Abstract: This paper deals with a model of repairable systems which are checked at a time. The system has two working modes (normal and abnormal) and two failure modes. The failure modes are not checked, and when the system is operating it is checked once every time period until it attains the failure modes or is detected to be in the abnormal modes. The system-checking may bring about wrong conclusions. The system reliability indices and the method for calculating the optimal checking cycle and the optimal critical value of the diagnostic parameter are obtained by using probability analysis, the supplementary variable technique and optimization method.