Aggregation methods for reliability and availability calculations

Aggregation is a way to reduce the size of Markovian reliability and availability problems. Since exact aggregation is only possible in exceptional cases, we introduce a canonical partition for the Markovian states for systems with 2-state components that allows a systematic study of approximate aggregation. Restriction and prolongation operators are introduced to define aggregation. Four methods are proposed to define approximate systems of birth and death type. Examples are given for k-out-of-4 systems and for a 7 component system.