This paper presents a method for dealing with parameter uncertainty in system design which is based on the study of the statistical properties of an ensemble of systems defined by a given structure and by aprioriparameter distributions rather than point parameter estimates. It is assumed that the model of the actual system is a random member of the ensemble. The object of the analysis is to design or modify the properties of the ensemble to ensure a high probability of adequate performance of the actual system. The primary statistical function employed is the sample distribution function. This function is used to estimate the true population distribution of a scalar variable chosen to measure the system property of interest. The sample distribution function is constructed from random samples of this figure of merit generated by a suitable digital computer programme. The accuracy of the estimation of the population distribution by the sample distribution is determined by application of statistical results of Kolmogorov and Rényi.