In this paper we estimate reliability of a system using Weibull distribution. Reliability is defined as when a product does not fail in an expected lifetime in specified conditions. In reliability applications Weibull Distribution is commonly used distribution. The Weibull distribution is a generalization of the exponential distribution. The two-parameter Weibull distribution can accommodate increasing, decreasing, or constant failure rates because of the great flexibility expressed through the model's parameter. This distribution is recognized today as industrial standard. This paper presents the maximum likelihood method for estimating the Weibull distribution parameters. Weibull distribution is widely used in engineering applications. Weibull distribution is analysis with the Weibull Data Plot depict failure analysis with extremely small samples. The Data plot is very helpful for engineers and managers.