Fault Tree Analysis
Master top-down fault analysis using Boolean logic and probability theory to quantify system failure rates and support ISO 26262 PMHF calculations.
- Chapters
- 15
- Chapters
- Interactive Tools
- 6
- Interactive Tools
- Case Study
- 1
- Case Study
- Video
- 1
- Video
Quick answers
- What is fault tree analysis in ISO 26262?
- Fault tree analysis (FTA) is a deductive, top-down safety analysis method standardized in IEC 61025. You start from an unwanted top event - typically the violation of a safety goal - and decompose it through AND, OR, and voting gates down to basic events such as component failures. In ISO 26262, FTA is one of the recognized deductive analysis methods of Part 9 Clause 8: the safety analysis tables recommend deductive analysis for higher ASILs, and quantified fault trees provide direct input to the PMHF evaluation of Part 5. The result shows which combinations of failures can cause the hazard and how probable they are.
- What is the difference between FTA and FMEA?
- FTA is deductive and top-down: it starts from one system-level failure and asks what combinations of causes can produce it, which makes it strong at finding multi-fault combinations and single points of failure. FMEA is inductive and bottom-up: it starts from each component failure mode and asks what effect it has, which gives systematic single-fault coverage but does not naturally find fault combinations. ISO 26262 treats them as complementary - higher ASILs call for both an inductive and a deductive analysis - and the course includes a comparator tool showing what each method finds on the same element.
Why it pays for itself
Build trees that hold up
Learn the disciplined top-down method - top event definition, immediate cause logic, gate selection, and completeness checks - that separates a review-ready fault tree from a decorative diagram.
Quantify, don't just draw
Apply Boolean reduction and probability math to compute minimal cut sets, importance measures, and top event probability, then feed the result straight into ISO 26262 PMHF verification against ASIL targets.
Practice on interactive tools
Six tools - fault tree builder, cut set solver, PMHF calculator, Boolean simplifier, probability calculator, and FTA vs FMEA comparator - let you rehearse every step before your real analysis.
What you’ll be able to do
Construct Correct Fault Trees
Build complete, correctly scoped fault trees using proper gate types, event definitions, and top-down decomposition methodology.
Identify Minimal Cut Sets
Apply Boolean algebra and algorithmic methods to find all minimal cut sets and rank failure paths by criticality.
Calculate System Failure Probability
Quantify top event probability from component failure rates and validate against ISO 26262 PMHF targets.
Support ISO 26262 PMHF Compliance
Use FTA results as direct input to ISO 26262 Part 5 hardware architectural metric calculations.
Integrate FTA with FMEA
Combine top-down FTA with bottom-up FMEA for comprehensive coverage of the system failure space.
Identify Critical Single Points of Failure
Use cut set analysis and importance measures to prioritize design improvements for maximum risk reduction.
Chapter by chapter
- 01
Introduction to FTA
Discover the origins, purpose, and automotive applications of Fault Tree Analysis for safety-critical systems.
- History & origins
- Top-down approach
- FTA in automotive
- 02
FTA Fundamentals
Grasp core FTA concepts: top events, intermediate events, basic events, and their relationships in the fault tree.
- Top event definition
- Event hierarchy
- Scope boundaries
- 03
FTA Methodology
Follow the disciplined FTA workflow from defining the top event to identifying immediate, necessary, and sufficient causes, with the Boolean algebra that underpins reduction and cut-set derivation.
- Immediate cause logic
- When to stop branching
- Boolean reduction
- 04
Gates & Symbols
Master all FTA gate types and symbols: AND, OR, K-of-N, inhibit, transfer, and event symbols.
- AND & OR gates
- K-of-N voting
- Transfer gates
- 05
Tree Construction
Build fault trees systematically from top event to basic events using structured top-down decomposition.
- Decomposition steps
- Level-by-level build
- Completeness checks
- 06
Cut Set Analysis
Identify minimal cut sets to find the shortest failure paths and critical combinations leading to the top event.
