The availability and hazard of a system under a cumulative damage process with replacements (Q607602)

For a system subject to a cumulative, compound damage process, the reliability function, hazard function and the failure time are considered. Here, the failure occurs if the damage process exceeds a certain threshold \(\beta\). Extending previous results, the hazard and the availability function is examined in the case that the system is replaced after each failure by a new one. After presenting the essential functions in case that there are no replacements, the case of instantaneous replacements and the case of random replacement times is studied.