The Reliability of Dependent Parallel or Standby N-Unit Redundancies

This paper is concerned with evaluating the reliability of a redundant configuration, given that at any random time its surviving components are operating with failure distributions that are dependent upon the set of failed components. An expression (9) is derived for the reliability of this class of configurations and is then generalized to obtain an expression (23) for the reliability of a similar configuration whose component failure distributions are dependent also upon the time of the last such failure. These expressions are then applied to evaluating the reliability of a stand-by configuration with off-line failures, and the reliability of a parallel configuration for which at least a certain number of components must survive in order that the configuration operate satisfactorily.