How is risk calculated in QRA?
Risk in a quantitative risk assessment is calculated by summing, over every failure case, weather class, wind direction and ignition outcome, the product of event frequency and the probability of fatality at the location of interest. The arithmetic is simple; the effort is in building consistent inputs.
The calculation chain
- Leak frequency per failure case, from parts count multiplied by generic leak frequency per hole size.
- Outcome probability from the event tree: immediate ignition, delayed ignition, explosion versus flash fire, no ignition.
- Weather and wind direction probability from the site wind rose.
- Consequence field for each combination — radiation, overpressure or concentration at each grid point.
- Fatality probability at each grid point from a probit or threshold vulnerability model.
- Summation of frequency times fatality probability over all combinations.
Individual risk
Location-specific individual risk is the annual probability of fatality for a hypothetical person present at that location continuously. Plotted across a grid it produces the familiar risk contours. Individual risk per annum for a real person applies occupancy and exposure fractions — the proportion of the year they are actually present in each area.
Societal risk
Societal risk accounts for population distribution. For every outcome the number of fatalities is estimated from population in the affected area, then the results are ranked and plotted as cumulative frequency of N or more fatalities against N — the F-N curve — and compared against a tolerability criterion line. Potential loss of life, the frequency-weighted average fatality count, is a useful single-number companion metric.
Where the uncertainty lives
- Leak frequency data, which carries wide confidence bounds.
- Ignition probability, which is often the single largest source of variation between studies.
- Vulnerability models and any credit for shelter, clothing or escape.
- Consequence model choice, particularly dense-gas and explosion treatment.
Frequently asked questions
What is an acceptable individual risk level?
Criteria are jurisdiction and company specific. Frequently referenced bands place worker risk broadly acceptable around 1E-6 per year and intolerable around 1E-3 per year, with the range in between requiring an ALARP demonstration. The applicable criteria must come from the governing regulator or corporate standard.
Why do two QRAs of the same plant give different numbers?
Different leak frequency databases, ignition models, weather sets, vulnerability assumptions and consequence models. This is why comparative use and transparent documentation of assumptions matter more than the absolute figure.
What is potential loss of life?
PLL is the expected number of fatalities per year, obtained by summing event frequency multiplied by the expected fatalities for each outcome. It is convenient for comparing risk reduction options.
Calculators for this topic
- Gas Discharge — Gas discharge rate calculator for pressurised releases
- Gas Dispersion — Atmospheric gas dispersion calculator
- Flare Radiation — Flare thermal radiation calculator