**31 DOE FULL FACTORIAL, 3 PREDICTORS
**In this 31st Minitab tutorial, we are in the axle material development department of Smartboard Company. We will accompany the development team how they reduce the brittleness in the skateboard Axles to a minimum, with the help of the so-called DOE, statistical design of experiment. In principle the higher the brittleness of the skateboard Axles the greater the risk that even the slightest impact loads can cause the Axles to break. The possible influencing factors that could have a potential impact on the brittleness of the Axles were determined by the development team as part of an Ishikawa analysis. The parameters chromium content in the axles, annealing temperature during heat treatment and the type of heat treatment furnace were identified as potential influencing factors. In view of the fact, that the development team is under time pressure and must also keep the scope of experimental tests on the production line to a minimum, so-called statistical design of experiment should be used to determine the optimum settings for the three influencing variables mentioned with little experimental effort, with the aim of reducing axis embrittlement to a minimum. This statistical design of experiments, often abbreviated to DOE is a very important and useful tool in the Six Sigma methodology, which deals with the statistical planning, execution, analysis and interpretation of cause-and-effect relationships. In order to be able to deal with this complex subject area in the necessary depth, this training unit is segmented into four parts. In the first part of this training unit, the fundamentals and basic ideas of statistical experimental design are explained in order to provide a good understanding of the most common of experimental design types. In particular we will get to know the important terms, such as center points, replications, and block variables, and understand why a discriminatory power analysis is always recommended for determining the number of required experimental replications. Well equipped with this basic knowledge, we will then enter the second part of our training unit, and get to know how to set up and analyze the appropriate experimental design, in our case the so-called factorial experimental design. We will see here, that it is very important to also carry out the test for normal distribution according to Anderson Darling, and we will also be able to understand why the so-called table of coded coefficients, plays a very useful role in the context in the DOE method. Another central topic in this part will be the so-called main effect plots and interaction effect plots, which we will construct manually step by step for didactic reasons, in order to be able to interpret the factor plots displayed in the output window in detail, and on this occasion, we will also get to know the useful Layout Tool function. With the knowledge gained from the first and second parts of this Minitab tutorial, we will then be well equipped to focus on the quality of our DOE model in the third part, for example to be able to evaluate the quality of our variance model by using the corresponding coefficients of determination, such as R-squared, R-squared adjusted, and R-squared predicted. In this context, we will also look at the associated regression equation in uncoded units, which was generated as part of the variance analysis for our DOE model, and basically represents the foundation for the upcoming response optimization. In this context, the so-called alias structure will play an important role which we will examine and interpret in detail. We will also get to know and discuss the useful so-called Pareto diagram of standardized effects, in order to be able to efficiently distinguish graphically significant terms from non-significant terms. We will learn, that the so-called residual scatter which cannot be described with our DOE model should follow the laws of normal distribution. For this purpose, we will work with the probability plot of the normal distribution and use all the important representations in the context of residual analysis, such as residuals versus fits, histogram of residuals, and residuals versus order. With this information regarding the quality of our DOE model, we can move on to the fourth and final part of this Minitab tutorial in order to start the Response optimization with the final DOE model. For this purpose, we will use the very helpful interactive response optimization window to set the three parameters in such a way that the undesirable embrittlement components in the skateboard axles are reduced to a minimum. As part of this response optimization, we will also understand for example, the difference between so-called individual and composite desirability. In particular, we will also understand how the corresponding confidence or prediction intervals are to be interpreted in the context of our Response optimization. So at the end of our multi-part Minitab tutorial session, we will be able to provide the management of Smartboard Company with a 95% reliable recommendation, on how the three influencing variables should be set in concrete terms so that the material brittleness in the skateboard axles after heat treatment, is as low as possible.

MAIN TOPICS MINITAB TUTORIAL 31, Part 1

- Overview of the most common experimental DOE design types
- Full-factorial, fractional-factorial and response surface design types
- Screening, mixture and Taguchi design types
- 2-Level factorial experimental design with standard generators
- Resolution levels of available factorial experimental designs
- Center points and replications
- Discrimination power analysis to determine the number of replications
- Standard order vs. run order
- Setting block variables

MAIN TOPICS MINITAB TUTORIAL 31, part 2

- Analysis of factorial experimental designs
- Test for normal distribution of the DOE response variable
- Analysis of the non-descriptive residual scatter using the 4 in1 residual plot
- Evaluation of the „Coded coefficients“ table
- Main effect plot and Interaction plot
- Dual interaction diagrams
- Construction of triple interaction diagrams
- Unstack response variables according to factor levels
- Working with the layout tool

MAIN TOPICS MINITAB TUTORIAL 31, Part 3

- DOE model coefficients R- sq, R- sq(adj) and R-sq (prog)
- Analysis of variance within the framework of the DOE
- Coded coefficients
- Regression equation in non-coded units
- Alias structures
- Pareto diagram of the standardized effects
- Probability plot of the normal distribution
- Residuals versus fit
- Histogram of the residuals
- Residuals versus order

MAIN TOPICS MINITAB TUTORIAL 31, part 4

- Response optimization
- Multiple Response Prediction Analysis
- Response variable goal: Minimize, target, maximize
- Working with interactive response optimization window
- Individual desirability
- composite desirability
- Confidence interval in the context of Response optimization
- Prediction interval in the context of Response optimization