Summary: The availability of systems undergoing periodic inspections is studied in this paper. A perfect repair or replacement of a failed system is carried out requiring either a constant or a random length of time. In Model A, the system is assumed to be as good as new on completion of inspection or repair. For Model B, no maintenance or corrective actions are taken at the time of inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. Unlike that studied in a related paper by

*J. Sarkar* and

*S. Sarkar* [J. Stat. Plann. Inference 91, No. 1, 77–90 (2000;

Zbl 0962.90012)], our model assumes that the periodic inspections take place at fixed time points after repair or replacement in case of failure. Some general results on the instantaneous availability and the steady-state availability for the two models are presented under the assumption of random repair or replacement time.