyze and Explain Response Surface Methodology
      • 4. Box-Behnken Response Surface Methodology
      • 5. Multiple Response Surface Design and Analysis
      • 6. Reference Response Surface Modeling
    • 11. Expected Mean Square EMS Basics to Advanced Design of Experiments
      • 11.1 Are You Performing the Correct ANOVA?
      • 11.2 EMS for All Fixed Factors Design
      • 11.3 EMS for All Random Factors Design
      • 11.4 Approximate or Pseudo F-Statistics/Tests
      • 11.5 EMS for Two Fixed and One Random Factors Design
      • 11.6 EMS for Fixed, Random and Nested Factors Design
      • 11.7 Expected Mean Square Using an Alternative Shortcut Method
      • 11.8 Restricted vs Unrestricted Models, Which is the Best One?
      • 11.9 References for EMS Module
    • 12. Mixed Factors Design of Experiments Nested Repeated Measure Split Plot
      • 12.1. Nested Hierarchical Design
      • 12.2. Repeated Measure Design
      • 12.3. Split-Plot Design
      • 12.4. Are Partially Nested, Repeated Measure and Split-Plot Designs differ
      • 12.5. Reference for Mixed Model Designs
    • 13. Taguchi Robust Parameter Design of Experiments
  • Econ
    • Econ Ch2
  • Ergo
    • Ergonomic Toolbox
  • Fluid
    • Fluid Power Lab Demo
  • Mechanics
  • Operations
  • Project
  • Quality
  • Statics
  • Assessment
    • Assessment of Student Learning Certificate
    • Program-Level Student Learning Assessment Certificate Training
  • CV/Resume
  • More
    • Home
    • DOE
      • 1. Introduction to Design of Experiments
        • 1. What is Design of Experiment
        • 2. Step 1 of DOE Introduction Hypothesis Research Question
        • 3. Step 2 of DOE Method
        • 4. Step 3 of DOE Results by Analyzing the Data
        • 5. Step 4 of DOE Contextual Conclusion
        • 6. Reference for Module 1 Intro to DOE
      • 2. Hypothesis Testing/ Inferential Statistics/ Analysis of Variance ANOVA
        • 0. All Data Module 2 Hypothesis Testing
        • 1. What is Hypothesis Testing
        • 2. Single Population Testing
        • 3. Single Sample Z-Test
        • 4. Single Sample T-Test
        • 5. Population Proportion Test Single Sample
        • 6. Comparing Two Populations Hypothesis Testing
        • 7. Two Sample Z-Test
        • 8. Two Sample T-Test Equal Variance
        • 9. Two Sample T-Test Unequal Variance
        • 10. Paired T-Test (Matched Pair/Repeated Measure)
        • 11. Two Sample Population Proportion Test
      • 3. One Way/Single Factor ANOVA
        • 0. All Data Module 3 CRD Single One-Way ANOVA
        • 1. What is One Way/Single Factor ANOVA
        • 2. Fixed Effect Model Analysis Basics for One-Way ANOVA
        • 3. Example One-Way/Single-Factor Fixed Effect Completely Randomized Design
        • 4. Diagnostic, Adequacy & Data Quality Check Fixed Effect One Way ANOVA
        • 5. Random Effect Model Analysis Bacis for One-Way ANOVA
        • 6. Example Problem Random Effect Model
        • 7. Diagnostic, Adequacy, & Data Quality Check Random Effect One Way ANOVA
        • 8. Reference
      • 4. Randomized Complete Block, Latin Square, and Graeco-Latin Design
        • 0. All Data Module 4 RCBD Graeco Latin Square Design
        • 1. What is Randomized Complete Block Design (RCBD)?
        • 2. Randomized Complete Block Design Example Problem
        • 3. Randomized Complete Block Design (RCBD) vs Completely Randomized Design
        • 4. Why Randomized Complete Block Design is so Popular?
        • 5. Latin Square Design of Experiments
        • 6. Latin Square Example Problem
        • 7. Graeco-Latin Square Design of Experiments
        • 8. Graeco-Latin Square Example Problem
        • 9. Reference
      • 5. Factorial Design of Experiments
        • 0. All Data Factorial Design of Experiment
        • 1. What is a Factorial Design of Experiment?
        • 2. Understanding Main Effects?
        • 3. Understanding Interaction Effects?
        • 4. How to Develop the Regression Equation from Effects?
        • 5. How to Fit a Response Surface?
        • 6. How to Construct the ANOVA Table from Effects?
        • 7. Practice Problem
      • 6. 2K Factorial Design of Experiments
        • 1. What is 2K Design
        • 2. Layout/Graphical Representation 22 Design
        • 3. Understanding Factor Effects
        • 4. Contrast, Effect, Estimate, Sum of Square, and ANOVA Table 22
        • 5. Practice Problem 22
        • 6. How to Design 2k Experiment
        • 7. Develop Treatment Combinations 2K Design
        • 8. Develop Generic Formulas 2K Design
        • 9. Manual Analysis Using MS Excel 2K Experiments
        • 10. MS Excel, Minitab, SPSS, and SAS
        • 11. Practice Problem 2k
        • 12. 2K Factorial Design of Experiments References
      • 7. Blocking and Confounding in 2K Design
        • 1. What is Blocking
        • 2. What is Confounding
        • 3. Confound an Effect Using -1/+1 Coding System
        • 4. How to Replicate
        • 5. Confound Two Effects Using -1/+1 Coding System
        • 6. Confound Three Effects Using -1/+1 Coding System
        • 7. Confounding and Blocking Using Linear Combination Method 0/1 Coding
        • 8. Confound Two Effects Using 0/1 Coding System
        • 9. Confound Three Effects with Eight Blocks Using the o/1 Coding System
        • 10. General Blocking and Confounding Scheme for 2k Design in 2p Blocks
        • 11. Complete versus Partial Confounding
        • 12. Reference Blocking and Confounding in 2K Design
      • 8. Fractional Factorial Design of Experiments
        • 1. What is it
        • 2. Primary Basics
        • 3. Design Resolution
        • 4. One-Quarter Fraction Design
        • 5. Alias structure
        • 6. One-Eighth Fraction Design
        • 7. Lowest Runs Design
        • 8. Analysis Example
        • 9. Plackett-Burman Design
        • 10. Reference Fractional Factorial Design of Experiments
      • 9. Applied Regression Analysis
        • 1. What is Regression Analysis
        • 2. Steps in Regression Analysis?
        • 3. Perform Regression Analysis
        • 4. Results Explained Regression Analysis
        • 4.1. Significance Test Regression Analysis
        • 4.2. Practical Test r-square: The Coefficient of Determination
        • 4.3. Functional Relationships Explained
        • 4.4. Diagnostics Regression Analysis
        • 4.4.1. Linearity Assumption Check
        • 4.4.2. Outlier, Leverage, and Influential Points Unusual Observations Check
        • 4.4.3. Residuals Analysis
        • 5. Lack-of-fit Test
        • 6. Practice Problem Regression
        • 7. Reference Regression
      • 10. Response Surface Methodology
        • 1. What is Response Surface Methodology
        • 2. Design Response Surface Methodology
        • 3. Analyze and Explain Response Surface Methodology
        • 4. Box-Behnken Response Surface Methodology
        • 5. Multiple Response Surface Design and Analysis
        • 6. Reference Response Surface Modeling
      • 11. Expected Mean Square EMS Basics to Advanced Design of Experiments
        • 11.1 Are You Performing the Correct ANOVA?
        • 11.2 EMS for All Fixed Factors Design
        • 11.3 EMS for All Random Factors Design
        • 11.4 Approximate or Pseudo F-Statistics/Tests
        • 11.5 EMS for Two Fixed and One Random Factors Design
        • 11.6 EMS for Fixed, Random and Nested Factors Design
        • 11.7 Expected Mean Square Using an Alternative Shortcut Method
        • 11.8 Restricted vs Unrestricted Models, Which is the Best One?
        • 11.9 References for EMS Module
      • 12. Mixed Factors Design of Experiments Nested Repeated Measure Split Plot
        • 12.1. Nested Hierarchical Design
        • 12.2. Repeated Measure Design
        • 12.3. Split-Plot Design
        • 12.4. Are Partially Nested, Repeated Measure and Split-Plot Designs differ
        • 12.5. Reference for Mixed Model Designs
      • 13. Taguchi Robust Parameter Design of Experiments
    • Econ
      • Econ Ch2
    • Ergo
      • Ergonomic Toolbox
    • Fluid
      • Fluid Power Lab Demo
    • Mechanics
    • Operations
    • Project
    • Quality
    • Statics
    • Assessment
      • Assessment of Student Learning Certificate
      • Program-Level Student Learning Assessment Certificate Training
    • CV/Resume

