On Predicting Failures in a Future Time Period From Known Observations

The problem of a prediction interval for the number of failures of a system during a future time period knowing the failures observed during a time interval in the past is considered. It is assumed that the failures follow a Poisson process. Now, if the failures in both time intervals were known, they could be used to test the hypothesis that the two observations were generated by the same Poisson law. By appropriately inverting the inequalities for the critical region of the above test, it is possible to generate the prediction limits for the number of failures in one time interval by observing the failures in the other time interval, provided both observations are subject to the same Poisson law.