Citation

Dunbar LC. Reliab. Eng. 1984; 7(3): 169-179.

Copyright

(Copyright © 1984, Elsevier Publishing)

DOI

10.1016/0143-8174(84)90015-5

PMID

unavailable

Abstract

This paper studies the probability of failure of a system of two or three redundant components. Failure for the system is defined as the failure of all components for the duration of a given finite time T. The implications of this condition of failure duration are discussed. Starting from standard expressions for the probability of failure and the probability of repair with constant failure and repair rates, expressions for the probability of failure as described above are derived. Particular attention is devoted to the part representing the failure to repair, whose derivation is described in detail. Expressions for systems of different components and of identical components are given.

Some mathematical properties of the expression for two identical components are discussed and these are related to the properties of the system. Two short examples are given to show the advantages of the application of the new formulae over less accurate expressions.