Box-Behnken Response Surface Methodology

Video 7. Box Behnken Response Surface Methodology RSM Design and Analysis Example using Minitab & MS Excel

Box-Behnken Design, BBD for the response surface methodology, RSM, is specially designed to fit a second-order model, which is the primary interest in most RSM studies. To fit a second-order regression model (quadratic model), the BBD only needs three levels for each factor (Figure 15), rather than five levels in CCD (Figure 14). The BBD set a mid-level between the original low- and high-level of the factors, avoiding the extreme axial (star) points as in the CCD. Moreover, the BBD uses face points, often more practical, rather than the corner points in CCD. The addition of the mid-level point allows the efficient estimation of the coefficients of a second-order model (Box et al., 2005). The BBD is almost rotatable as the CCD. Moreover, often, the BBD requires a smaller number of experimental runs. 

Figure 14. Central Composite Design, CCD for Rotatability (left) and Face Center Design (right). Note. The central composite design, CCD with the axial points at the face is known as the face-centered central composite design or the face-centered cube if the axial points are placed at the face.

Figure 15. Two Representation of the Box-Behnken Design, BBD for RSM

How to Design the Box-Behnken RSM

Video 8 demonstrates an overview of the design, analysis, and explanation of the results for the Box-Behnken Design, BBD. 

