Robust　analysis　is　important　for　designing　and　analyzing　algorithm　for　global　optimization.　In　this　paper,　we　introduced　a　new　concept,　robust　constant,　to　quantitatively　characterize　robustness　of　measurable　sets　and　measurable　functions.　The　new　concept　is　consistent　with　the　robustness　proposed　in　literature.　This　paper　also　showed　that　robust　constant　had　significant　value　in　the　analysis　of　some　random　search　algorithms　for　solving　global　optimization　problem.　©　Springer　International　Publishing　Switzerland　2015.