A Birnbaum importance measure is the rate of change in the top gate probability with respect to the change in the unavailability of a basic event. Therefore, the ranking of events obtained using the Birnbaum importance measures is helpful when selecting the event to improve when the actual efforts for improvement is the same for all events. The Birnbaum importance measure for event A can also be calculated as the difference in the probability of the top event given that event A did occur minus the probability of the top event given that event A did not occur.

The Birnbaum importance measure is defined as:

Where:

The Birnbaum importance measure for event A can also be viewed as the probability that the system is in such a state that event A is critical for the occurrence of the top event. Birnbaum importance measures play a crucial role in defining several other importance measures and calculating several system performance measures such as system failure frequency.

If unavailabilities of individual events are unknown, then the Birnbaum importance measure can be calculated by setting event unavailabilities to 0.5 to find the events that are critical to the top event. This importance measure is known as the structural importance measure.

While the Birnbaum importance measure is useful, it does not directly consider how likely event A is to occur. This measure is independent of the actual unavailability of event A, which can lead to assigning high importance measures to events that are very unlikely to occur and may be very difficult to improve. Therefore, to focus on events that are not only critical to the top event but also are more likely to occur, a modified Birnbaum importance measure known as the criticality importance measure is typically used to determine the next basic event to improve.