Fault Tree Analysis (FTA)

Composed By Muhammad Aqeel Khan
Date 22/9/2025

What Is Fault Tree Analysis (FTA)? Definition & Origins

Fault Tree Analysis (FTA) is a deductive, top-down methodology used in safety engineering and reliability engineering to explore how undesired events (failures, faults, accidents) can occur in a system. You begin with a specified top event (the system-level failure or event you want to guard against) and then work downward to identify all combinations of basic events (component failures, human errors, environmental conditions, etc.) that could lead to that top event. FTA uses logic diagrams built with logic gates like AND, OR, XOR, inhibit, priority-AND, etc.

Historical Background & Standards

FTA was first developed in 1961-1962 by H.A. Watson at Bell Laboratories under contract with the United States Air Force, for analyzing the Minuteman I missile launch control system. superengineer.net+2arXiv+2
Since then, it has been adopted across aerospace, healthcare, and other industries. Key standardization includes IEC 61025 (Fault Tree Analysis).

Key Components of FTA: Events, Logic Gates, Top Events & Probability

To properly perform a Fault Tree Analysis, it helps to understand its fundamental building blocks:

Term	What It Means
Top Event	The undesired overall system failure you want to analyze (for example “Power Plant Shutdown” or “Patient Mortality in Hospital Ventilator”). It is the root of the fault tree.
Basic Events	The lowest-level causes that are not further decomposed (component failures, human error, environmental triggers). These are leaves in the tree.
Intermediate Events	Those events which are combinations of other events via logic gates; they form internal nodes between the top event and basic events.
Logic Gates	Boolean operators that define how events combine: – OR Gate: top event occurs if any of its input events occur. – AND Gate: top event occurs only if all of its input events occur. – XOR, inhibit, priority-AND, voting gates etc. for special logical or temporal conditions.

Probability Calculations & Quantitative Aspects

In quantitative FTA, one assigns failure rates, probabilities or unavailability values to basic events, and then propagates them upward through the tree to compute the probability of the top event.
For AND gates (assuming input events independent):

$P(\text{AND}) = P(A) \times P(B) \times \cdots$ $P (AND) = P (A) \times P (B) \times \dots$
For OR gates:

$P(\text{OR}) = P(A) + P(B) - P(A \cap B)$ $P (OR) = P (A) + P (B) - P (A \cap B)$
If events are mutually exclusive (or assumption simplifies), this often approximates to sum of probabilities.
The concept of Minimal Cut Sets (MCSs): smallest combinations of basic events that, if they all occur, the top event happens. These sets help prioritize which risk contributors are most critical.

How to Perform Fault Tree Analysis (FTA): Step-by-Step Guide

Here is a practical, stepwise method to carry out FTA, suitable for both beginners and trained engineers.

Define the Scope & Top Event
- Identify clearly what undesired failure or event you want to prevent. (e.g. “Total power loss in generator system”, “Critical software crash”, “Radiation leak”).
- Define system boundaries, operational context, environmental conditions.
Understand the System
- Gather system schematics, process flows, component functions.
- Consult subject matter experts. Identify possible failure modes and interactions.
Construct the Fault Tree (Qualitative Phase)
- Start from the top event. Decompose into contributing events using logic gates.
- Identify intermediate events, basic events. Use standard symbols (as per IEC 61025) for gates and event types. iTeh Standards+1
- Optionally include transfer symbols to modularize large trees.
Qualitative Analysis
- Identify minimal cut sets—combinations of basic events critical for the top event.
- Determine importance measures, i.e. which events are most critical / which combinations are highest risk.
Quantitative Analysis
- Assign probabilities, failure rates, or unavailability to basic events (from historical data, empirical databases, manufacturer specs).
- Propagate probabilities through logic gates to compute top event probability and intermediate event probabilities.
- Use analytical equations or software tools (many tools implement FTA).
Interpret Results, Identify Mitigation Paths
- Find which basic events or combinations have the highest risk or importance.
- Propose design or operational changes (e.g. redundancies, higher quality components, maintenance schedules, procedural safeguards).
Validation and Documentation
- Validate assumptions (independence, constant failure rates) and test sensitivity analysis.
- Document fault tree diagrams, data sources, minimal cut sets, probability calculations.
- Follow relevant standards (IEC 61025, ISO, etc.).

