We investigate a refinement of the local, average and closed binding number of a graph in terms of mean closed binding number. Like the closed binding number itself, the mean closed binding number cbind mof G measures graph vulnerability, which is more sensitive. In this study, we define the parameter and find some bounds on the mean closed binding number of some special graphs. Further, some results have been obtained from graph operations. The closed binding degree of a graph is defined and its value for different graphs is obtained.