This paper describes a general method for convolving discrete distributions using Fast Fourier Transforms. It can be used in evaluating reliability of any system involving discrete or discretised convolution. It has been used in power system studies to deduce capacity-outage probability tables and to solve probabilistic load flows. These studies have shown it to be much less time-consuming and more efficient than the conventional direct methods. The method is used in the paper to evaluate the loss of load probability of a generating system in order to demonstrate the method's application and inherent merits.