Calculating mean system-failure frequency with prescribed accuracy

To calculate mean system-failure frequency (MSFF) for good engineering designs, an approximation with prescribed accuracy is possible, starting from mincuts, viz, from a sum-of-products form of the fault-tree Boolean-function. Bonferroni-type inequalities, for which a new proof is included, are used. There is a far-reaching similarity between certain kinds of bounds for MSFF (of coherent systems) and for system unavailability. However, this similarity Is not complete. For most real systems, omitting the less-important mincuts yields lower bounds not only for unavailability but also for MSFF. Because an equivalent of the first Bonferroni inequality also holds with MSFF, it is possible to determine an upper bound of the contribution of the deleted mincuts or, the other way around: given a maximum error, determine a set of less-important mincuts, which can be deleted prior to a standard (exact) analysis of the rest. Since 1977 there is a valuable insight that Bonferroni-type inequalities hold also for MSFF (and since 1995 for mean electronic-system life). However, if the difference between the first upper and lower bounds is not small enough, then the investigation of further bounds might be rather cumbersome. However, there is a straight-forward mincut-based approximation to MSFF. As for approximate values of system mean time to failure (MTTF) and mean time to repair (MTTR), upper and lower bounds can be readily found via MSFF=unavailability/MTTR=availability/MTTF using upper and lower bounds for unavailability and MSFF in an obvious way. Of course, these bounds might not be sufficiently tight initially