System Failure Events Research Articles

Calculations of systems unreliability by algebraic manipulation of failure event

Computations of reliability of a given system is an important field of research in reliability engineering. There are many techniques available in the literature. Some of these are based on Boolean algebra's relations. In these papers unions of events have been reduced to give the reliability of a system. Reduction of union of events involve a lot of work and give rise to a large number of terms. In this paper we have adopted a different approach. We first set up some simple algebraic lemmas on intersections and give their proofs. Next we represent the system failure event as the intersection of paths failure events. By applying our lemmas on this intersection of events step by step we are able to expand the system failure event in the form of unions of mutually exclusive events. Simple substitution of probabilities of success or failure, as the case may be, of the events involved in the union of expanded form gives the unreliability of the system. The algorithm is explained by an example.

First-order concepts in system reliability

The reliability of structural systems is determined by use of first-order concepts. Probability estimates for the components are calculated by linearization of the boundary of the failure domain after transforming an arbitrary vector of uncertain variables into an independent, standard normal vector. A first-order solution to the multinormal integral occurring in the formulation for elementary series or parallel systems is given and a sequence of certain probability bounds on the union of failure events involving the failure probability of any parallel subsystem and the probability of the intersection of any two or three parallel subsystems is derived. The system failure event is represented by the minimal cut set of componental failure events. The accuracy of approximations is systematically investigated and shown to be sufficient for most practical purposes. The method is illustrated with a simple example.