| name | event-tree-analysis |
| description | Event tree analysis (ETA) — initiating event, safety function sequences, event tree construction, conditional probabilities, end state frequencies, integration with FTA, LOPA, IEC 61511, process safety. |
| metadata | {"priority":7,"promptSignals":{"phrases":["event tree analysis","ETA","event tree","initiating event","safety function","LOPA analysis"],"minScore":3}} |
Event Tree Analysis (ETA) — Complete Skill
ETA Fundamentals
Event Tree Analysis: forward-looking analysis starting from an initiating event; traces accident sequences through binary success/failure of safety functions
Contrast with Fault Tree Analysis (FTA):
FTA: backward (what causes the top event?); deductive
ETA: forward (what happens given the initiating event?); inductive
Purpose:
- Identify all possible accident sequences following an initiating event
- Quantify frequency of each end state (outcome)
- Identify dominant accident sequences
- Evaluate effectiveness of safety systems
Event Tree Construction
Step 1: Define Initiating Event
Initiating event (IE): event that starts the accident sequence
Examples:
- High-pressure vessel rupture
- Pump failure (loss of cooling)
- Control system failure
- Loss of containment (LOC)
- Ignition of flammable vapor
IE frequency (λ_IE): from OREDA, PERD data, or plant history [events/year]
Typical: loss of cooling flow: 0.01–0.1/yr; control valve failure: 0.02–0.1/yr; pump seal failure: 0.05–0.5/yr
Step 2: Identify Pivot Events (Safety Functions)
Pivot events: safety systems/procedures that respond after IE
Order: chronological; first-responding system first
Typical safety function sequence:
IE → Alarms/Detection → Emergency Shutdown (ESD) → Active Safety System → Passive Safety System → Emergency Response
Conditional probability (P_success, P_failure):
P_success = 1 - PFD [PFD = probability of failure on demand from FTA/LOPA]
Typical PFD ranges:
Alarm detection: PFD = 0.01–0.05 (90–99% reliable)
SIL 1 SIS: PFD = 0.01–0.1
SIL 2 SIS: PFD = 0.001–0.01
SIL 3 SIS: PFD = 0.0001–0.001
Step 3: Draw Event Tree
Structure:
IE → pivot 1 (S/F branches) → pivot 2 (S/F) → ... → End State
Each branch: success (upper, probability P_s) + failure (lower, probability P_f = 1 - P_s)
Number of sequences: 2^N_pivots (N = number of pivot events)
Step 4: Calculate Sequence Frequencies
Sequence frequency = λ_IE × Π (conditional probabilities along path):
f_sequence = λ_IE × P_1 × P_2 × P_3 × ... [events/year]
Sum check: Σ f_sequences = λ_IE (all sequences must sum to IE frequency)
Step 5: Assign End States
End states: outcome categories
- Safe outcome (no harm)
- Minor release (controlled)
- Significant release (reportable)
- Major accident (fatality potential)
- Catastrophic (multiple fatalities)
Assign consequence categories: each accident sequence → harm potential → consequence model (PHAST, dispersion, explosion)
Quantification
Frequency of outcome i:
f_i = Σ f_sequences that lead to outcome i
Risk = frequency × consequence:
Risk_i = f_i × C_i [fatalities/year, or $/year]
Individual Risk (IR):
IR = Σ f_i × P(fatal|event) [yr⁻¹]
Acceptable IR: < 1×10⁻⁶ /yr (workers, UK HSE); < 1×10⁻⁵ /yr (workers, Netherlands)
Societal risk (F-N curve):
F = cumulative frequency of events causing ≥ N fatalities
Plot F vs. N on log-log → compare against F-N risk criteria (Dutch CPR 18E; UK HSE)
LOPA (Layer of Protection Analysis)
LOPA: simplified version of ETA + FTA; quantifies IPL effectiveness
IPL (Independent Protection Layer): each safety function that reduces risk
Mitigated event frequency:
f_mitigated = f_IE × Π PFD_IPL_i [IPL PFDs multiply]
LOPA risk tolerance:
Tolerable risk: 1×10⁻⁴ to 1×10⁻⁶ /yr per scenario (depending on severity)
Required risk reduction = tolerable risk / unmitigated frequency → determine required SIL
SIL determination from LOPA:
Required PFD_SIS = f_tolerable / (f_IE × Π PFD_other_IPLs)
→ SIL 1: PFD 0.01–0.1; SIL 2: 0.001–0.01; SIL 3: 0.0001–0.001
Generic IPL credit (CCPS LOPA guidelines):
BPCS (basic process control): 0.1 PFD (0.1 credit)
Pressure relief valve: 0.01 PFD
High-pressure trip (SIS SIL1): 0.1 PFD
Dike/bund: 0.1–0.01 (depends on maintenance)
Human response (with procedure, trained): 0.1 PFD
Integration with FTA
FTA provides: PFD of individual safety functions (used in ETA branches)
ETA provides: overall accident sequence frequencies → input to risk assessment
Combined approach:
FTA → PFD of each safety function → input to ETA pivot event probabilities → ETA → accident frequencies → risk
Bow-tie model: combines FTA (left, causes → IE) + ETA (right, IE → consequences) in one diagram
Prevention barriers (left): reduce IE frequency
Mitigation barriers (right): reduce consequence severity
Standards
| Standard | Scope |
|---|
| IEC 61511 | Safety instrumented systems; LOPA basis |
| IEC 61025 | Fault tree analysis (complementary) |
| API 14J | Recommended practice for risk analysis |
| CCPS Guidelines | Event tree analysis methodology |
| ISA-84.00.01 | SIS design (ISA equivalent of IEC 61511) |
| NFPA 820 | Ventilation and fire protection; ETA applicable |
Output
Provide: initiating event (description and frequency λ_IE [/yr]), list of pivot events (safety functions in sequence), conditional probability P_s and PFD for each pivot, event tree structure (number of sequences = 2^N), sequence frequencies f_i [/yr] for all significant sequences, end state categories with frequency, dominant accident sequence (highest frequency major consequence), LOPA mitigated frequency [/yr] vs. risk tolerance, required SIL for each SIS from LOPA, individual risk IR [/yr] vs. criterion, F-N curve comparison, and applicable standard (IEC 61511, CCPS LOPA guidelines, API 14J).