The BBD uses the 22 full factorial design to generate for the higher number of factors by systematically adding a mid-level between the low and the high levels of the factors. Table 5 and Table 6 provide the Box-Behnken designs for three, four, and five factors, respectively. Many designs can be found in any standard statistical package such as Minitab, Design Experts, JMP and SAS. To design the BBD, simply the 22 full factorial is used as the base design and then orthogonal blocks are created using the mid-levels for the other factors. Therefore, it becomes a three-level factorial design, for which a full quadratic (second order) model can be fitted for the response surface. 

Table 5

Box-Behnken Design for Three and Four Factors

Table 6

Box-Behnken Design for Five Factors

How to Analyze and Explain the Results 

Video 8 demonstrates an overview of the design, analysis, and explanation of the results for the Box-Behnken Design, BBD. The analysis and the explanation for the results are exactly the same as the central composite design, CCD. Let’s look at the human comfort study with the lighting factor, X3 added to it. The X1 and X2 are the temperature (degree Fahrenheit) and the humidity (%), respectively. Data is collected from randomly selected 15 individuals with the specified room temperature, humidity, and lighting level conditions (Table 7). 

 Table 7

Human Comfort vs Temperature, Humidity, and Lighting

The design can be either created in MS Excel or Minitab, or using any software demonstrated in Video 8. Although the CCD and the BBD are different, their analyses are exactly the same and so the interpretations of the results. For example, the overall model and the quadratic square terms are significant (ANOVA table in Figure 16). The variations in the response are also explained well by the model terms, which is about 99% (the model summary table in Figure 16). The Pareto analysis shows that most effects are coming from the square terms of both the humidity and temperature only. 

Figure 16. Box-Behnken Example Analysis Results

Figure 17. Box-Behnken Pareto Analysis of the Effects

The response surfaces and the contour plots for all combinations for variables are provided in Figure 18. The response surface between the humidity and the temperature shows the curvature, the effects from both square terms (top-left graph in Figure 18). The Oval dark reason in the contour plot between the humidity and temperature shows the maximum comfort (top-right graph in Figure 18). As the lighting effect was observed to be insignificant, the contour plots show almost vertical parallel lines when plotted against either of the significant variables of humidity or temperature (bottom four graphs of Figure 18). These vertical parallel lines indicate that as we proceed along the X3 variable (lighting factor), no changes in comfort are observed. However, as we proceed along either the X1 or X2, there is a significant change observed in the comfort values as it can be seen through the color gradients. The response surfaces show a significant curvature (effect of the square terms) for both humidity and temperature while plotted against the lighting factor. 

Figure 18. Box-Behnken Response Surfaces and Contour Plots

The optimization results in Figure 19 indicate that both the middle level of the humidity and the temperature are observed to be the best to achieve the maximum human comfort. The selected lighting conditions do not affect human comfort in this study. 

Figure 19. Box-Behnken Response Surfaces Optimization Output

Is Box-Behnken a Better Design than the Central Composite Design? 

Video 9 shows a comparison analysis between the central composite design, CCD, and the Box-Behnken Design, BBD.

Video 9. Is Box Behnken Better than the Central Composite Design in the Response Surface Methodology

All models are wrong (Box et al., 2005)! Therefore, developing a less inaccurate model would be preferable. Any model within a smaller reason is more accurate than a wider range, the Box-Behnken will arguably provide a better estimation of the parameters, as the levels are not too extreme as the central composite designs. For example, in the study of human comfort by the temperature and the humidity, the low level of the temperature of 65-degree Fahrenheit is already low (Table 8). If the axial points are placed even further lower than this level, this could be a wastage of resources because we already know that this temperature will produce a lower comfort rating. It does not make much sense to study something that we already know. Moreover, in Box-Behnken, most treatment combinations use the mid-levels of the other factors. Therefore, the study is conducted around the expected optimum reasons in the most experimental runs. For example, there is a total of 150 mid-levels as compared to only 40 low or high levels in five-factor Box-Behnken Design in Table 6. This experiment will be more practical to conduct than a central composite design with five factors as the central composite will contain many extreme points. 

Table 8

Comparison between the Central Composite and the Box-Behnken Designs

Nevertheless, the central composite design is the traditional fractional factorial design of experiments. Therefore, it has all the advantages of the fractional factorial design. Moreover, the CCD is rotatable, while the Box-Behnken is nearly rotatable or rotatable for some specific designs. 

As the central composite design consists of five levels for each factor, it will be possible to test up to a fourth-order model. However, the Box-Behnken design consists of only three levels for each factor. Therefore, only a second-order model is possible for the Box-Behnken design. 

Generally, for more well-informed processes, Box-Behnken could be more useful, while the central composite could be more useful in relatively unknown processes. This could be the reason why the central composite design is used more than the Box-Behnken design because most studies are conducted on to find something new. Nevertheless, for more refinement and optimization, Box-Behnken will provide more precision. 

In summary, both designs have their advantages and disadvantages. The designers can choose any of these two depending on the optimization goals. 

Next Topic 

How to Design and Analyze Multiple Response Surface

The Open Educator is Created by Shaheen AhmedThe Open Educator is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.Feel free to contact us at email@theopeneducator.com if you have any questions or concerns.Copyright © Shaheen Ahmed
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