In this paper we presents the reliability and mean time to failure estimation of a system where the deteriorationrates follow the Weibull distribution. The system is two unit active parallel system where the units operates si-multaneously and maintenance is not allowed. We are particularly interested in the effect of the shape parameter(from Weibull Distribution) on the system reliability. Explicit expression for Mean time to failure of the systemis obtained analytically. Numerical study of the system using assumed data has shown that the choice of theshape parameter influences the time taken by the system to reach the failure state. Also, high values of the shapeparameter decreases system reliability. The Model developed in this paper is important to engineers, maintenancemanagers, and plant management for good maintenance decision.