Using a general approach for discretization of continuous life distributions in the univariate & bivariate situations, we have proposed a discrete Rayleigh distribution. This distribution has been examined in detail with respect to two measures of failure rate. Characterization results have also been studied to establish a direct link between the discrete Rayleigh distribution, and its continuous counterpart. This discretization approach not only expands the scope of reliability modeling, but also provides a method for approximating probability integrals arising out of a continuous setting. As an example, the reliability value of a complex system has been approximated. This discrete approximation in a nonnormal setting can be of practical use & importance, as it can replace the much relied upon simulation method. While the replication required is minimal, the degree of accuracy remains reasonable for our suggested method when compared with the simulation method.