Extending Contract theory with Safety Integrity Levels

In functional safety standards such as ISO 26262 and IEC 61508, Safety Integrity Levels (SILs) are assigned to top-level safety requirements on a system. The SILs are then either inherited or decomposed down to safety requirements on sub-systems, such that if the sub-systems are sufficiently reliable in fulfilling their respective safety requirements, as specified by the SILs, then it follows that the system is sufficiently reliable in fulfilling the top-level safety requirement. Present contract theory has previously been shown to provide a suitable foundation to structure safety requirements, but does not include support for the use of SILs. An extension of contract theory with the notion of SILs is therefore presented. As a basis for structuring the breakdown of safety requirements, a graph, called a contract structure, is introduced that provides a necessary foundation to capture the notions of SIL inheritance and decomposition in the context of contract theory.