π Lesson 18
D5
ALARP Justification Calculations: Cost per Fatality Averted
ALARP justification using cost per fatality averted means figuring out how much money itβs reasonable to spend to prevent one death, balancing safety gains against practical costs.
π― Learning Objectives
- β Calculate cost per fatality averted (CPFA) for a proposed blasting safety upgrade using exposure, probability, and cost data
- β Explain how CPFA supports ALARP decision-making in accordance with regulatory guidance (e.g., UK HSE's 'Reducing Risks, Protecting People')
- β Analyze whether a proposed control measure (e.g., remote initiation system) is ALARP-compliant by comparing its CPFA against benchmark thresholds
- β Apply sensitivity analysis to assess how changes in fatality probability or intervention cost affect CPFA conclusions
π Why This Matters
In mining and blasting operations, a single misfire or premature detonation can cause multiple fatalities β yet every safety upgrade (e.g., wireless blast monitoring, exclusion zone enforcement, or automated shutoff systems) carries significant cost. Regulators donβt demand zero risk β they demand *reasonably practicable* risk reduction. CPFA provides the objective, defensible basis for justifying why you stopped investing in safety at a particular point β a critical skill during regulatory audits, incident investigations, and mine closure reviews.
π Core Principles
ALARP requires demonstrating that risks have been reduced to a level where further reduction would be grossly disproportionate to the safety benefit achieved. CPFA operationalizes this principle by converting risk reduction into economic terms: it quantifies how much society (or the company) is willing to pay to avoid one statistical fatality. The calculation hinges on three pillars: (1) baseline fatality probability (e.g., 1 Γ 10β»β΄ per year for manual drill-and-blast crews), (2) risk reduction factor (e.g., 90% lower probability with remote initiation), and (3) lifecycle cost of the control. Critically, CPFA is not a standalone threshold β it must be interpreted alongside qualitative factors (technical feasibility, operational impact, precedent) and compared against benchmark values established by national regulators and industry bodies.
π Key Calculation
CPFA is calculated by dividing the total incremental cost of a risk-reduction measure by the number of fatalities it prevents over a defined period β derived from the reduction in annual fatality probability multiplied by exposed personnel and time horizon. It is applied only to *incremental* risk reduction, not absolute risk.
Cost per Fatality Averted (CPFA)
CPFA = C_total / (ΞP_f Γ N Γ T)Quantifies the cost incurred to prevent one statistical fatality through a specific risk-reduction measure.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| C_total | Total incremental cost | USD | Net present value of all costs associated with implementing and maintaining the control over its service life |
| ΞP_f | Reduction in annual fatality probability per exposed person | fatalities/person-year | Difference between baseline and post-control fatality probability (must be evidence-based) |
| N | Number of exposed personnel | persons | Average number of individuals directly at risk from the hazard addressed by the control |
| T | Time horizon | years | Service life or evaluation period over which risk reduction applies |
Typical Ranges:
Mining blasting controls (e.g., remote initiation): $2M β $8M
Regulatory upper tolerability (UK HSE): Β£1M β Β£2M (~$1.3Mβ$2.6M USD)
π‘ Worked Example
Problem: A surface mine employs 48 blasters annually. Historical data shows a baseline fatality probability of 2.5 Γ 10β»β΄ per blaster-year due to misfire-related injuries. Installing a certified remote initiation system reduces this probability by 85%. The system costs $320,000 (CAPEX + 5-yr OPEX). Calculate CPFA over 5 years.
1.
Step 1: Compute baseline annual fatalities = 48 blasters Γ 2.5 Γ 10β»β΄ = 0.012 fatalities/year
2.
Step 2: Compute risk reduction = 0.012 Γ 0.85 = 0.0102 fatalities/year averted
3.
Step 3: Compute total fatalities averted over 5 years = 0.0102 Γ 5 = 0.051
4.
Step 4: CPFA = $320,000 Γ· 0.051 = $6,274,510 per fatality averted
Answer:
The result is $6.27 million per fatality averted, which exceeds the UK HSE's indicative upper bound of Β£1β2 million (~$1.3β2.6M USD) and suggests the measure may not be ALARP without additional justification (e.g., reputational risk, legal liability exposure, or synergistic benefits).
ποΈ Real-World Application
In 2021, Rio Tintoβs Pilbara operations conducted an ALARP review for transitioning from wired to fiber-optic blast initiation across 12 open pits. Baseline fatality risk was estimated at 1.8 Γ 10β»β΄ per blaster-year (based on 12 years of incident data). The fiber-optic system reduced misfire-related exposure probability by 92% and cost $4.7M over 7 years. CPFA was calculated at $3.8M/fatality β below Australiaβs Safe Work Australia βupper tolerabilityβ benchmark of AUD $5.5M (2021). The justification included sensitivity analysis showing CPFA remained < $5M even under conservative assumptions (e.g., 70% risk reduction), enabling formal ALARP sign-off by the siteβs Independent Competent Person (ICP) and acceptance by WA Department of Mines, Industry Regulation and Safety.
π Case Connection
π Grain Elevator Dust Explosion Mitigation Using ASTM E1226-Based Risk Model
Historic dust explosions (3 incidents since 1995); inadequate housekeeping and venting
π Offshore LNG Transfer System Fault Tree Analysis and SIS Architecture Optimization
High consequence of LNG spill + ignition in congested maritime corridor; existing SIS used single-channel logic