Most of the existing methods for the analysis and optimization of multiple responses require some kinds of weighting of these responses, for instance in terms of cost or desirability. Particularly at the design stage, such information is hardly available or will rather be subjective. An alternative strategy uses loss functions and a penalty matrix that can be decomposed into a standardizing (data-driven) and a weight matrix. The effect of different weight matrices is displayed in joint optimization plots in terms of predicted means and variances of the response variables. In this article, we propose how to choose weight matrices for two and more responses. Furthermore, we prove the Pareto optimality of every point that minimizes the conditional mean of the loss function.

A joint optimization plot, shortly JOP, graphically displays the result of a loss function based robust parameter design for multiple responses. Different importance of reaching a target value can be assigned to the individual responses by weights. The JOP method simultaneously runs through a whole range of possible weights. For each weight matrix a parameter setting is derived which minimizes the estimated expected loss. The joint optimization plot displays these settings together with corresponding expected values and standard deviations of the response variable. The R package JOP provides all tools necessary to apply the JOP approach to a given data set. It also returns parameter settings for a desirable compromise of achieved expected responses chosen from the plot.

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The detection of structural changes in time series from industrial processes monitoring is of great interest. We investigate the limits and possibilities of two recently developed methods, one for the off-line detection of changed volatilities [Wied et al., 2011] and one for the on-line detection of changes in the course of the time series [Borowski and Fried, 2011]. The investigation is carried out on several time series from thermal spraying processes. The processes are deliberately manipulated to produce structural changes at known time points.

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