We survey reliability models of a server system connected with the Internet, and treat several stochastic models. It is important to detect cyber attacks in the early stage. However, when the number of checks increases, the total cost of the checking increases. That is, if the check is performed frequently, the overhead of system processing becomes larger. Therefore, in terms of monitoring, it is necessary to perform checking under appropriate management policy. In this chapter, we formulate stochastic models in which the nth attack causes damage to a server system. Moreover, we formulate stochastic models in which attacks cause small damage and big damage. Furthermore, we modify these models considering two different types of attacks and non-linear parameter. In these models, expected costs until cyber attacks are detected are derived. Further, optimal policies which minimize them are discussed. Finally, numerical examples are given.