Robust　analysis　is　important　for　designing　and　analyzing　algorithms　for　global　optimization.　In　this　paper,　we　introduce　a　new　concept,　robust　constant,　to　quantitatively　characterize　the　robustness　of　measurable　sets　and　functions.　The　new　concept　is　consistent　to　the　theoretical　robustness　presented　in　literatures.　This　paper　shows　that,　from　the　respects　of　convergence　theory　and　numerical　computational　cost,　robust　constant　is　valuable　significantly　for　analyzing　random　global　search　methods　for　unconstrained　global　optimization.