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Product performance varies with respect to time and space in many engineering applications. This paper discusses how to measure and evaluate the robustness of a product or component when its quality characteristics (QCs) are functions of random variables, random fields, temporal variables, and spatial variables. At first, the existing time-dependent robustness metric is extended to the present time- and space-dependent problem. The robustness metric is derived using the extreme value of the quality characteristics with respect to temporal and spatial variables for the nominal-the-better type quality characteristics. Then, a metamodel-based numerical procedure is developed to evaluate the new robustness metric. The procedure employs a Gaussian Process regression method to estimate the expected quality loss that involves the extreme quality characteristics. The expected quality loss is obtained directly during the regression model building process. Four examples are used to demonstrate the robustness analysis method. The proposed method can be used for robustness analysis during robust design optimization (RDO) under time- and space-dependent uncertainty. 

Product performance varies with respect to time and space in many engineering applications. This work discusses how to measure and evaluate the robustness of a product or component when its quality characteristics are functions of random variables, random fields, temporal variables, and spatial variables. At first, the existing time-dependent robustness metric is extended to the present time- and space-dependent problem. The robustness metric is derived using the extreme value of the quality characteristics with respect to temporal and spatial variables for the nominal-the-better type quality characteristics. Then a metamodel-based numerical procedure is developed to evaluate the new robustness metric. The procedure employs a Gaussian Process regression method to estimate the expected quality loss that involves the extreme quality characteristics. The expected quality loss is obtained directly during the regression model building process. Three examples are used to demonstrate the robustness analysis method. The proposed method can be used for robustness assessment during robust design optimization under time- and space-dependent uncertainty.