Why Semi-Quantitative

Qualitative studies such as HAZOP tell you a scenario exists and list safeguards. Full quantitative risk assessment tells you a frequency with uncertainty bounds, at considerable cost. LOPA sits between: it estimates scenario frequency to within an order of magnitude, which is usually enough to decide whether more protection is needed.

The core arithmetic

Frequency of the consequence equals the initiating event frequency multiplied by the probability of failure on demand of each independent protection layer:

f(consequence) = f(initiating event) × PFD₁ × PFD₂ × ... × PFDₙ

Because each term is expressed as a power of ten, the calculation is usually done by adding exponents. An initiating event at 10⁻¹ per year with two layers at 10⁻² and 10⁻¹ gives 10⁻⁴ per year.

What makes it valid

The multiplication is only valid if the layers are genuinely independent. Dependency is where LOPA studies most often go wrong, and it is why the definition of an independent protection layer is enforced strictly.