In process industry, SIL determination is a risk assessment process through which target Safety Integrity Levels (SIL) are allocated to Safety Instrumented Functions (SIF). A target SIL represents the significance of the hazard against which the SIF protects the plant. This paper introduces new SIL determination methods by taking an optimization approach. Unlike the conventional methods, which are generally focused on calculating the gap between the existing and tolerable levels of risk, the methods introduced in this paper are aimed at optimizing the marginal cost or the benefit-cost ratio. By incorporating the cost factor into the SIL determination process, these methods deliver the most reasonably practicable solutions that can minimize the risk while taking into account the cost of solution. The new methods are formulated for corporate risk and the risk to community (i.e. ALARP). Both methods are derived for demand and continuous modes of SIF operation. Furthermore, a new Safety Index is introduced to combine the SIL and the average Probability of Failure on Demand (PFD) or Frequency of Failure per Hour (PFH). The application of the mathematical models is demonstrated through a practical example from power industry. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.