Calculations with context

LOPA calculator

Calculate an illustrative consequence frequency from initiating frequency and protection-layer assumptions; inspect independence and credit limits.

Educational model · assumptions remain visible

One scenario. Explicit credit.

Explore one initiating event and one consequence endpoint in a simplified low-demand model. Unconfirmed protection and conditional factors receive no numerical credit. Checking an assumption does not verify a real installation.

Scenario and endpointInitiating frequency · events per operating year

0–1,000,000,000,000 per operating year. This arithmetic limit is not a recommended engineering range. Do not enter a per-demand probability or discount exposure twice.

Candidate protection layers

Layer 1

Distinct layer / protective function namePFD · dimensionless, 0–1

Evidence, timing and dependency noteFor this scenario, I assume this layer is effective, timely and independently justified relative to the initiator and the other credited layers.

Layer 2

Distinct layer / protective function namePFD · dimensionless, 0–1

Evidence, timing and dependency noteFor this scenario, I assume this layer is effective, timely and independently justified relative to the initiator and the other credited layers.

I have considered shared sensors, power, final elements, environment, maintenance and human actions across the claimed layers. For this teaching case, the remaining credited paths are assumed independent.

Optional conditional probabilities

These are endpoint conditions, not protection layers. Use a correctly conditioned sequence and avoid overlap with the initiating frequency, another factor or the endpoint definition. No optional factor is needed for the guide example.

I have specified the conditioning basis and checked for overlap or double-counting. These probabilities apply to the selected endpoint and event sequence.

Calculations run in this page. Nothing entered here is saved or sent by this calculator. CSV downloads start only when you choose Download CSV.

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Worked example · removing an unjustified credit

The existing transfer guide assumes 0.2 initiating events per operating year, layer A PFD 0.1 and layer B PFD 0.02. If both are independent and effective, 0.2 × 0.1 × 0.02 = 0.0004/year. If the initiating sensor failure defeats A, give A no credit: 0.2 × 1 × 0.02 = 0.004/year. B’s independence and effectiveness remain separate assumptions.

0.2 × 0.1 × 0.02 = 0.0004 / year
0.2 × 1 × 0.02 = 0.004 / year

Read the independent-protection guide · Examine shared-sensor dependence

Read the factors before the product

Frequency = initiating frequency × applicable conditional probabilities × qualified independent-layer PFDs. Frequency carries the time basis; PFD and conditional probabilities are dimensionless. The output is a modeled frequency, not the probability of at least one event in a year.

A layer must protect against this initiating cause and this endpoint, with suitable capacity and response time. Separate names or screens do not establish independence. A shared sensor, utility or final valve can invalidate a product of individual PFDs.

For dependent failures, the relevant quantity is a justified joint or conditional failure probability. In general P(A and B) = P(A) × P(B given A). This small calculator does not fit a common-cause model. Leave unresolved layers uncredited and investigate the dependency.

Optional factors can duplicate exposure or endpoint conditioning already present in the input data. Record what each probability is conditional on. Multiplying several marginal probabilities without that reasoning is not a substitute for a scenario model.

The initial values are teaching assumptions, not equipment failure data. No tolerability target, safety-integrity-level assignment, certification or operational authorization is calculated. Real decisions need an approved method, evidence and competent review.

Method sources and scope

Source checks: 8 October 2026. Numerical examples and rubric are authored teaching assumptions, not values prescribed by these sources.

Read the method and its limits

Related project: AURA

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