Strategies for multi-response parameter design using loss functions and joint optimization plots

The development of high-quality products or production processes can often be greatly improved by statistically planned and analysed experiments. Taguchi methods proved to be a milestone in this field, suggesting optimal design settings for a single measured response. However, these often fail to meet the needs of today’s products and manufacturing processes, which require simultaneous optimization over several quality characteristics. Current extensions for handling multi-responses assume that all responses are weighted beforehand in terms of costs due to deviations from desired target settings. Such information is usually unavailable, especially with manufacturing processes. As an alternative solution, we propose strategies that use sequences of possible weights assigned to each of the multiple responses. For each weighting a design factor combination is derived, which minimizes a respective estimated multivariate loss function and is optimal with respect to some compromise of the responses. This compromise can be graphically displayed to the engineer, who can thereby gain much more insight into the production process and draw more valuable conclusions.