Complete Learning Module

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.

12
Chapters
6
Interactive Tools
1
Case Study
1
Video

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.

1

Introduction to FTA

Discover the origins, purpose, and automotive applications of Fault Tree Analysis for safety-critical systems.

History & originsTop-down approachFTA in automotive
2

FTA Fundamentals

Grasp core FTA concepts: top events, intermediate events, basic events, and their relationships in the fault tree.

Top event definitionEvent hierarchyScope boundaries
3

Gates & Symbols

Master all FTA gate types and symbols: AND, OR, K-of-N, inhibit, transfer, and event symbols.

AND & OR gatesK-of-N votingTransfer gates
4

Tree Construction

Build fault trees systematically from top event to basic events using structured top-down decomposition.

Decomposition stepsLevel-by-level buildCompleteness checks
5

Quantitative Analysis

Apply probability theory to calculate top event probability from basic event failure rates and exposure times.

Probability mathFailure rate inputsConfidence levels
6

Cut Set Analysis

Identify minimal cut sets to find the shortest failure paths and critical combinations leading to the top event.

Minimal cut setsImportance measuresCriticality ranking
7

PMHF Calculation

Apply FTA results directly to ISO 26262 Probabilistic Metric for Hardware Failures calculation and verification.

PMHF formulaASIL targetsContribution analysis
8

Boolean Algebra

Use Boolean algebra to simplify fault trees, identify redundancies, and derive cut sets analytically.

Boolean reductionAbsorption lawsIdempotency
9

ISO 26262 Integration

Integrate FTA into ISO 26262 Part 4 and Part 5 safety analyses as a formal dependent failure analysis method.

Part 4 & 5 linkageWork product mappingEvidence requirements
10

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-upComplementary useCombined approach
11

Common Pitfalls

Recognize frequent FTA mistakes including incomplete tree construction, wrong gate types, and data quality issues.

Incomplete treesGate selection errorsData pitfalls
12

FTA Calculator & Simulator

Use an interactive FTA calculator to build trees, compute cut sets, and calculate PMHF contributions in real time.

Interactive builderCut set solverPMHF export
Interactive Learning

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.

Real-World Application

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

MCS-1: {WSS-FL failure} - Probability: 4.2 × 10⁻⁹ h⁻¹, Importance: 0.73
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Work through 12 structured chapters with interactive tree builders and a complete ESC PMHF case study.

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12 Chapters6 ToolsCase StudyVideo