This paper presents an analysis and explanation of the system performance calculations performed by the reliability and service probability subroutines of the Ionospheric Communication Analysis and Prediction Program (IONCAP) and an IONCAP derivative, termed VOACAP. A review of the three components needed to properly statistically describe the performance of a communications system or link is presented. These components are needed to account for the short-term and long-term statistical variations of the desired signal and the interference and also the inherent prediction errors. A detailed numerical example is given for illustration and explanation. Suggestions for modification and improvement are also given.