SC QUALITY GUILDFault tree analysis
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Start from the failure you want to prevent, break it down through AND and OR gates to basic events, and get the top-event probability, the minimal cut sets and the events that matter most.
ON THE EXAM · CSSBB VI.D.2, CSQP II.B.1, IV.C, CMDA V.A, CQE III.E.4 · FREE · NOTHING YOU TYPE LEAVES YOUR BROWSER
Q-BotClick for an explanation of this tool.For educational use. This page is a study aid. The method behind it has far more depth and detail than one page and one tool can cover, and what you see here is not everything the method offers or everything this site offers. For full understanding and application, use the governing standards and texts, and seek further education, training or qualified advice. Results depend on the data you enter, so check them before relying on them.
What a fault tree does
Fault tree analysis (FTA) starts with one undesired event, the top event, and works down to the combinations of lower-level events that could cause it. It is deductive, top down. An FMEA is the opposite: it starts from each component or step and asks what its failure would lead to. FMEA finds the effects of known failure modes; FTA finds the combinations that lead to one effect.
Gates and events
- OR gate: the output occurs if any input occurs. For independent inputs, P = 1 − ∏(1 − Pi). For small probabilities this is close to the sum.
- AND gate: the output occurs only if all inputs occur. For independent inputs, P = ∏ Pi. AND gates are where redundancy shows: two pumps both have to fail.
- Basic event: where the tree stops, with a probability from data.
- Undeveloped event: a cause not broken down further, for lack of information or because it does not matter enough.
Minimal cut sets
A cut set is a set of basic events that together cause the top event. A minimal cut set is one with nothing to spare: remove any event and it no longer causes the top event. The minimal cut sets are the clearest output of a fault tree:
- A cut set of one event is a single point of failure.
- A cut set of two or more needs all of them at once, which is usually far less likely.
- Ranking the cut sets by probability shows where to act.
Repeated events and common causes
When the same basic event feeds more than one gate, multiplying gate by gate counts it twice and gives the wrong answer. This tool calculates from the basic events themselves, so repeats are handled exactly. In the worked example a shared power supply feeds both pumps. It appears as a single point of failure, which the "redundant" pump design hides.
Every figure assumes the basic events are independent. A common cause, such as one power supply, one maintenance error or one batch of bad parts, breaks that assumption. Model it as its own event.
Importance
The Fussell-Vesely importance of a basic event is the share of the risk coming from cut sets that contain it. A high value means improving that event lowers the top-event probability the most.
On the exam
CSQP names FTA among the tools for analyzing supplier risk (II.B.1) and for supplier root cause analysis (IV.C). CMDA lists it among the quality tools (V.A). CSSBB includes fault tree analysis in root cause analysis (VI.D.2). CQE covers reliability, safety and hazard assessment tools (III.E.4). Expect to read a fault tree, compute AND and OR gate probabilities, and say how FTA differs from FMEA.