The reliability analysis of the engineered safety systems of nuclear power plants requires the calculation of the pointwise and average unavailabilities of redundant systems under periodic test and maintenance. The complexity of the calculations usually requires simulation for realistic results. However, simple analytical expressions showing the significant contributions to the unavailability provide insights concerning the relative importance of the potential failure modes of the systems, such as hardware failures, demand-type failures, human errors, and various types of dependent (common cause) failures. These expressions can be used for a quick calculation of the unavailability as well as the propagation of uncertainties by analytical methods, e.g., the method of moments.