How is the required frequency PFD determined in SIL classification (LOPA analysis)?

In LOPA analysis, the demand frequency PFD (Probability of Failure on Demand) is estimated using the system’s failure data and maintenance records. Specifically, it is calculated based on the historical failure data of the safety instrument system and the testing interval time. Simply put, the demand frequency PFD refers to the probability that the system cannot respond properly when a demand occurs. It is one of the key parameters for evaluating system reliability and determining the Safety Integrity Level (SIL). .

In SIL classification (LOPA analysis), the Probability of Failure on Demand (PFD) is an important parameter used to measure the average failure probability of a system when it is required to function. Determining this probability is crucial for assessing the security and integrity of the system. The calculation method for PFD is mainly based on Markov analysis. Markov analysis is a forecasting method that predicts future changes in random variables by analyzing their current state. In SIL verification, Markov models are used to classify safety-related systems into several distinct states, with each state having a certain probability of transitioning to other states. A key feature of this approach is that the future state of the system is independent of its historical states and depends only on its current state. Specifically for the calculation of PFD, for the calculation of PFD for a single piece of hardware (of the same type), the random function PFD=1-e-λt can be used, and its approximate value can be expressed as PFD=λDU*(T1/2+MTTR)+λDD*MTTR. As for the calculation of the system PFD, it is determined by calculating and combining the average failure probabilities of all subsystems that provide safety functions under required conditions. This can be expressed as PFDSYS = PFDS + PFDL + PFDFE, where PFDS is the average failure probability when the sensor subsystem is considered, PFDL is the average failure probability when the logical subsystem is considered, and PFDFE is the average failure probability when the final component subsystem is considered. Therefore, the determination of the demand frequency PFD is based on predictions from the Markov analysis method, combined with the failure probabilities of various subsystems in the system. The purpose of this process is to accurately assess the failure probability of the system under specified conditions, thereby providing an important basis for determining the SIL level.

For this table, by dividing the enterprise’s tolerable risk level (for example, 1.0E-6 for safety or personnel losses) by the total frequency of intermediate events, which is 1.2E-4, we get 8.33E-3. This value represents the difference between the probability of an accident occurring and the risk level that the enterprise is willing to accept; it is the desired probability – that is, the value required to reduce the risk to an acceptable level. The reciprocal of this value is the RRF, which is the risk reduction factor, equal to 120