Foundations of Factorial DOE for Breakthroughs
Initiate your journey by acquiring insights into the application of factorial designs to identify crucial factors that demand your attention. Uncover hidden interactions that frequently hold the solution to success. Seamlessly integrate these aspects by mastering the utilization of robust ANOVA analysis techniques that instill confidence in your conclusions. Contact us for the Design Expert training on Factorial DOE.
During this workshop on Factorial DOE, you will discover how to effectively:
- Implement the DOE planning process
- Interpret analysis of variance (ANOVA)
- Discover hidden interactions
- Use power to properly size factorial designs
- Determine when to use transformations
- Explore multilevel categoric factors
- Optimize multiple responses
- Familiarity with fundamental statistics (mean and standard deviation) and experience with elementary comparative experiments (such as a two-sample t-test) are prerequisites.
- A foundational understanding of the 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.
Model selection and analysis of a 2-level factorial
This tutorial showcases the application of Design Expert software in the context of two-level factorial designs. These designs are instrumental in efficiently screening numerous factors to uncover the critical few, and potentially explore their interactions.
- In a 2-level full factorial design, each factor is tested at two levels.
- Experimental runs encompass all possible combinations of these factor levels.
- While 2-level factorial designs might not thoroughly explore a broad factor space, they yield valuable insights with a limited number of runs per factor.
- These designs can uncover significant trends, guiding supplementary experimentation.
- For instance, when exploring a potentially optimal region, a central composite design can be created by augmenting a factorial design.
Design enhancements - replicates, power
Design enhancement in Design Expert is simpler to play with.
- The Constraints node enables the adjustment of pre-existing constraints post-design construction, eliminating the need to reconstruct the design.
- Importing data is simplified via the Import Data Set function, involving pasting data and indicating column properties, with factor coding inferred from the data.
- Round factor values conveniently by right-clicking column headers; non-mixture factors allow rounding by decimal or significant digits.
- Mixture components, constrained by equality, can be rounded only to a specified number of significant digits.
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 to remove noise
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."
Multilevel categoric design
Within the Design Expert software, you'll find a "Multilevel Categoric" alternative, also recognized as a "general factorial," accessible on the "Factorial" design tab.
- Multilevel Factorial designs are employed for analyzing the impacts of q quantitative factors.
- The process commences by defining the range for each factor's variation and the count of levels for its study.
- A datasheet is generated encompassing all permutations of varying levels of the variables.