An implicit method for incorporating common-cause failures in system analysis

A general procedure incorporates common-cause (CC) failures into system analysis by an implicit method; i.e., after first solving the system probability equation without CC failures. Components of subsets are assumed to be equally vulnerable to CC of any particular multiplicity. The method allows for age-dependent hazard rates, repairable and nonrepairable components, systems with multiple CC groups, and systems where not all components are statistically-identical or subject to CC failures. Key equations are given both for reliability block-diagrams and fault-trees (success and failure models), considering the system reliability, availability and failure intensity functions. Initial failures and certain human errors are included, mainly for standby-system applications. The implicit method can dramatically simplify the Boolean manipulation and quantification of fault trees. Possible limitations and extensions are discussed.