Fault Tree Analysis
15 chapters Master top-down fault analysis using Boolean logic and probability theory to quantify system failure rates and support ISO 26262 PMHF calculations.
How You Learn
Video and text stay in sync. As you scroll through the chapter, the video jumps to the matching explanation automatically.
Learning Objectives
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.
Chapters
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.
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.
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.
Cut Set Analysis
Identify minimal cut sets to find the shortest failure paths and critical combinations leading to the top event.
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.
ISO 26262 Integration
Integrate FTA into ISO 26262 Part 4 and Part 5 safety analyses as a formal deductive and 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.
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.
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.
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.
FTA Calculator & Simulator
Use an interactive FTA calculator to build trees, compute cut sets, and calculate PMHF contributions in real time.
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.
Interactive Tools
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 15 structured chapters with interactive tree builders and a complete ESC PMHF case study.
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