New methodologies for rationally safeguarding a nuclear system in terms of economics have been developed based on the Bayesian decision theory and the risk management approach. Two methodologies are formulated and presented. In the first method, the two terms in which the cost for an error (Type-I or Type-II error) event is multiplied by the probability of that event occurring and are linearly combined. Second method is formed by utilizing the ratio of two types of risks for each type of error event. The two methods proposed generate adjusted and optimized S (detection threshold) values under given conditions and depending on the expectation of costs for error events. The results show that the methods suggest adjusted S values in terms of the risk and the cost benefit based on the error values. For instance, the Type-II error event is more forbidden for the system that treats more special nuclear materials (e.g. Pu) during a short period. Moreover, the long-time period without inspection could enhance opportunities for the Type-II error event occurring. These methods could contribute to a better understanding for managing the Type-I and Type-II error events in a nuclear system which should be safeguarded.