**32 DOE FULL FACTORIAL, CENTER POINTS, BLOCKS
**In this 32nd Minitab tutorial, we are in the wind tunnel laboratory of Smartboard Company. The aerodynamic properties of newly developed high-speed racing suits are currently being tested here. These racing suits are designed to minimize air resistance on the skateboard pilots in high-speed championships, in order to achieve maximum speeds on the race track. To determine the air resistance, the respective skateboard pilot in the racing suit is exposed to a defined air flow in the wind tunnel and the drag coefficient, the so-called cd-value is measured as a measure of the aerodynamic behavior of the racing suit. The lower the cd value, the lower the aerodynamic drag, which in turn has a positive effect on the maximum achievable speed. The parameters to be varied on the racing suit which have a potential influence on the aerodynamics of the racing suit were determined as part of an Ishikawa analysis. The parameters surface roughness, seam width and material thickness on the racing suit were identified as potential influencing factors. The aim of this Minitab tutorial will be, to use statistical test planning to determine an optimum combination of surface roughness, seam width and material thickness so that the drag of the racing suit can be reduced to a minimum. We will see how the development team sets up and implements a full factorial design plan with so-called center points and blocks. In the first part of this Minitab tutorial, we will focus on determining the required number of replications and the discrimination, as well the first and second type of error. In this context, we will learn how to use a discriminatory power analysis, to determine the appropriate number of replications for our experimental design, and how in this context the relationship between the discriminatory power quality, and the first and second type of error can be easily understood in the context of hypothesis testing.

The main topics in the second part of this Minitab tutorial then concentrate on drawing up the actual DOE test design. Here we will learn how to set up the full factorial experimental design step by step. In this context, we will also understand what center points are, and why the setting of so-called block variables can play an important role depending on the task. On this occasion we will get to know the useful function random generator, for randomizing data sets which can also be very helpful for other tasks in general, in order to randomize data. Furthermore, we will learn to work with so-called interval plot, in the context of DOE and experience that these interval plots are always very useful to get a visual impression of the trends and tendencies from the experimental runs. The focus in the third part of this Minitab tutorial will then be to analyze our DOE model in terms, of its quality and capability, with the question of how well this DOE model can actually represent the technical cause-effect relationships realistically. To this end, we will discuss and use the coefficients of determinations, R-squared, R-squared adjusted and R-squared predicted, in order to assess the quality of our DOE model. At this point, the table of coded coefficients becomes important again. And we will use the previously set center points, to check the linearity of our DOE model. With the help of our block variables, we will also be able to analyze whether there are significant differences in the blocked test runs. We will then learn how to use main effect and interaction plots to identify the corresponding cause-effect relationships. We will also learn how to perform a hierarchical reduction of the variance model based on the Pareto diagram of the standardized effects, in order to optimize the predictive quality of our DOE model. For this optimization of our DOE model we will get to know and use the method of manual backward elimination for a better understanding.

As part of the residual analysis, we will evaluate the corresponding residual diagrams to check, whether our residuals also follow the laws of normal distribution. We will use the probability plot of the residuals, as well as the diagrams residuals versus fit, residuals versus order and the residuals histogram, to check whether the residual scatter that cannot be described with our model, shows undesirable trends or tendencies, that could possibly falsify our results in the target value optimization. With the knowledge we have learned up to this point, we will then move on to the final part of this Minitab tutorial and start with Response optimization. Here we will use the very useful interactive response optimization window to set the influencing variables, so that the required target value of the response variable can be achieved. We will get to know the important graphics, contour plot, cube plot, and surface plot and see, that these forms of representation are particularly suitable in day-to-day business for defining the respective working areas for parameter settings so that, for example, the desired target value can still be achieved even in the event of undesirable, unexpected process variations. At the end of this multi-part Minitab tutorial, we will be able to make concrete recommendations for action based on the corresponding confidence and prediction intervals, to the technical management of Smartboard Company as to how the influencing factors or the working ranges for the influencing factors should be set, so that the required target value in our response variable can be achieved with a 95% probability.

MAIN TOPICS MINITAB TUTORIAL 32, part 1

- Determination of the required number of replications
- Discrimination power analysis
- Discrimination quality vs. 1st type error, 2nd type error

MAIN TOPICS MINITAB TUTORIAL 32, part 2

- Set up DOE design plan
- Randomization using the random generator
- Interval plot for visualizing cause-effect relationships
- Setting center points and block variables

MAIN TOPICS MINITAB TUTORIAL 32, Part 3

- Analyze factorial experimental design
- Evaluation of the table Coded coefficients
- Evaluation of linearity using the center points
- Evaluation of the block variables
- Evaluation of the main effect diagrams
- Evaluation of the interaction diagrams
- Assessment of model quality using the coefficients R- sq, R- sq (adj) and R-sq (pred)
- Optimization of the DOE model
- Evaluation of the table Variance analysis
- Pareto diagram of the standardized effects
- Hierarchical backward elimination
- Manual backward elimination
- Residual analysis
- Residual probability plot
- Residuals vs. adjustments
- Residuals vs. fits
- Residual histogram

MAIN TOPICS MINITAB TUTORIAL 32, part 4

- Response optimization
- Individual and composite desirability level
- Working with the interactive response optimization window
- DOE-Contour diagram Interpretation
- DOE-Cube diagram Interpretation
- DOE-Surface plot Interpretation