Comparing FTA with Other Risk Assessment Methods: FMEA, RBD, Event Trees

To choose the right tool(s), it helps to understand how FTA compares to related methods:

Method	Direction / Approach	Strengths of FTA vs Method	Limitations vs Method
FMEA (Failure Mode and Effects Analysis)	Inductive (bottom-up): you start from components/failure modes and see their effects.	FTA excels at modeling combinations of failures, calculating top-event probabilities, and system-level analysis.	FMEA is more exhaustive for single-component failure modes; better for early design phase; FTA may miss some rare component failure paths if these weren’t included.
Reliability Block Diagram (RBD)	Also inductive / success-tree oriented.	FTA allows modeling of more complex logical interactions and is better for unsafe or undesired event modeling. RBD is more intuitive for reliability (success) modeling.	RBD less suitable where interdependencies or conditional events are complex. FTA more complex to build & calculate for large systems.
Event Tree Analysis (ETA)	Starts from initiating event(es) and branches forward to possible outcomes.	FTA works backward (top-down) and helps ensure that you cover all cause combinations for a particular top event. ETA is better for modeling sequences and progression of events.	The two are complementary; often both are used.

Applications of Fault Tree Analysis (FTA) in Industries

FTA is used widely in sectors where safety, system reliability, and risk tolerance are critical.

Aerospace & Aviation: To assess failure of flight control systems, redundant systems, reliability of emergency shutdowns, etc. The huge costs and safety risks make combinations of failures particularly important.
Healthcare / Medical Devices: Ensuring devices like ventilators, imaging machines, or monitoring systems do not fail in combinations that cause harm. Considering human error plus device failure.
Manufacturing / Process / Chemical Industries: Preventing catastrophic process failures (chemical leaks, explosions), analyzing shutdowns, redundant safety systems.
Software / IT & Safety-Critical Systems: For embedded systems, control systems, automotive safety (e.g. ISO 26262). FTA helps when multiple faults or rare fault combinations may lead to system failure.

Real-World Case Studies of FTA Implementation

Here are examples showing FTA in action:

Minuteman Missile Launch Control System
- The origin of FTA. The USAF commissioned Bell Labs in 1961-62 to study how system failures (top event) could originate from subsystems. This shaped early quantitative FTA practice.
Survey of FTA State-of-the-Art (Ruijters & Stoelinga, 2015)
- A survey of over 150 papers on FTA methods, including dynamic fault trees, repairable systems, how modern tools handle modeling. Demonstrates scale, tool support, and growing complexity in real systems.
Industrial Systems Safety (Moraru et al.)
- An example in mechanical / manufacturing systems where probabilistic calculations using minimal cut sets were used to estimate system failure probability and guide component improvements. utgjiu.ro

Benefits & Limitations of Fault Tree Analysis

Key Benefits of FTA

System-level understanding: Helps see how combinations of faults lead to failure.
Quantification of risk: Can compute probabilities, failure rates, unavailability.
Prioritization: Identifies which basic events or components contribute most to risk; helps allocate resources to mitigation.
Compliance & documentation: Valuable for regulatory, safety, certification contexts; standardised approaches (e.g., IEC 61025).
Design improvement & redundancy: Insights from FTA often lead to better design, redundancy, improved monitoring.

Limitations & Challenges

Data scarcity: Accurate probability data for all basic events may be unavailable or uncertain.
Complexity explosion: In large systems, fault trees can become huge; minimal cut set calculations become complex.
Assumptions of independence / constant failure rates: These may not hold in real life (e.g., common-cause failures, aging, dependencies).
Temporal and dynamic behaviour: Standard FTA struggles to model temporal sequences, repairs, changing conditions unless using dynamic fault trees or specialized extensions.
Maintenance and updating: System changes, environmental changes, or operational changes can invalidate parts of the tree. FTA needs to be maintained.

