Response Surface Methodology

This course on RSM is broken into two consecutive two-day sections. The first two days is a comprehensive course on RSM basics, including demonstration of and insight regarding the use of modern computer software for RSM. Topics covered include:

• the method of steepest ascent for quickly finding the region of the optimum

• fitting second-order models and using them for process optimization

• methods for optimizing several responses simultaneously

• designs for fitting response surfaces including the standard designs (central composite and Box-Behnken designs)

• use of optimal designs to create custom designs to satisfy specific requirements of sample size, blocking considerations, and constrained factor spaces

• RSM methods for problems with both quantitative and qualitative variables, and the response surface approach to robust parameter design and process robustness studies.

The second two days focuses on mixture or formulation problems. Mixture problems involve design factors that are the components or ingredients of a mixture, and the response depends on the proportions of the ingredients that are in the mixture and not on the amount. The formulation of many products in the food, beverage, pharmaceutical, and chemical industries involves mixture experiments. In addition, many industrial processes involve mixture systems, such as finishing, coating, etching, and plating. Topics covered in this portion of the course include:

• the basic mixture problem and associated designs, including the simplex lattice and simplex centroid designs

• the use of Scheffé polynomials for fitting mixture models

• lower and upper bounds to form constrained mixture regions, use of design optimality to form designs for constrained regions

• methods for comparing and evaluating designs

• multiple responses in mixture problems

• using ratios of components

• inclusion of process variables in mixture experiments

• An illustration and discussion of software that supports experiments with mixtures.

This course is structured so that participants desiring a comprehensive of RSM and mixture experiments can attend all four days. Participants who are interested primarily in RSM can attend only the first two days and participants who are interested primarily in formulation problems and mixture experiments can attend only the last two days.

Course Outcomes

• To show how sequential experimentation is used to move from screening factors in a process or system to determining optimum operating conditions.

• To teach the fundamental concepts of using experimental design for product and process optimization.

• To familiarize participants with the state-of-the-art in experimental strategy for RSM and mixture experiments.

• To demonstrate how most of the major software packages (Design-Expert, JMP, Minitab) support the practical implementation of RSM and mixture experiments.

Program Schedule

Days 1 And 2: Response Surfaces

• Overview of RSM

• Finding the region of the optimum – the method of steepest ascent

• The use of second-order models in RSM

• Fitting and optimization of a second-order model

• The importance of contour plots and other graphics

• Optimizing multiple responses

• Experimental designs for fitting response surfaces

• Factorial and fractional designs for first-order models

• Standard designs for second-order models (central composite, Box-Behnken, face center cube designs)

• Optimal designs for RSM (D and I optimal designs)

• Designs for small sample sizes, unusual blocking conditions, constrained spaces

• Design and analysis methods for computer experiments

• Robust parameter design and process robust studies using the RSM framework

Days 3 and 4: Mixture and Formulation Experiments

• Introduction to mixture and formulation problems

• Geometry of mixture spaces

• Simplex lattice and simplex-centroid designs

• Scheffé polynomials for fitting mixture models

• Other mixture modeling strategies

• Modeling and optimization, including multiple responses

• Screening mixture components

• Constraints on the basic mixture region

• Designs for constrained regions, including optimal designs

• Methods for evaluating, comparing, and selecting designs

• Experimenting with ratios of mixture components

• Including both process variables and mixture components in the experiment

• Software capabilities and features that support mixture experiments

Who Should Attend

Anyone responsible for product and process design and development, or other activities associated with product realization. This includes anyone involved with managing and improving product and process performance, including engineers, scientists, engineering managers, product designers and developers, product formulators, and process/manufacturing engineers.Technical personnel in quality engineering will also benefit from this course.

Course participants should have previous background in design of experiments and be familiar with the use of factorial and fractional factorial designs and the associated methods of data analysis.

Textbook and Materials

The textbook required for the program is included in the program fee.

Myers, R.H., Montgomery, D.C., & Anderson-Cook, CM, 2009, Response Surface Methodology; Process and Product Optimization using Designed Experiments, Wiley.

Participants are encouraged to bring a laptop for use in the course. No software is required for the program, but if you have experimental design software on your laptop, it can be used to show how to implement RSM.

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