The First Passage Time Distribution for a Parallel Exponential System with Repair.

摘要

In system reliability studies, one obtains via a fault tree analysis, the various combinations of possible events which lead to system failure. These events can be characterized by a collection of minimal cut sets; a minimal cut set of components has the property that if all components in the set are simultaneously out of order the system fails, independently of the behavior of other components, and is minimal in that none of its proper subsets has this property. The author obtains the generating function, moments and asymptotic distribution for the first passage time distribution of a parallel system. These, used in conjunction with the Esary-Proschan inequality, should yield good approximations to system reliability.