Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2014.2854.2856El DamsesyMedhat AhmedMohammed El GenidyMohammedEl GazarAhmed Mohammed1220141421This study relied on applications of statistical methods used in the field of physics, specifically study the relationship between the strength and stress of a component in the mechanical system and so the performance of the mechanical system can be estimated. The study dealt with the estimation of the system performance R where R is equal to P[Y<X] and [X,Y] are independent random variables represent the strength of a component in the system and stress, respectively belonging to Pareto distributions with three parameters. The maximum likelihood was implemented to estimate the values of the parameters. On the other hand, simulation study was applied to investigate the measure of the system performance R and a numerical application was presented to illustrate the implementation of mathematical procedures, moreover the steps method used in this study enables the researchers to apply it in their fields.]]>Adeyemi, S. and M.O. Ojo,2004El Desoky, E.A.,2006Gholipoor, M. and S. Shahsavani,2008Hassan, C.S., P. Hussain and M. Awang,2011Li, J. and Z. Kou,2013Mohebbi, M., K. Nourijelyani and H. Zeraati,2007Nugraha, J.,2011Peiravi, A. and H.T. Kheibari,2008Proschan, F.,1963Chu, S.L.,2013