34 DOE: RESPONSE SURFACE DESIGN, PART 1

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