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How to Calculate Toxic Risk Metrics: Understanding Probit Equations, LSIR, and Potential Loss of Life

In process safety engineering and chemical facility design, evaluating the impact of accidental toxic gas releases—such as Hydrogen Sulfide (H2S)—is a fundamental requirement. Carrying out a Quantitative Risk Assessment (QRA) translate hazardous dispersion models into concrete numerical metrics: Location Specific Individual Risk (LSIR), Potential Loss of Life (PLL), and Fatal Accident Rate (FAR).

In this guide, we will break down the mathematical workflow used to determine toxic risk metrics using real-world QRA data and a toxicity-based Probit equation.

Essential Terminology

  • Probit (Pr): A statistical measure converting toxic dose (concentration and duration) into a probability of fatality.
  • Pf (Probability of Fatality): The percentage likelihood that an exposed individual will suffer a fatal outcome.
  • LSIR (Location Specific Individual Risk): The annual fatality risk or serious injury to a person in the vicinity of a hazard, assuming the person is there 365 days a year, 24 hours a day
  • PLL (Potential Loss of Life): The total expected human fatalities per year across an exposed population (societal risk measure).
  • FAR (Fatal Accident Rate): The estimated number of fatalities per 108 person-hours of exposure.

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