System failure frequency is a very useful measure in reliability engineering. The cost of a system not only depends on the system downtime but also on the number of failures. Total number of failures within an interval can be found by integrating the failure frequency over that interval. Further, frequency can be used to find the approximate reliability of complex systems.

Failure frequency is the summation of frequencies of all transitions from good states to failed states. This means that all of the transitions that lead to system failure are summed. For example, consider the system shown in Figure 8-2. The system failure frequency is P2(t)λ2+P3(t)λ1.

Using this same method, system recovery (repair) frequency can also be found. In this case, however, the transitions from failed states to good states should be considered. Under steady-state conditions, system failure frequency is equivalent to system recovery (success) frequency.