Entry-time processes are finite-state continuous-time jump processes with transition rates depending only on the two states involved in transition, the calendar time, and the most recent arrival time, which is termed as entry-time. The entry-time processes have the potential to provide a significantly greater range of applicability and flexibility than traditional reliability tools for case studies related to equipment and components in nuclear power plants. In this dissertation, the finite difference approximation of the integrodifferential Chapman-Kolmogorov equations for the entry-time processes was developed, and then it was verified by application to some hypothetical examples that are solved by alternative means, either (semi-)analytically or via simulation. To demonstrate the ability of entry-time model to applications in nuclear power plants for a RIAM based scenario, the entry-time approach is applied to the maintenance of main generators in nuclear power using the data from INPO-EPIX database. In this application, both reliability and financial performances acquired using the entry-time approaches corresponding to different maintenance policies are presented and discussed to help make maintenance decisions for the plant management. The ability of the EPIX database to provide time-dependent failure rates is demonstrated and the techniques for extraction of failure rates from the database for main generators are also discussed.