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1 Electronics and Telecommunications Quarterly

1 2008

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Arithmetic and Boolean techniques for derivation of system reliability expressions

Falkowski B. J., Lozano C. C., Łuba T.

Electronics and Telecommunications Quarterly

2008

Vol. 54, No 2

167-177

Reliability analysis of a system conducted in the Probabilistic (Arithmetic) domain is lengthy and error-prone. 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. In order for the conversion of the reliability expression from Boolean domain back to the Probabilistic domain to be on a one-to-one basis, the Boolean expression should be fully disjoint. In this article basic properties and definitions of Probabilistic and Boolean domains are presented. 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 to obtain disjoint cubes representation of the path set expression of the system are also shown.