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Multiresponse quality design and possibilistic regression

Multiresponse quality design techniques are used to identify settings of process parameters that make the product's performance close to target values in the presence of multiple quality characteristics. In many situations, these quality characteristics and thus their functional relations are imprecise to some degree due to nonspecificity, measuring errors, incomplete knowledge, vagueness of definitions and so on. Here, possibility distributions and possibilistic regression models are used to model these imprecise natures and induced imprecise functional relationships. We first integrate and extend existing possibilistic regression methods to obtain unified measures of predictive quality characteristics or responses. We then propose a multiple objective programming model to obtain an appropriate combination of process parameter settings based on the obtained possibility distributions of imprecise predictive responses. We not only optimize the most possible responses values, but also minimize the imprecision or deviations from the most possible values.