In this paper we have proposed a method of moments to calculate the parameters of a Weibull distribution. The proposed method belongs to the family of nonparametric methodologies. It is based on the nonparametric determination of the values of the cumulative distribution, given the assigned sample. The parameter estimates, performed by the proposed methodology, appear to be robust enough, if compared to the classical method of moments. For this reason, the proposed methodology can be indicated for analysing the real working conditions of mechanical systems (e.g., transmissions, rolling organs, kinematics couples, etc) or time series analysis.