# Probability of Failure on Demand

The Probability of Failure on Demand (PFD) is a measure of the effectiveness of a safety function. It expresses the likelihood that the safety function does not work when required to.

The PFD for a loop depends on the failure rates of all the components in the loop. In order to calculate failure rates for transmitters, logics and valves, data must be collected on all the possible failure states, including states that can be detected, states that cannot be detected (by the built-in diagnostic software), states that lead the component to default to a safe state and states that lead to a dangerous state for the component as a whole. In practice, this data is available for new “SIL compliant” components but not often for legacy components.

A further key determinant of the PFD is the frequency with which the system is tested. It is assumed that failures that are detected by the system itself (by means of built-in diagnostic software ) can be quickly repaired. Those failures however that cannot be detected by the system itself will only become apparent during a full system test. During the period of time between the failure occurring and the test taking place, the system may not be available, should a demand occur.

As an example, consider the following two components (say, pressure switches), which are characterized by the given failure rates λdu and λdd, for which no redundant switches are installed (so no voting), which are subject to a system test every six months and which both take around 8 hours to repair:

Sample PFD calculation

Component A and B have similar total failure rates, of 4.0•10-6 per hour. Yet component B is of better design as the built-in diagnostic software allows it to detect certain failures. As a result, the PFD of component B is much lower.

In terms of Safety Integrity Level: both components can be used in a SIL-2 loop (PFD higher than 0.001 but below 0.01) provided that the other components in the same loop (logics, barriers, actuators) do not add too much to the overall dangerous failure rates such that the PFD for the loop as a whole remains below 0.01.

At Beldick we are happy to perform all the necessary calculations such that you can focus on the application. We will state the input data required and suggest reasonable assumptions as necessary. We will interpret and explain the results and suggest ways to improve the PFD of your loops with the lowest impact on your budget.