Due to increased diversity of user needs and market globalization, use application and environment of the products have diversified. This causes the products are difficult to be designed. In other words, it is difficult for designers to find a unique design parameter value (a unique design solution) which assures the fluctuant products performance to be satisfied the design requirements. In such cases, the designers derive several values (range) of design parameters which can be adjusted by users or manufacturers and enable to satisfy the product performance by the adjustment. Unfortunately, the kind of design problems have not discussed sufficiently in the conventional robust design researches. This paper describes a robustness index which is applicable to such design problems and a mathematical consideration on a calculating method of the index using the Monte Carlo method.