Example Trends in Fault Tree Models and Cut Sets

This example demonstrates how the cut sets can be identified and constructed for different arrangements of OR and AND gates logically defining a top event occurrence. Generally, the number of cut sets increases by increasing the number of OR gates in the tree. For example, Figure 9.13 shows this trend by comparing cases a, b, and d. On the other hand, increasing the number of AND gates results in increasing the number of events included in the cut sets as shown in case c of Figure 9.13.

Common cause scenarios are events or conditions that result in the failure of seemingly separate systems or components. Common cause failures complicate the process of conducting risk analysis because a seemingly redundant system can be rendered ineffective by a common cause failure. For example, an emergency diesel generator fed by the same fuel supply as the main diesel engine will fail with the main diesel generator, if the fuel supply is the root source of the failure. The redundant emergency diesel generator is not truly redundant due to a common cause failure. Another example of common cause events is the failure of two separate but similar pieces of machinery due to a common maintenance problem, two identical pieces of equipment failing due to a common manufacturing defect, or two pieces of equipment failing due to a common environmental condition such as the flooding of a compartment or a fire in the vicinity of both pieces of machinery. A method for calculating the reliability of a system while taking into account common cause effects is the beta-factor model. Other methods include multiple Greek letter model, alpha-factor model, and beta-binomial failure-rate model.

FIGURE 9.12 (a) Success tree for the pipe system example. (b) Fault tree for the pipe system example.

Case a

Case c

Top event 1

Top event 3

Cut Sets:


Case b

Top event 2


Case d

Cut sets:

Top event 4

Cut sets:

FIGURE 9.13 Trends in fault tree models and cut sets. (From Maryland Emergency Management Agency (MEMA), 2006, State of Maryland Guide for the Protection of Critical Infrastructure and Key Resources for Homeland Security, Volume 1: Critical Asset & Portfolio Risk Assessment (CAPRA) Methodology, Office of Homeland Security, Annapolis, MD.)

Part of risk-based decision analysis is pinpointing the system components that result in high-risk scenarios. Commercial system reliability software provides this type of analysis in the form of system reliability sensitivity factors to changes in the underlying component reliability values. In performing risk analysis, it is desirable to assess the importance of events in the model, or the sensitivity of final results to changes in the input failure probabilities for the events. Several sensitivity or importance factors are available and can be used. The most commonly used factors include (1) Fussell-Vesely factor and (2) Birnbaum factor. Also, a weighted combination of these factors can be used as an overall measure.

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