Mostafa Borouomand Zadeh - Faculty Member, Department of ICT, Payam Noor University, Khuzestan of IRAN
Sayed Mohsen Hashemi - Young Researchers Club, mayboad Branch, Islamic Azad University, mayboad, Iran

Nowadays , service providers in their services, in addition to the quality and service assurance have high focus on reduce the cost of services and acceleration in offering them .To a chive this , defining the quality and performance indicators modeling service , analysis service layers and relevant substrate are the most important operating and applied procedure .So in this paper ,mathematics and statistics and finally MATLAB software ,effectiveness rate ,efficiency and the importance of elements related to mother service has been challenged by definition of subservices relations (child nodes) with mother service (parent node) and manual and systematic sampling from it in a network or mail service . This process will be extended to all service and their related structures.

Service Assurance, modeling service, random variables, tree structure, key performance indicator (KPI)