Abstract: In this paper, a two-failure-mode system is discussed. It is assumed that while the system is working in a normal stage, it can enter failure 1 immediately or failure 2 after passing through an abnormal stage. Failure modes are self-announcing modes whereas normal modes and abnormal modes are non-self-announcing modes. While the system is working, it is inspected once every time interval to make sure it is normal or abnormal until it fails, or until the result of inspection is that it is abnormal. The duration of the inspection is a random variable. The reliability indices and the optimal inspection polices of the system are derived by using the density evolution method.