- Minimal cut sets
- Importance measures
- Criticality ranking
- 07
Quantitative Analysis & PMHF
Apply probability theory to calculate top event probability from basic event failure rates, then feed the result straight into ISO 26262 Probabilistic Metric for Hardware Failures (PMHF) verification against ASIL targets.
- Probability math
- PMHF formula
- ASIL targets
- 08
ISO 26262 Integration
Integrate FTA into ISO 26262 Part 4 and Part 5 safety analyses as a formal deductive and dependent failure analysis method.
- Part 4 & 5 linkage
- Work product mapping
- Evidence requirements
- 09
FTA vs FMEA
Compare and contrast FTA and FMEA approaches, understand when to use each, and how they complement each other.
- Top-down vs bottom-up
- Complementary use
- Combined approach
- 10
Common Pitfalls
Recognize frequent FTA mistakes including incomplete tree construction, wrong gate types, and data quality issues.
- Incomplete trees
- Gate selection errors
- Data pitfalls
- 11
Best Practices
Apply the practices that make fault trees review-ready: consistent naming, documented assumptions, justified failure data, and traceability from each basic event back to its source analysis.
- Consistent naming
- Documented assumptions
- Traceable data
- 12
FTA Tools & Software
Survey the tool landscape from spreadsheets to dedicated FTA packages, with the qualification, exchange-format, and quantification considerations that matter for ISO 26262 evidence.
- Tool categories
- Tool qualification
- Model exchange
- 13
FTA in the Safety Process
Place FTA in the development lifecycle: when to run it, how it iterates with architecture and FMEDA, who reviews it, and how it feeds the safety case and confirmation measures.
- Lifecycle timing
- Iteration with FMEDA
- Review and sign-off
- 14
FTA Calculator & Simulator
Use an interactive FTA calculator to build trees, compute cut sets, and calculate PMHF contributions in real time.
- Interactive builder
- Cut set solver
- PMHF export
- 15
Worked Examples
Walk through complete automotive fault trees end to end, from top event and gate logic to minimal cut sets and a quantified PMHF result.
- End-to-end trees
- Automotive cases
- Quantified results
Not just text: the visual toolkit
Fault Tree Builder
Construct fault trees interactively with drag-and-drop gates, events, and automatic Boolean simplification.
PMHF Calculator
Calculate Probabilistic Metric for Hardware Failures from fault tree basic event rates with ASIL compliance check.
Cut Set Solver
Identify all minimal cut sets from your fault tree and rank them by importance measure.
Boolean Algebra Simplifier
Enter Boolean expressions and simplify fault tree logic using algebraic reduction rules.
Probability Calculator
Compute top event probability from basic event failure rates with AND/OR gate combinations.
FTA vs FMEA Comparator
Compare analysis coverage and results between FTA and FMEA for the same system element.
FTA for an ASIL-D Electronic Stability Control (ESC) Unintended Activation
Analyze an ESC system for the top event "Unintended brake intervention on a single wheel" using full quantitative FTA and PMHF verification.
- Top event decomposed into 6 intermediate events and 23 basic events across 4 tree levels
- Minimal cut set analysis: 3 singleton cuts identified, 11 dual-event cuts ranked by importance
- Quantitative result: top event probability 1.8 × 10⁻⁸ h⁻¹ versus ASIL-D target
- Critical path: wheel speed sensor failure combined with valve driver latch - importance index 0.73
- Design recommendation: add cross-channel sensor plausibility reducing PMHF by 62%
Unlock in course
Who this guide is for
- Safety engineers assigned the deductive safety analysis for an ASIL C or D item
- Hardware analysts who need FTA results as input to PMHF and cut set arguments
- FMEA practitioners adding the complementary top-down view of the failure space
- Reviewers who must judge whether a supplier's fault tree is complete and correctly gated
Frequently Asked Questions
Common questions about Fault Tree Analysis
Start the course today
A free account unlocks one full concept guide, 3 work product templates, 1 guided process, the Markov simulator, and 5 practice exams per month. The Pro and Expert plans unlock more of the 78-guide library. No credit card required.