In this research a simply supported beam is used as a master structure with unknown number of attachments (fuzzy substructure) which is modeled as a system of 1-DOF attachments. Two types of attachments models were studied, namely 1-DOF mass attachment model and 1-DOF mass-spring attachment model. It is shown that the effect of attachments on the master structure natural frequencies when modeled as (mass-spring substructure) is larger than that when modeled as (mass substructure) for the same attachment mass. Engineering Statistics and normal distribution were used to find the values of the attachments to be added to the simply supported beam to improve the dynamical properties of the master structure and to find the best distribution of the attachment. The results also show that the distribution of the additional substructure can produce a great change in the natural frequencies so that the proposed statistical approach can be used to find the best distribution of attachments and number, value and location of the additional substructure .