Standards & Best Practices: IEC 61025 and Others

IEC 61025: International standard that defines Fault Tree Analysis—terms, symbols, qualitative and quantitative analysis requirements. The 2023 revision (prEN IEC 61025:2023) extends on calculating probabilities, dealing with non-coherent trees, dynamic elements, etc. iTeh Standards
NASA Fault Tree Handbook with Aerospace Applications: Guidance tailored for aerospace systems.
Other standards / guidance: ISO 26262 (automotive safety), MIL-STD, safety-critical system standards. These often require or recommend FTA or similar tools.

Best practices include rigorous documentation, validating probability data, performing sensitivity analyses, using software tools for large or complex systems, and combining FTA with complementary methods (FMEA, Event Trees, RBD).

Practical Example: A Simple Fault Tree Analysis

Let’s consider a simple example: a hospital’s backup power generator failing during an emergency.

Top Event: Generator fails to supply backup power when main power is lost.
Intermediate Events:
- A1: Main generator engine failure (basic event)
- A2: Fuel delivery failure (basic)
- A3: Switchgear malfunction (basic)
- A4: Control system error (basic)
Structure:
- Top Event = OR(Engine failure AND Control system error, OR(Fuel delivery failure, Switchgear malfunction))
- More precisely:
  - If both Engine & Control system fail (AND gate), then top event occurs.
  - OR if either Fuel delivery fails OR Switchgear fails.
Quantitative Data (hypothetical):
- P(A1) = 0.001 (engine failure)
- P(A2) = 0.0005 (fuel delivery failure)
- P(A3) = 0.0008 (switchgear failure)
- P(A4) = 0.002 (control system error)
Compute:
- For AND gate (A1 & A4): P = 0.001 * 0.002 = 0.000002
- OR between A2 and A3: P ≈ 0.0005 + 0.0008 − (0.0005*0.0008) ≈ 0.0012996 (nearly sum since product small)
- Finally, top event = OR( AND result, OR result ) ≈ 0.000002 + 0.0012996 − (0.000002 * 0.0012996) ≈ ~0.0013016
Interpretation: Top event has probability ~0.0013 or 0.13% in given reference time. Then engineers might focus on reducing risk by improving fuel delivery or switchgear reliability, since those contribute more.

Conclusion

Fault Tree Analysis (FTA) is a powerful tool for engineering, safety, and reliability contexts. It provides a structured way to understand how failures combine (via basic events and logic gates) to cause major system‐level failures (top events). By carefully following a qualitative and quantitative process, applying probability calculations, referencing standards like IEC 61025, and comparing with other tools (like FMEA, Event Trees), engineering teams can better identify critical risk contributors, allocate mitigation resources, and design safer, more reliable systems.

While FTA has its challenges—data quality, assumptions, complexity—it remains central in industries where risk is high and safety cannot be compromised. Used well, FTA doesn’t just identify what might go wrong—it suggests what actions will most reduce risk. For anyone concerned with system safety, risk engineering, failure analysis, or quality assurance, mastering Fault Tree Analysis is a key step.

References

“Fault Tree Analysis.” Wikipedia.
Ruijters, Enno; Mariëlle Stoelinga (2015). “Fault tree analysis: A survey of the state-of-the-art.” Computer Science Review.
“Basic Computations in Fault Tree Analysis (FTA)” by Hamid Jahanian, TÜV Rheinland.
Relyence guide: “How To Perform a Fault Tree Analysis.” Relyence
Moraru, Roland Iosif, etc., “Application of FTA in industrial systems safety.” utgjiu.ro
IEC prEN IEC 61025:2023, standard definition and extension for Fault Tree Analysis. iTeh Standards

See also

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Fault Tree Analysis (FTA)