Nuclear power plant operations that follow current testing and maintenance requirements sometimes result in inadvertent reactor trips, and operating staffs devote a significant amount of time and effort in complying with these requirements. Significant benefits could result from changes in current technical specifications. The benefits and impacts of changes in allowed outage times (AOTs) and surveillance test intervals (STIs) are evaluated for an alternative system that consists of multiple trains and whose operation is alternated train by train. Because of testing and AOT requirements, the alternating system exhibits semi-Markovian characteristics that change states in accordance with a Markov process but take an arbitrarily distributed amount of time between changes. The state probabilities are quantified by memorizing the necessary number of past state probabilities. Two measures of plant performance, namely, core damage probability and plant unavailability (reactor downtime), were calculated for the evaluation of AOT and STI. Results indicate that there is an optimal point that gives the lowest core damage probability and that the methodology developed in this study can be applied to existing alternating systems to evaluate accurately the various alternatives in the technical specifications.