The calculation of the probability of failure of the Safety Instrumented Functions (SIF) that are part of a Safety Instrumented System (SIS) is executed in accordance with the requirements defined in the IEC 61511-1 standard by following the guidelines contained in IEC 61511-2.
Depending on the mode of operation of each individual SIF: continuously, or on demand, is calculated the probability of a dangerous failure per hour (PFH), or is calculated the probability of a dangerous failure of the safety function on demand (PFD). Usually this calculation coincides with the calculation of the probability of failure of a SIS control loop including: acquisition chain, the controller (eg a PLC) and the execution chain .
To perform the calculation of the probability of failure of the various blocks that constitute a control loop using the calculation techniques given in IEC 61508-6 employing all available data for each individual element of the control loop:
• Failure Rate: (total λ, fraction of dangerous failures λD, fraction of dangerous failures detected λDD, fraction of failures not detected λDU, etc.);
• diagnostic coverage (DC);
• fraction of common mode failures (with a common cause) not recognized (β);
• fraction of common mode failures detected (βD);
• mean time to recovery (MTTR);
• interval between periodic tests (T1);
• interval between requests (T2).
If not all the necessary data are available, some of them can be calculated (for example by referring to what is stated in the same IEC 61508-6 ). Alternatively, the data contained in appropriate date basis, or estimated data available in the literature with appropriate safety margins, can be used.
The overall failure rate of the control loop is carried out using various methods such as the reliability block diagram (RBD), the fault tree analysis (FTA), the Weibull analysis, and so on. In more complex cases, specific software that can be purchased on the market, are used.