Analysing the results of a designed experiment when the response is a curve: Methodology and application in metal injection moulding

In (designed) industrial experiments, the response observed often takes the form of a curve representing, for example, the evolution of a quality characteristic over a period of time. In such a context, the polynomial regression approach, usually used in response surface analysis to predict the response as a function of the experimental factors, should be adapted to the functional character of the response. This paper reviews several possible methods of analysing the results of a designed experiment when the response is a curve and compares them with a case study from the metal injection-moulding industry. Three different approaches are first presented to fit a model to the (functional) data: two-step nonlinear modelling; pointwise functional regression; and smoothed functional regression. All of the models derived are able to predict the functional response from any design factor setting chosen in the experimental domain. Two inferential problems are then discussed: the significance testing of experimental factor effects and the calculation of prediction intervals around predicted curves. Asymptotic results and bootstrap procedures are compared in this context. Copyright (c) 2005 John Wiley & Sons, Ltd.