The Uncertainty of System Failure-Rate Predictions

The relative uncertainty involved in the prediction of the failure rate of a system is often considerably less than the uncertainty associated with the failure rate of the average component. For example, if we are 60 percent uncertain of the failure rate of each of nine component types, then, at best, we are only 20 percent uncertain of the system failure rate. This result is a consequence of the variety of component types, not the number of each type present in the system. The relative uncertainty associated with the prediction of the number of future system failures is always greater than that associated with system failure rate. As an example, let the uncertainty in system failure rate be 20 percent. If the Poisson process yields a 40 percent uncertainty in the number of failures for an interval t1, then the actual uncertainty is 45 percent; for a larger interval t2, if the Poisson process yields 10 percent, the actual uncertainty is 22 percent. The fault is not with the Poisson process, but rather with the assumption that the estimated failure rate can be treated as the true failure rate.