Modeling Components and Systems with Buffers Providing a Grace Period

Most repairable systems have been modeled so far under the assumption that component failures have an immediate influence on the output reliability of a system. Modern technology provides many examples in which a failure of a component affects the system later than the failure occurs, and only if repair is not completed within a certain time T, a grace period. A clear distinction is made here between component failures and output failures which occur conditionally with delay T and often with a shorter downtime than the repair time. Some examples: * A pumping system with an intermediate storage. The output fails only if and when component repair is not completed within the time it takes to empty the storage. * A waste treatment system with buffer tanks. The output fails only if the buffer is filled before repairs are completed. * Room cooling (or heating) systems. Failures are harmful only if repair is not completed before the temperature goes above (or below) a critical limit. * Power generation systems with or without standby units. Severe consequences take place only when a power outage lasts longer than a critical time limit. * Space missions: failures are repairable as long as repairs are completed within a grace period. The very first output failure is catastrophic, but several short component failures may precede such an event.