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Content:

- 31 DOE FULL FACTORIAL, 3 PREDICTORS, PART 1
- 31 DOE FULL FACTORIAL, 3 PREDICTORS, PART 2
- 31 DOE FULL FACTORIAL, 3 PREDICTORS, PART 3
- 31 DOE FULL FACTORIAL, 3 PREDICTORS, PART 4
- 32 DOE FULL FACTORIAL, CENTER POINTS, BLOCKS, PART 1
- 32 DOE FULL FACTORIAL, CENTER POINTS, BLOCKS, PART 2
- 32 DOE FULL FACTORIAL, CENTER POINTS, BLOCKS, PART 3
- 32 DOE FULL FACTORIAL, CENTER POINTS, BLOCKS, PART 4
- 33 DOE FRACTIONAL FACTORIAL, 6 PREDICTORS, PART 1
- 33 DOE FRACTIONAL FACTORIAL, 6 PREDICTORS, PART 2
- 33 DOE FRACTIONAL FACTORIAL, 6 PREDICTORS, PART 3
- 34 DOE: RESPONSE SURFACE DESIGN, PART 1
- 34 DOE: RESPONSE SURFACE DESIGN, PART 2

**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

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

**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

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

**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

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

**34 DOE: RESPONSE SURFACE DESIGN
**In this 34th Minitab tutorial, we are visiting the painting and coating department of smartboard company. Here the skateboard decks are coated with liquid paint, according to customer requirements in an automated painting process. The painting process must be designed in such a way, that the applied paint layer has a minimum adhesive force to withstand external stresses, such as impact and shock loads. The adhesive force of the paint layer on the skateboard decks achieved during the painting process, is determined in the laboratory by using a standardized scratch test. In this scratch test, a diamond pin is pressed vertically into the paint layer with a constantly increasing test force and simultaneously moved horizontally over the paint layer. The maximum test force achieved in the scratch test which leads to the first flaking of the paint layer, and the existing crack characteristics which are evaluated microscopically, determine the adhesive force of the paint layer. The automated painting process for the skateboard decks can be divided into three main process steps: priming, painting, and drying. In the first process step priming, the skateboard decks are subjected to continuous immersion priming in a dip tank, in order to reduce irregularities and open pores on the skateboard deck surface. In preliminary tests the team identified the layer thickness of the primer as the main influencing factor in this process step. In the second process step, the final layer of paint is applied by continuously passing the skateboard decks through a paint booth, and coating them using robot-controlled spray nozzles. In preliminary tests the team identified the spray nozzle distance to the skateboard deck surface as the main influencing factor in this process step. However, these preliminary tests also showed that this distance should be as high as possible, as the gloss level of the paint layer improves, the greater the distance between the nozzles. In the subsequent third process step drying, the painted skateboard decks are passed through a continuously operating multi-zone dryer to remove the existing water content in the paint layer. In preliminary tests, the team identified the average drying temperature as the main influencing factor in this process step.

Recently however skateboard decks have often had to be scrapped, because an above-average number of paint layers were unable to achieve the required minimum adhesion strength. For this reason a quality team was formed to use the DOE Methodology, to identify the parameter effects and interaction effects, that have a significant effect on the adhesive force. The core topic in this Minitab tutorial will therefore be, to mathematically model and analyze the influence of these three parameters on the adhesive force by using a suitable statistical design of experiments, and to optimally adjust them using response value optimization, so that the required minimum adhesive force is achieved. Since the team had already found out during full-factorial preliminary tests, that non-linear cause-effect relationships exist, it has been decided to work with the so-called response surface design. The central topic in this Minitab tutorial will therefore be the response surface design. This will then also be applied in order to be able to describe non-linear cause-effect relationships. To this end, we will first learn what distinguishes a response surface design from a factorial or a differently fractionated experimental design. The important so-called star points, will also play a central role in this context, and we will get to know the difference between star points and center points, and experience that the so-called star point distance alpha, plays a very important role. We will learn what a central composite design is, and what a Box-Behnken design is. and by constructing 3-D scatter plot, we will discuss the corresponding mathematical requirements with regard to orthogonality, which a central composite design effective should ideally possess.

With the help of the so-called 3-D scatter plot, it will then also be very easy for us to understand the difference between star points, and center points. We will learn how to use the corresponding significance values from the hypothesis tests, to assess whether the corresponding terms are significant, or non-significant. And we will learn how to assess the corresponding effect sizes using the Pareto chart of standardized effects. We will then use the useful corresponding factor diagrams, to discuss the corresponding effect sizes, and the directions of the respective effects. With this knowledge we will then be able to determine the optimal parameter settings, as part of the final response optimization. In this context, we will also learn how to create a so-called contour plot, in order to define process-safe working ranges for the parameter settings, so that the required minimum adhesive force of the coating layer is still achieved, even in the event of unplanned process fluctuations. We will also create and discuss the useful graphic effect surface plot, to get a very good three-dimensional visual impression of the trend of our response variable depending on the influencing variables. At the end of this Minitab tutorial, we will be able to use all the available analysis results and in particular the corresponding confidence and prediction intervals, to make concrete recommendations to the technical management of Smartboard Company, on what the optimum parameter settings should be in order to achieve the required minimum adhesive force of the paint layer on the skateboard decks, even with these existing non-linear cause-and-effect relationships.

MAIN TOPICS MINITAB TUTORIAL 34, part 1

- Response surface design, fundamentals
- Central composed experimental design
- Box- Behnken design
- 1/2 – central composed Response surface design
- 1/4 – centrally composed Response surface design
- 1/8 – centrally composed Response surface design
- Create a Response surface design plan
- Point types: cube points, center points, star points
- Identification of different point types in the 3D scatter diagram

MAIN TOPICS MINITAB TUTORIAL 34, part 2

- Analyze Response surface design
- Coded coefficients
- Main effect plots
- Interaction plots
- Coefficients of determination of the DOE model
- Interpretation of the analysis of variance
- Regression equation in non-coded units
- Pareto diagram of the standardized effects
- Residual analysis
- Response optimization
- Multiple Response Prediction
- Define process areas
- Contour plot
- Surface plot

MAIN TOPICS MINITAB TUTORIAL 34, part 2

- Analyze Response surface design
- Coded coefficients
- Main effect plots
- Interaction plots
- Coefficients of determination of the DOE model
- Interpretation of the analysis of variance
- Regression equation in non-coded units
- Pareto diagram of the standardized effects
- Residual analysis
- Response optimization
- Multiple Response Prediction
- Define process areas
- Contour plot
- Surface plot