Probability of Component or Subsystem Failure Before System Failure

A method of determining the probability of having a given set of components failed and another set of components working at the time of system failure is based on the notion of boundary probability. The method is simple and easily applied to any s-coherent system for which the reliability structure is known. The application of this method is limited to the case of continuous probability distributions of time to failure because no simple method of computing boundary probabilities in the discrete case could be found. This is not, however, a major limitation of the method since in the majority of practical applications continuous random variables representing times to failure are used. The method can be extended to the case of non-s-independent random variables. Several examples illustrate the procedure.