10.1 Introduction to DOE principles

Design of Experiments (DOE) is a powerful tool for optimizing prototypes. It helps you figure out which factors matter most and how to tweak them for the best results, all while saving time and resources.

In prototyping, DOE lets you test multiple factors at once, seeing how they interact. You'll learn to set up experiments smartly, use randomization and replication, and analyze both main effects and interactions to improve your designs.

Design of Experiments Principles

Systematic Approach to Experimentation

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• Design of Experiments (DOE) employs a systematic method for planning, conducting, analyzing, and interpreting controlled tests
• Evaluates factors controlling parameter values or groups of parameters
• Aims to maximize information gained from minimal experiments reducing time and resource expenditure
• Utilizes statistical methods to analyze results enabling quantitative decision-making
• Facilitates continuous improvement through iterative experimental cycles

Objectives in Prototyping Context

• Efficiently optimize product or process performance
• Identify most influential factors and their optimal settings
• Provide comprehensive understanding of the system under investigation
• Enable prediction of prototype performance under various conditions

Factorial Design Principle

• Allows simultaneous study of multiple factors and their interactions
• Employs treatment combinations representing specific sets of factor levels
• Uses experimental design matrix to outline complete set of treatment combinations
• Ensures balanced and comprehensive investigation of factors and interactions

Components of a Well-Designed Experiment

Experimental Variables

• Factors independent variables manipulated to observe effects on response variables (temperature, pressure)
• Levels different values or settings assigned to each factor (low, medium, high)
• Responses dependent variables measured as result of factor changes (yield, strength)
• Control variables factors held constant throughout experiment (ambient humidity)

Experimental Structure

• Experimental unit entity receiving specific treatment combination (individual prototype, batch of material)
• Treatment combination specific set of factor levels applied to experimental unit (high temperature + low pressure)
• Experimental design matrix outlines complete set of treatment combinations
• Ensures balanced and comprehensive investigation of factors and interactions

Randomization, Replication, and Blocking

Randomization Principles

• Randomly assigns treatment combinations to experimental units
• Minimizes impact of unknown or uncontrolled variables on results
• Ensures validity of statistical inferences
• Distributes unknown biases evenly across all treatment combinations

Replication Strategies

• Repeats each treatment combination multiple times
• Estimates experimental error and increases precision of results
• Enables calculation of confidence intervals and hypothesis testing
• Enhances reliability and generalizability of experimental conclusions

Blocking Techniques

• Controls known sources of variability not of primary interest
• Groups similar experimental units to reduce impact of nuisance factors
• Improves efficiency by reducing unexplained variability
• Increases precision of treatment effect estimates

Main Effects vs Interaction Effects

Main Effects Analysis

• Direct impact of single factor on response variable
• Averaged across all levels of other factors in experiment
• Easier to interpret and often primary focus in initial experimentation stages
• Provides insight into individual contributions of each factor
• Visualized using main effects plots

Interaction Effects Evaluation

• Occurs when impact of one factor depends on level of another factor
• Indicates non-additive relationship between factors
• Reveals complex relationships not apparent from main effects alone
• May necessitate simultaneous optimization of multiple factors
• Visualized using interaction plots

Effect Hierarchy Principle

• Main effects generally more significant than two-factor interactions
• Two-factor interactions more significant than higher-order interactions
• Guides interpretation and prioritization of effects in complex designs
• Influences selection of factors for further investigation or optimization