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In many complex experiments, nuisance factor may have large effects that must be accounted for. Covariates are one of the most important kinds of nuisance factors that can be measured but cannot be controlled within the experimental runs. In this paper a novel approach is proposed, based on goal programming, to find the best combination of factors so as to optimize multiresponse-multicovariate surfaces with consideration of location and dispersion effects. Furthermore, it is supposed that several covariates considered in the experiment have probability distributions of known form. One objective is to find the most probable values of each covariate. For this purpose, a multiobjective mathematical optimization model is proposed and its efficacy is demonstrated by two numerical examples. Copyright

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In many real-world applications, the quality of a process or a particular product can be characterized by a functional relationship called profile. A profile builds the relationships between a response quality characteristic and one or more explanatory variables. Monitoring the quality of a profile is implemented to understand and to verify the stability of this functional relationship over time. In some real applications, a fuzzy linear regression model can represent the profile adequately where the response quality characteristic is fuzzy. The purpose of this paper is to develop an approach for monitoring process/product profiles in fuzzy environment. A model in fuzzy linear regression is developed to construct the quality profiles by using linear programming and then fuzzy individuals and moving-range (I-MR) control charts are developed to monitor both intercept and slope of fuzzy profiles to achieve an in-control process. A case study in customer satisfaction is presented to show the application of our approach and to express the sensitivity analysis of parameters for building a fuzzy profile.

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