Date: 5 March 2024
Time: 3pm – 5pm (GMT)
Topics and Speakers:
Response surface basics – Designs and models for response surface modelling
Robert Collis (Minitab)
Practical challenges in Response Surface Modelling - Alternative models and simulation
Stephen L R Ellison – LGC Limited, Middx, UK
Summary
Response surface modelling is one of the essential statistical tools in the process optimisation armoury. It provides economical experimental designs for situations involving a response that depends in a non-linear fashion on a number of continuous factors and, sometimes, on a small number of qualitative factors. The methodology is widely used to find optimal process settings or mixture compositions for industrial production, typically maximising key quality characteristics. This event included two presentations, covering the foundations of effective response surface modelling and exploring some of the challenges encountered in practice.
After a brief introduction, Robert Collis (Minitab) began with a thorough description of the most common experimental designs for response surface modelling, together with a look at recommended practice for analysis of the resulting data. The most common experimental designs are so-called ‘central composite’ designs, which Robert described in detail. These give good coverage of the region of interest, give equally confident prediction at each design point, and can be separated into shorter experiments.
Another useful design is the family of Box-Behnken designs which can require a smaller number of runs, but are harder to separate into shorter experiments. Fitting a smooth curve through the data gives a ‘response surface’ that can be used, numerically or graphically, to choose the best combinations of operating parameters for the process. Data analysis was illustrated with an example of process optimisation from the paper industry. The data analysis typically involves elimination of unimportant terms (‘model reduction’); the presentation included detailed recommendations for the best approach to model reduction.
Steve Ellison (LGC Teddington) presented three examples of optimisation using response surface modelling, each illustrating different challenges and solutions. An example of optimisation of conditions for quantitative magnetic resonance imaging (MRI) for diagnostic purposes initially involved a very large number of individual parameters because of the complicated sequences of radiofrequency pulses used in the process. The problem as simplified by focusing on the main control parameters, such as the primary Rf pulse width and the width for repeated sequences, and partly by use of familiar ‘screening’ experiments. The study had been complicated by the need to optimise simultaneously over nine different imaging targets; separate response surface models for all nine, however, allowed researchers to show that shorter pulse sequence durations led to usefully reduced estimation errors as well as a shorter overall imaging time – important when a patient has to be stationary for imaging. An example of chromatographic analysis for pharmaceutical purity control showed that a real response surface could be very complex, underscoring a need to check for a smooth response and find a good ‘starting point’ before embarking on large experiments. Finally, an example of measurement of tin, a contaminant in foodstuffs, showed that the most commonly used model is not always appropriate; in this case a model based on knowledge of typical chemical processes gave a more realistic description of the response, while a simple smoothing model proved useful for quick visualisation.
Discussion after the presentations included the use of different criteria for model reduction, and pointers for optimal placement of additional points in a design. For optimal sampling, using acquired data, use of a relatively new technique, Bayesian Adaptive Design, was suggested; this can maximise information gain to give an efficient survey of the region of interest.