Availability of Series Systems with Various Shut-off Rules

In series systems (reliability block diagram), failure of any component leads to system failure. However, depending on the shut-off rule, some components may continue to operate with the system down. In this paper we consider several shut-off rules for series systems performance. We calculate limiting system availability under these shut-off rules. In particular, availability results for 2-and 3-unit systems with constant failure and repair (hazard) rates are extended to systems of arbitrary size.