Predicting software's minimum-time-to-hazard and mean-time-to-hazard for rare input events

This paper turns the concept of input distributions on its head to exploit inverse input distributions Al though such distributions are not always true math ematical inverses they do capture an intuitive prop erty inputs that have high frequencies in the original distribution will have low frequencies in the inverse distribution and vice versa We can use the inverse distribution in several di erent quality checks dur ing development Here we will provide a fault based fault injection method to determine minimum time to failure and mean time to failure for software sys tems under normal operational and non normal op erational conditions meaning rare but legal events In our calculations we will consider how various pro grammer faults design errors and incoming hardware failures are expected to impact the observability of the software system