Table of Contents
- 1 Modern DOE for Process Optimization
- 1.1 Introduction to Factorial Design
- 1.2 Enhancements for Design and Analysis of Factorials
- 1.3 Data Transformations
- 1.4 Blocking
- 1.5 Fractional Factorial Designs
- 1.6 Small Factorial Designs
- 1.7 Factorial with Center Points and RSM Introduction
- 1.8 Response Surface Designs and Analysis
- 1.9 Central Composite Designs
- 1.10 Optimal Designs
- 1.11 Brief intro to Mixture Design
Modern DOE for Process Optimization
Explore a comprehensive Modern Design of Experiments (DOE) course, a workshop grounded in case studies that covers everything from factorial to response surface designs. This single-stop course offers insights into harnessing the potential of DOE techniques for driving substantial improvements. Start your journey by delving into factorial designs, aiding in the identification of crucial focus factors. Unearth concealed interactions that often hold the key to success. Optimize resource utilization through contemporary small-run designs that economize time and finances in experimentation. Seamlessly transition from factorials to response surface methods for the enhancement of your products and processes. Finally, cement your knowledge with proficient ANOVA analysis techniques that bestow confidence in your findings. Contact us for the Design Expert training on Modern DoE.
This workshop covers the practical aspects of DOE. During this Modern DOE workshop, you will discover how to effectively:
- Grasp the rationale behind factorial designs
- Execute the DOE planning process
- Decode analysis of variance (ANOVA) outcomes
- Uncover concealed interactions
- Utilize compact fractional designs for effective screening or characterization
- Apply power and precision to right-size designs
- Identify optimal instances for data transformations
- Investigate multilevel categoric factors
- Follow the experimental strategy from screening to response surface methods
- Establish central composite (CCD) and optimal designs
- Choose suitable regression models with model reduction
- Optimize numerous response variables
- Knowledge of basic statistics (mean and standard deviation)
- Exposure to simple comparative experiments (e.g. two-sample t-test) are recommended
- Basic knowledge of Design Expert software is expected
Introduction to Factorial Design
Factorial designs are primarily utilized to assess the significance of factors within a process. This can involve screening to pinpoint essential factors from an array of possibilities or examining how established factors interact and independently impact the process. Such designs frequently serve as initial stages for delving into more intricate response surface modeling.
- A factorial design is a form of structured experiment that enables the examination of how multiple factors can influence a response.
- Conducting experiments by simultaneously varying levels of all factors allows the study of factor interactions.
- A factorial design with center points helps assess curvature in response surfaces, albeit limited to the center point.
- Fitted values can be computed only at corner and center points, preventing the creation of a contour plot.
- Modeling curvature across the entire response surface requires quadratic terms, achievable through a response surface design.
- Augmenting a factorial design with axial points enables the creation of a central composite response surface design.
Enhancements for Design and Analysis of Factorials
Analyze Factorial Design to examine a planned experiment. This enables the analysis of four distinct types of factorial designs:
- 2-level factorial design
- General full factorial design
- Plackett-Burman design
- Split-plot design
The majority of data transformations can be characterized using the power function, where the power provides a scale that meets the equal variance prerequisite of the statistical model.
- Response transformation is a crucial aspect of data analysis.
- Transformation becomes necessary when error (residuals) is linked to the response's magnitude (predicted values).
- Design-Expert offers robust diagnostic tools to assess the adherence of data analysis to statistical assumptions.
- The normal plot of residuals tests their normal distribution.
- A pattern in the residuals vs. predicted response values plot can signal issues.
- Response transformation's impact is minimal unless the ratio of maximum to minimum response is substantial.
Blocking is a method employed to mathematically eliminate the variation introduced by identifiable changes occurring during the experiment's progression.
- Instances requiring blocking include the use of distinct raw material batches or the experiment's duration spanning multiple shifts or days.
- Such changes might cause shifts in response data, which blocking counteracts, essentially "normalizing" the data.
- Design-Expert presents multiple blocking options, contingent on the number of runs chosen.
- The default option of 1 block signifies "no blocking"
Fractional Factorial Designs
A fractional design refers to an experimental arrangement where researchers execute only a specific subset or "fraction" of the complete runs found in a full factorial design:
- Fractional factorial designs suitable for resource constraints or numerous factors
- Utilize fewer runs compared to full factorial designs
- Subset of full factorial design, leading to confounding of main effects and 2-way interactions
- Higher-order interactions intertwined and indistinguishable
- Often assumptions made about negligible higher-order effects
- Gather data on main effects and low-order interactions with fewer runs.
Small Factorial Designs
These designs are used when the number of factors is relatively small, and they explore the main effects and interactions between factors using a manageable number of experimental runs.
- Limited number of factors and levels
- Investigates main effects and interactions
- Suitable for initial screenings or resource-limited situations
Factorial with Center Points and RSM Introduction
This approach is particularly useful for optimizing processes in situations where multiple factors interact to influence the outcome.
- Combine factorial designs with center points
- Introduce response surface methodology (RSM)
- Achieve deeper insights into factor-response relationships
- Identify optimal factor settings
- Address non-linearity in processes
Response Surface Designs and Analysis
Apply Analyze Response Surface Design to capture data curvature and determine optimal settings.
- Typically used post-factorial or fractional factorial experiments.
- Comes after identifying key process factors.
Central Composite Designs
The most popular response surface method (RSM) design is the central composite design (CCD).
- Central composite designs utilize 5 factor levels: -Alpha, -1, 0, 1, +Alpha
- Notable trait: Sequential experimentation supported by design structure
- Central composite experiments can be conducted in blocks
Optimal designs are necessary when there are unequal component ranges, multi-component constraints, or a custom model is being fit to the responses.
- Optimal designs offer enhanced flexibility
- Unlike simplex designs, optimal designs use an algorithmic point selection approach
- Points are chosen to achieve specific properties
- Multiple statistically equivalent sets of design points often exist
- This can lead to slight design variations for the same factors and model information
Brief intro to Mixture Design
The analysis of a mixture design is based on the same principle as linear regression.
- Employ Analyze Mixture Design for designed experiment analysis
- Suitable when response hinges on mixture component proportions, e.g., bread dough ingredients
- Incorporate process variables and total mixture quantities in analysis