Introduction to Full Factorial Design PDF

Introduction to Full Factorial Design A type of experiment where we study how multiple factors (variables) affect a response "Full" = considers every possible combinations of factors and levels The input variables are called factors, while the output variables are response or target variable Identif...

Introduction to Full Factorial Design A type of experiment where we study how multiple factors (variables) affect a response "Full" = considers every possible combinations of factors and levels The input variables are called factors, while the output variables are response or target variable Identifies main effects, interaction effects, and potential non-linear relationships in factors The goal is to study how various input variables affect an output variable When to Use It? Recommended for up to 4 factors at 2 levels (e.g., "high" and "low") Practical when the number of factors is small since the number of experiments grows exponentially as factors increase Key Features Replications: Repeating trials Main Effects & Interactions: improves reliability by Main effects show how a reducing the influence single factor impacts the of random variations outcome Interaction effects show how two or more factors work together to influence the Randomization: outcome Helps minimize bias and ensures results are robust One-Factorial Method Investigates the impact of one factor on the response at different levels Factors can be: Qualitative (e.g., supplier, material): No predictions beyond tested levels Quantitative (e.g., temperature, load): Can predict and investigate effects if enough data are available One-Way ANOVA is used to: Compare means of two or more groups Identify differences and ranges of means  Two-Factorial Method The most common full factorial design where factors have only two levels It helps study the main effects and interactions between factors but doesn’t capture curvature in the response It’s often used as a screening experiment to identify the most critical factors before deeper exploration.  General Factorial Design To study the effects of two or more factors, each having different levels Examines all possible combinations of factor levels (both main effects and interactions between factors) Helps to explain how various factors interact and affect outcomes 2 methods of calculating number of experimental runs (n): n = (Levels of F1) x (Levels of F2) x (Levels n = (Levels of F1)^2 x (Levels of F2)^2 x... x of F3) x... x (Levels of Fn) x (replications) (Levels of Fn)^2 x (replications) Account for general combinations of factors Aims to capture complex interactions or with replications repeated measures between squared factors  Example Full Factorial Design Case Study Application of Factorial Design to Study the Effect of Moisture and Rice of Varieties on the Production of Paddy Husker Machine  Background The quality of peeled rice is influenced by various factors, including rice strain, feeding rate, milling component clearance, and moisture content (optimally below 14%) Milling removing the bran layer from brown rice to produce white rice (depending on amount of bran removed) significantly affects nutritional quality and edibility of rice optimal process can help reduce waste and increase product marketability MLGX25A Air Pressure Automatic Rubber Roller Rice Husker Machine Hence it is essential to understand how specific conditions can influence the production outcomes in paddy husking process  Purpose of this study By applying statistical methods like design of experiments (DOE) and analyzing interactions between factors, this study aims To investigate the effects of two variables: rice moisture levels and rice varieties using a full factorial design To identify the optimal conditions for maximizing the quality and yield of processed rice To optimize the production of a paddy husker machine using a full factorial design The findings provide insights into improving production efficiency and ensuring better outcomes in rice milling Experimental Variables 1. Moisture content Product Yield (%) (% of good rice) 2. Rice varieties (type) Dependent Independent Variables Variables  1 DOE Order Khao Dawk Mail 105 Defines the sequence of variable introduction in response surface 2 RD6 analysis 2 parameters: 1. Rice of moisture (RM) 3 Riceberry 2. Rice of varieties (RV) DOE Parameters Code Level Parameter Variable 0 1 -1 Moisture content X1 10 12, 14 16 (Moisture %). Rice varieties X2 1 2 3 (type). Number of experiments: DOE Parameters Code Level Parameter Variable 0 1 -1 Moisture content X1 10 12, 14 16 (Moisture %). Rice varieties X2 1 2 3 (type). Number of experiments: 4 x (3^2)  Why 4×(3)^2 instead of 4×3×3? Focus on Model Statistical Optimization Interactions Complexity Design Goals Indicates interest Develop polynomial Squared term More complex in rice varieties regression model reflect multiple interaction model interaction with to explore not only measurements or provides deeper moisture, either main effects but trials taken at each insights on how the with itself or also interactions of level, enhancing factors work combined with rice varieties with robustness and together to affect other levels varying moisture reliability product output Therefore, this approach is better to enhance the depth and applicability for practical applications in agricultural technology All done, Good job! Onto the next section Results and Discussion Experimental Design of this Case Study ANOVA is used to determine the significance of the effects and interactions of different experimental factors. For this study, the factors analyzed were: 1. Moisture content of rice (RM) 2. Rice varieties (RV) Highly significant with a p-value of 0.000. This indicates the overall model is a good fit for the data All terms in the model were statistically significant (p-value < 0.05) F-Value Measures the ratio of explained variance to unexplained variance. Higher values indicate stronger effects Regression Model A second order polynomial regression equation was developed to predict the rice yield Coefficient of determination (R²) = the ratio of variation explained by the model to the total variation in the data Higher R² value indicates a better fit of the model to the observed data The model achieved a high predicted R² value (99.69%), indicating excellent predictive capability and accuracy Interaction Effect Occur when the influence of one factor depends on the level of another factor The lines are not parallel, indicating a significant interaction between Moisture levels and Rice Varieties The effect of moisture on yield depends on the rice variety  Optimal Conditions Best performance: Rice variety Khao Dawk Mali 105 at 12% moisture level Resulted high yield (89%) good rice which closely matched predicted value (88.8%) Model Validation Residual analysis showed no significant lack of fit, confirming the model's adequacy The data followed a normal distribution, supporting the validity of the regression model Statistical Analysis Regression Model A second order polynomial regression equation was developed to predict the rice yield The model achieved a high adjusted R² value of 99.69%, indicating excellent reliability and accuracy Analysis of Variance (ANOVA) The ANOVA results confirmed that both independent variables (moisture and variety) and their interactions significantly influenced rice yield All terms in the model were statistically significant (p-value < 0.05) Interaction Effects The interaction between moisture levels and rice varieties showed significant effects on the yield Conclusion The study demonstrates that full factorial design is a powerful and practical method for post-harvest processing optimization Full factorial design is an effective method for optimizing agricultural machinery performance It provides a framework for making data-driven decisions to enhance efficiency and product quality