This document can be used where a risk assessment according to ISO 12100 has been conducted for a machine or process plant and where a safety related control function has been selected for implementation as a protective measure against specified hazards. This document describes an example basic logical rationale to assign a safety integrity requirement to the selected function. The description is generic and as far as reasonably possible independent from any specific tool or method that can be used for assignment of a safety integrity requirement. The requirement can be expressed as a safety integrity level (SIL), or performance level (PL). An example basic rationale is described that is embodied by such methods and tools, as far as they follow a risk based quantitative approach. Conversely, the logic described in this document can be used as a reference for assessing specific methods or tools for safety integrity assignment. This can clarify how far the respective tool/method is following a risk based quantitative approach, and where deviations from that approach are imposed by other considerations. In real applications, the quantitative risk based approach can be modified or overridden by other considerations in many cases and for Good reasons. It is not within the scope of this document to discuss or evaluate such reasons. Usually the reasons for deviations from a given tool or method from a quantitative logic are provided, so that this can be discussed in the proper frame. Examples for such analyses are provided for common assignment tools in the format of risk graphs and risk matrices. This document can be used for safety related control functions in all modes of application: continuous mode, high demand mode and low demand mode of application.