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.
What You'll Learn
Build complete competency in fault tree analysis through structured, progressive learning.
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.
12 Comprehensive Chapters
Each chapter builds your fault tree analysis expertise systematically from foundations to advanced application.
Introduction to FTA
Discover the origins, purpose, and automotive applications of Fault Tree Analysis for safety-critical systems.
FTA Fundamentals
Grasp core FTA concepts: top events, intermediate events, basic events, and their relationships in the fault tree.
Gates & Symbols
Master all FTA gate types and symbols: AND, OR, K-of-N, inhibit, transfer, and event symbols.
Tree Construction
Build fault trees systematically from top event to basic events using structured top-down decomposition.
Quantitative Analysis
Apply probability theory to calculate top event probability from basic event failure rates and exposure times.
Cut Set Analysis
Identify minimal cut sets to find the shortest failure paths and critical combinations leading to the top event.
PMHF Calculation
Apply FTA results directly to ISO 26262 Probabilistic Metric for Hardware Failures calculation and verification.
Boolean Algebra
Use Boolean algebra to simplify fault trees, identify redundancies, and derive cut sets analytically.
ISO 26262 Integration
Integrate FTA into ISO 26262 Part 4 and Part 5 safety analyses as a formal dependent failure analysis method.
FTA vs FMEA
Compare and contrast FTA and FMEA approaches, understand when to use each, and how they complement each other.
Common Pitfalls
Recognize frequent FTA mistakes including incomplete tree construction, wrong gate types, and data quality issues.
FTA Calculator & Simulator
Use an interactive FTA calculator to build trees, compute cut sets, and calculate PMHF contributions in real time.
6 Interactive Tools
Experiment with visual tools that bring fault tree analysis concepts to life.
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%
FTA Cut Set Analysis
Ready to Master Fault Tree Analysis?
Work through 12 structured chapters with interactive tree builders and a complete ESC PMHF case study.
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