Reliability analysis based on arithmetic and Boolean representations

Reliability analysis of a system conducted in the Probabilistic (Arithmetic) domain is lengthy and errorprone. An alternative method is to consider the system reliability components to be Boolean variables rather than Probabilistic variables and to treat the whole problem as if it were Boolean. This method allows the use of powerful Boolean reduction theorems to contain the size of the problem. The Boolean expression should be fully disjoint so that the conversion back to the Probabilistic domain would be on a one-to-one basis. Besides presenting basic properties and definitions of Probabilistic and Boolean domains, evaluation of reliability of a system directly from Arithmetic expansion is also discussed. Since the reliability expression may be directly obtained from disjoint cube representation, two methods are shown.