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Design of experiment, Example - Coggle Diagram

- - - - Factors
        
        Type of sugar: Brown, White
        
        Type of egg: Chicken, Duck
        
        Type of flour: Fine, Coarse
      - Process
        
        Baking
  - - - Determine relationship between different input factors
        
        -> process and output(y)
  - - - One or two factor which affects the response more
        
        e.g. swiss cake, type of sugar and flour will affect taste the most
    - - a response near the desired result
        
        e.g. a swiss cake will taste better when white sugar + Chicken Egg + Fine flour (controllable factors)are used
      - Variability in outcome is small
      - Minimise impact of uncontrollable variables
        
        e.g. humidity can affect taste of swiss cake, we change the controllable factor(e.g. type of flour) to minimise impact
- - - - 2 or more factors with different levels to be investigated simultaneously
    - - OFAT is based on individual observations
      - factorial experiment is able to estimate interaction between factors systematically
      - factorial experiment improved prediction of responses -> more efficient process optimization
    - - saves time and costs
      - reveals main effect and interactions between factors
    - - effect of each factor on the response
      - effect of interaction between 1 or more factors
      - test for curvature in responses including center points
    - - design
        
        2^k full factorial design with each factors having 2 levels.
        
        e.g. 2^3 = 8 runs (3 factors)
      - yates order
      - replication
        
        varied outcome
        
        verifies results and give better estimation of variable and effects of factors
        
        more replicates = more accurate
- - - - Factorial Regression
        
        Factorial Plots
        
        Main effect plot
        
        Shows how step the gradient is for each factor.
        
        More steeper the gradient, more significant the factor is on the response
        
        Able to refer back to p-value in factorial regression table to check if result is consistent
        
        The least steeper gradient is highly the factor that is not significant on the response.
        
        1 more item...
        
        Interactive plot
        
        Shows interaction between 2 factors
        
        If 2 lines are exactly parallel, there is zero interaction between the 2 factors
        
        Greater the angle between 2 lines, stronger the interaction between the 2 factors
        
        1 more item...
        
        Coded Coefficient
        
        Blocks
        
        p-value
        
        Less than 0.05
        
        Significant difference between replicates
        
        More than 0.05
        
        No significant difference between replicates
        
        Factors
        
        p-value
        
        More than 0.05
        
        No significant difference between using different level of factors
        
        Less than 0.05
        
        Significant difference between using different level of factors
        
        Interactions
        
        p-value
        
        More than 0.05
        
        No interactive effect between factors
        
        Less than 0.05
        
        Interactive effect between factors
        
        Model Summary
        
        R-Square
        
        ~90%
        
        Model explain variance well
        
        Less than 90%
        
        Model does not explain variance well
        
        R-Square (Adjusted)
        
        More than 10% difference from R-square
        
        Presence of significant difference in model
        
        Less than 10% difference from R-square
        
        Presence of insignificant difference in model
        
        R-Square (Predicted)
        
        Predictability within range
        
        High
        
        Suitable to predict using regression equation
        
        Low
        
        Not suitable to predict using regression equation
        
        Analysis of Variance
        
        Blocks
        
        p-value
        
        Less than 0.05
        
        Significant difference between replicates
        
        More than 0.05
        
        No significant difference between replicates
        
        Factors
        
        p-value
        
        More than 0.05
        
        No significant effect on response
        
        Less than 0.05
        
        Significant effect on response
        
        Interactions
        
        p-value
        
        More than 0.05
        
        No interactive effect between factors
        
        Less than 0.05
        
        Interactive effect between factors
        
        Normal Plot
        
        Factors
        
        Red
        
        Significant effect
        
        Blue
        
        Not significant effect
        
        Interaction
        
        Red
        
        Significant interactive effect
        
        Blue
        
        Not significant interactive effect
        
        Pareto Chart
        
        Factors
        
        Cross red line
        
        Significant effect
        
        Do not cross red line
        
        Not significant effect
        
        Interaction
        
        Cross red line
        
        Significant interactive effect
        
        Do not cross red line
        
        Not significant interactive effect
        
        Regression equation
        
        Used to predict response within range of data used
        
        Suitability depends on R-Square (Predicted)
        
        Residual Plots
        
        Normal Probability plot
        
        Close to straight line
        
        No major concern
        
        Far from straight line
        
        Outlier
        
        Versus Fits
        
        Should be evenly spread above and below zero line
        
        Furthest away from zero line
        
        Outlier
        
        Histogram
        
        Bell shaped
        
        Normally distributed
        
        Not bell shaped
        
        Not normally distributed
        
        Versus Order
        
        Should not show any pattern
        
        Fit and diagnostic unusual observation
        
        Show outlier
      - Overview of response
        
        Average response from all blocks
      - Factors for each response
        
        Easy visualization of all factors for best response
        
        Can know which factor combination contribute to the greatest/lowest response
    - - Number of factors
      - Type of factors
        
        Text
        
        Low - Either Level
        
        High- Either Level
        
        Numerical
        
        Low - Smaller Number
        
        High - Bigger Number
    - - To better estimate true effect of the responds due to variation
        
        E.g. if a experiment has 3 factors and 2 levels and has 3 replicates/blocks. There will be a total of 2^3 x 3 = 24 runs
    - - It is a standard order of the various factor levels before running a DOE
        
        2 levels of a factor will group as a cluster
        
        Ensure MiniTab DOE is in standard order before placing values from excel into MiniTab