What is fault tree analysis?
Fault tree analysis (FTA) is a top-down, deductive failure analysis. You start with a single undesired outcome, the top event, and ask "what could cause this?" At each level, a logic gate states whether any one cause is enough (OR) or several must happen together (AND). You continue until you reach basic events: component failures, human errors or external events that need no further breakdown.
Developed at Bell Labs in the 1960s for missile launch control systems, FTA is now standard in aerospace, nuclear, automotive (ISO 26262), medical device risk management (ISO 14971) and process safety; the method itself is described in IEC 61025. It also works well as a structured root cause analysis when a failure needs more than one condition to occur.
Fault tree symbols
| Symbol | Name | Meaning |
|---|---|---|
| Rectangle | Event | The top event or an intermediate event that is developed further through a gate. |
| OR gate (pointed shield) | OR | The output occurs if at least one input occurs. |
| AND gate (flat bottom, rounded top) | AND | The output occurs only if all inputs occur. |
| Circle | Basic event | A root failure or error with a known probability; not developed further. |
| Diamond | Undeveloped event | An event not developed further for lack of information or because it is out of scope. |
How fault tree probabilities are calculated
For independent input events with probabilities p1…pn:
- AND gate: P = p1 × p2 × … × pn
- OR gate: P = 1 − (1 − p1) × (1 − p2) × … × (1 − pn)
The tool also derives the minimal cut sets using top-down Boolean expansion (MOCUS) with absorption. The probability of each cut set is the product of its basic events. Ranking cut sets by order and probability shows where a single extra safeguard would have the most effect.
Fault tree example
The example analyses an infusion pump over-infusion. The top event can be caused by a hardware free-flow fault (pump mechanism AND anti-free-flow clamp fail), by a wrong rate that dose error reduction does not catch, or by a software defect. The tree gives a top event probability of about 7.05 × 10-4, dominated by the human-error branch. Four minimal cut sets result, including one single point of failure (the software defect) that should be addressed through design verification.
When to use fault tree analysis
- When a serious event needs a rigorous analysis of how independent failures combined.
- In design risk management to check that no single failure can lead to a hazard.
- In root cause investigations where a fishbone or 5 Whys is too linear to describe the interaction of causes.
- To evaluate safeguards: see how adding an AND condition (a barrier) lowers the top event probability. Pair it with a barrier analysis.
How to use this Fault Tree Analysis tool
- Define the top event. Describe the undesired event precisely, including the system and conditions, for example "Infusion pump delivers an over-infusion".
- Identify immediate causes. Add the events that directly cause the top event and choose an OR gate (any one is enough) or an AND gate (all are needed).
- Develop each branch. Keep breaking intermediate events down until you reach basic events, such as component failures or human errors, that need no further development.
- Mark undeveloped events. Use undeveloped events for causes outside the scope of the analysis or without enough information.
- Add probabilities. Enter a probability for each basic and undeveloped event. The tool calculates every gate and the top event live.
- Review cut sets and export. Check the minimal cut sets for single points of failure, then export the tree and tables to PDF, PNG or Excel.
Frequently asked questions
What is fault tree analysis (FTA)?
Fault tree analysis is a top-down, deductive method that starts from an undesired event (the top event) and breaks it down, through AND and OR logic gates, into the combinations of lower-level failures and errors that can cause it. It is used in reliability engineering, safety analysis and root cause investigations.
What is the difference between an AND gate and an OR gate?
An OR gate means the output event occurs if any one of its input events occurs; its probability is 1 minus the product of (1 - p) of the inputs. An AND gate means all input events must occur together; its probability is the product of the input probabilities.
What is a minimal cut set?
A minimal cut set is the smallest combination of basic events that, if they all occur, causes the top event. Removing any event from the set means the top event no longer occurs. Cut sets with a single event are single points of failure and usually deserve priority.
What is the difference between FTA and FMEA?
FMEA is bottom-up: it starts from each component or process step and asks how it can fail and what the effect would be. FTA is top-down: it starts from one undesired outcome and works out every combination of failures that can lead to it. They are complementary and often used together in risk management, for example under ISO 14971.
How does this tool calculate the top event probability?
It combines the probabilities of basic and undeveloped events through each gate, assuming the events are statistically independent and each appears only once in the tree. For trees with repeated events or dependent failures, use the minimal cut sets with a dedicated reliability package.
Can I use fault tree analysis without probabilities?
Yes. Many teams use FTA qualitatively during root cause analysis to map how failures combine and to find single points of failure. The minimal cut sets are calculated even when probabilities are missing.