# Strategies and Methods for the Fault-Tolerant Function Development of Multi-Domain Systems +
## 3 State of the Art
### Function Development  
In today's scientific literature, diverse notions and definitions of the term \"function\" are used, but across disciplines, it is agreed that a function describes the intended or expected behaviour of a system aimed at achieving certain objectives [42]. In this paper, the term \"function\" is used for an abstract description of all kinds of processes and state changes within a technical system that enable the fulfilment of functional requirements. It is important to note that a function is usually extended by other functions (Figure 3). As represented in Figure 3, a main function can be extended by other functions, such as control, diagnosis, safety, communication, or supply functions [7]. The main intention of function development (frequently carried out by a system architect or a system architecture team in an industrial company) is to create--starting from customer functions--more detailed functional descriptions of the mechanical and electrical components as well as the software functions (which in the following can be transferred to software code manually or automatically) regarding all boundary conditions [7]. The function development also helps to integrate systems both for project management and for verifying them. In industrial companies, function development is in integral part of systems engineering. Certain companies even have dedicated departments called \"Functional Development\" providing a central viewpoint on the mechatronic product. In the fall of 2020, the guideline VDI/VDE 2206 was republished and the name was changed to \"Development of cyber-physical mechatronic systems (CPMS)\" [43]. The intention of this guideline is to assist design engineers and system architects during the essential activities pursued in the product development of cyber-physical systems. The guideline describes the logical relationships in the form of an inherent logic of the information flows mainly consisting of the system models. The central representation is an updated and extended form of the well-known V-model originating from software development [44]. The main intention of the reworking of the guideline is adaptation to contemporary alterations in industrial environments, which are, amongst others, a consequence of increasing cyber-physical system content (a larger share of mechatronics components and intensified computerised control and diagnosis, together with interconnected control and synchronisation of the distributed system elements) and enhanced and expanded computer-aided synthesis and analysis methods and tools. Research groups around the globe are currently expanding investigations in this topic area, focusing on the study of changes in risk requirements [45], on automated parameter selection ([PERSON] et al., 2021), on domain-specific modelling approaches [46], the incorporation of time-dependent behaviour [47], and artificial intelligence methods in the V-model [48]. Important research activities are concentrating on model-based system engineering (MBSE--[49; 50; 51]). An innovative approach is the application of graph-based design languages (GBDLs--see, e.g., ref. [52]). The essential elements of industrial system development processes of mechatronic and cyber-physical systems are represented by the V-model in Figure 4 (based on VDI/VDE 2206--focusing on function development [43]). This model emphasises the large role of systems engineering and places function development in the context of system design. \"Function development\" is an initial part of \"system design and system architecture development\", is logically precedent to the domain-specific implementation of system elements, and includes physical and non-physical considerations. Visibility is also a \"product management\" function, which is currently emphasised in most industrial companies. The persons undertaking this function within the company translate customer needs and expectations as well as marketing issues into the engineering context. In the centre of the V, several verification levels are represented.