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This paper regulates a rational approach of robust design in material machining process on basis of the probability method for multi-objective optimization. As an expansion, it takes the arithmetic mean value of the performance index of the alternative and its deviation as twin independent responses to make contributions of two parts of the partial favorable probability individually; the arithmetic mean value of the performance index represents the performance index according to its function and preference in the assessment, and the deviation exhibits an index with the characteristic of the smaller the better in general. Furthermore, the product of the above twin parts of partial favorable probability forms the actual favorable probability of the performance index of each alternative in the treatment, which is the unique indicator of the performance index of the alternative in the robust optimum. Moreover, examples are given to illustrate the application of the approach. [ABSTRACT FROM AUTHOR]

Till now the previous methods for multi-objective optimization adopt the "additive" algorithm for the normalized evaluation indexes, which has the inherent shortcoming of taking the form of "union" in the viewpoint of set theory. In fact, "simultaneous optimization of multiple indexes" should be more appropriate to take the form of "intersection" for the normalized evaluation indexes in the respects of set theory and "joint probability" in probability theory. In this paper, a new concept of favorable probability is proposed to reflect the favorable degree of the candidate material in the selection; All material property indicators are divided into beneficial or unbeneficial types to the material selection; Each material property indicator correlates to a partial favorable probability quantitatively, and the total favorable probability of a candidate material is the product of all partial favorable probabilities in the viewpoints of "intersection" of set theory and "joint probability" in probability theory, which is the sole decisive index in the competitive selection process. Results of the application examples indicate the validity of the new method.