**33 DOE FRACTIONAL FACTORIAL, 6 PREDICTORS
**In the 33rd Minitab tutorial, we are at the test department for skateboard wheels. Here we will accompany the materials testing team as they optimize the abrasion behavior of a newly developed material for skateboard wheels, made of Kevlar fiber-reinforced plastic. Kevlar is used in the industry as a material for bulletproof vests and cut-resistant gloves, and the aim is to test the extent to which Kevlar components in the wheel material could reduce the abrasion of the skateboard wheels. Smartboard Company has a specially designed test station for this purpose, in which the skateboard wheel to be tested is fixed to an axle, driven by an electric motor. The skateboard wheel is then rolled on a counter body at a defined speed and a defined contact pressure. The surface properties of the counter body correspond to the properties of a typical road surface. At the end of the test period the material abrasion of the skateboard wheels, is determined in grams by calculating the difference between the wheels, weight before and after the wear test. The amount of abrasion in grams is therefore our response variable, which should ideally be as low as possible. This means that the lower the abrasion, the higher the wear resistance of the skateboard wheel, and the higher the customer satisfaction. However, as the research project is under great time pressure, the DOE team decides to use a so-called. fractional factorial statistical design under the given boundary conditions and the available technical expertise.

In order to understand the subject area of fractional experimental designs in the necessary depth, this training unit is divided into four parts. In the first part in our Minitab tutorial unit we will look at the fundamentals of fractional experimental design types, and learn what distinguishes a fractional factorial experimental design, from a full factorial experimental design, and how to set up a fractional factorial experimental design properly. We will learn that these fractional factorial experimental designs inevitably always have to accept certain mixing structures of influencing factors, also known as alias structures. We will therefore also learn why the DOE team’s high level of technical expertise with regard to the potential cause-effect relationships, in the context of fractional experimental design, plays a decisive role in drawing up a usable fractional experimental design, that is actually capable of theoretically and mathematically modeling the real cause-effect relationships. Well equipped with this knowledge, we will then be able to properly set up, and analyze a fractional experimental design in the second part in our Minitab tutorial. For example, by evaluating the table of coded coefficients, and working with the Pareto diagram of standardized effects. We will learn how to interpret the so-called PSE Lenth parameter, in the context of the Pareto chart of standardized effects. We will optimize our DOE model by performing a hierarchical backward elimination of non-significant terms, by removing non-significant terms from our model by hierarchical backward elimination based on the corresponding coefficients, model quality parameters, p-values and the Pareto diagram of standardized effects.

In this context, we will also return to the present so-called, alias structure, in the fractional experimental design. Which shows us which mixing structures we have accepted due to the fractional factorial experimental design, as the price for keeping the number of experimental trials as low as possible, due to the high number of influencing factors. After backward elimination, we can then assess the final model quality of our optimized DOE model, by using the corresponding coefficients of determination such as R-squared adjusted, and R-squared predicted. Finally, at the end of the second part, we will evaluate the required corresponding analysis of the non-descriptive residual scatter. In the third and final part of our Minitab tutorial, we will then use the final optimized DOE model to enter the response optimization phase in order to determine the optimum parameter settings, to reduce abrasion on the skateboard wheels to a minimum. In this context, we will also look at the corresponding interaction diagrams. Once we have determined the optimum parameter settings by using the response optimization, we will then define specific working ranges for the parameter settings. For this purpose, we will get to know the useful display forms of contour plot, and cube plot actively create, and interpret them in order to define the permissible tolerance ranges for our parameter settings, so that, for example, the required target value in our response variable is still achieved even with unexpected process instabilities.

MAIN TOPICS MINITAB TUTORIAL 33, Part 1

- Introduction to fractional design of experiments
- Establishment of a fractional design plan
- Overview of possible design plan types
- Interpretation of the alias structures in the fractional experimental design

MAIN TOPICS MINITAB TUTORIAL 33, part 2

- Analysis of a ¼-fractional design plan
- Table of coded coefficients
- Pareto diagram of the standardized effects
- The PSE Lenth parameter
- Hierarchical backward elimination of non-significant terms
- Interpretation of the main effect plots
- Coefficients of determination of the DOE model
- Evaluation of the alias structures
- Residual analysis

MAIN TOPICS MINITAB TUTORIAL 33, Part 3

- Interpretation of the interaction plots
- Response optimization
- Contour diagram for defining optimum parameter settings
- Cube plot for data means, based on the DOE regression equation
- Cube plot for fitted means, based on the experimentally determined data