In product design and manufacturing, axiomatic design provides a systematic approach for the decision-making process. Two axioms have been defined such as the Independence Axiom and the Information Axiom. The Information Axiom states that the best design among those that satisfy the independence axiom is the one with the least information content. In other words, the best design is the one that has the highest probability of success. On the other hand, the Taguchi robust design is used in the two-step process; one is "reduce variability," and the other is "adjust the mean on the target." The two-step can be interpreted as a problem that has two FRs (functional requirements). Therefore, the Taguchi method should be used based on the satisfaction of the Independence Axiom. Common aspects exist between the Taguchi method and Axiomatic Design in that a robust design is induced. However, different characteristics are found as well. The Taguchi method does not have the design range, and the probability of success may not be enough to express robustness. Our purpose is to find the one that has the highest probability of success and the smallest variation. A new index is proposed to satisfy these conditions. The index is defined by multiplication of the robustness weight function and the probability density function. The robustness weight function has the maximum at the target value and zero at the boundary of the design range. The validity of the index is proved through various examples.gh various examples.