The international standards IEC 61508 and IEC 61511 give safety integrity requirements to safety-instrumented systems (SISs) that are used in the process industry. A SIS performs one or more safety-instrumented functions (SIFs). IEC 61508 distinguishes between SIFs operated in low-demand and high-demand/continuous mode, whereas IEC 61511 distinguishes between demanded and continuous mode of operation. In the past, almost all attention has been paid to low-demand SIFs, and this is reflected in IEC 61511, the available guidelines, and the scientific literature. Recently, however, suppliers of SISs to the process industry have been met with safety requirements to SIFs operated in high-demand and continuous mode. This paper intends to help suppliers and reliability analysts who are familiar with the mathematical formulas in IEC 61508-6 for safety integrity assessment of low-demand SIFs to verify the safety integrity of SIFs in high-demand and continuous mode. This is done by highlighting the similarities and differences between the required approaches and by presenting two new sets of approximation formulas for the PFH of general koon:G voted groups. One set of PFH formulas extends the IEC formulas for PFH based on the ideas applied in IEC 61508-6. The other set of PFH formulas is derived considering the risk contribution also from DD-failures when the demand rate is high. The results of the IEC formulas of PFH and the two new sets of PFH formulas are compared and discussed. (C) 2014 Elsevier Ltd. All rights reserved.