RISK5002 Chap.7 Event Trees and Fault Trees
Event Trees and Fault Trees
Scenario trees start from one event and branch. Event trees use forward logic from an initiating event through the success or failure of each control, multiplying a frequency by conditional probabilities to give outcome frequencies that sum back to the start.
Fault trees use backward logic from an undesired top event, linking causes with AND and OR gates, multiplying probabilities of independent events and adding those of mutually exclusive events, and listing cut sets. This chapter works a kitchen fire event tree and a vaccine fridge fault tree, sets out the symbols and construction rules, and practises the past exam choice between a fault tree and scenario analysis.
The arithmetic rules are where most marks are lost, so the chapter states them precisely: probabilities multiply at AND gates only for independent events, they add at OR gates only for mutually exclusive events, two frequencies are never multiplied, and probabilities are never added to frequencies.
Worked checks, such as summing event-tree outcomes back to the initiating frequency, catch errors before they reach the final answer. The chapter also explains the symbols you may be asked to draw and the strengths and limitations that decide between methods.
What this chapter covers
- 01
Two kinds of scenario tree
- 02
Forward logic and conditional probabilities
- 03
Fault tree symbols and rules
- 04
AND and OR gate arithmetic
- 05
Cut sets and routes to failure
- 06
Choosing between a fault tree and scenarios
Worked example · free
Top-event probability for a vaccine fridge fault tree
- +1AND gate: P(both supplies fail) = 0.05 x 0.2 = 0.01.
- +1OR gate, treating inputs as mutually exclusive: P(top) = 0.01 + 0.01 = 0.02.
- +1Cut sets: {outage, generator failure} and {thermostat failure}, so T = A.B + C.
- +1The single-event cut set carries half the risk, so a second independent thermostat is the first control to add.
Key terms
- Event tree
- A diagram of the mutually exclusive outcomes that follow an initiating event through each control.
- Fault tree
- A diagram linking the causes of an undesired top event through logic gates.
- AND gate
- A fault tree gate whose output occurs only if all of its inputs occur.
- Basic event
- A basic initiating fault or failure at the bottom of a fault tree.
- Initiating event
- The first event from which an event tree's branches of success and failure follow.
Event Trees and Fault Trees FAQ
When do I multiply and when do I add in a fault tree?
Multiply probabilities at AND gates when the input events are independent, and add probabilities at OR gates when the inputs are mutually exclusive. Two frequencies must never be multiplied together, and a probability must never be added to a frequency.
What does an event tree tell a manager?
It shows every outcome that can follow an initiating event, how often each is expected, and how much each control contributes. Comparing outcome frequencies with and without an improved control reveals which barrier is most worth strengthening.
What are the limitations of fault tree analysis?
It is hard to know whether every important pathway has been included, time dependencies are not modelled, only success or failure states are allowed, each tree has a single top event, and large systems produce very large trees.
What is a cut set and why does it matter?
A cut set is a group of basic events that is enough on its own to cause the top event. Expressing the top event as a sum of cut sets shows every route to failure. Cut sets containing a single event matter most, because one failure alone brings the system down, so they are usually the first places to add redundancy or another control.
Exam move
Draw one event tree and one fault tree each day for a week, each from a different setting, and quantify both. Check event trees by summing outcomes back to the initiating frequency, and check fault trees by listing cut sets and confirming each one alone produces the top event. Prepare a reasoned paragraph choosing between a fault tree and scenario analysis that always ends with a conclusion.
Before each practice question, write the four arithmetic rules at the top of the page and tick each one as you use it, so the conventions become automatic under exam time pressure.
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