## 5 Exemplary Application of the Combined Model  
The combined model allows novel investigations of the function model. Three general approaches are briefly illustrated subsequently, which showcase the merit of the combined approach. The first approach is a function path analysis, which allows, for instance, to assign risks to certain functions. This analysis can be applied to improve functions, processes and function carriers that are especially important for the overall system function. This also allows analysis of the consequences of engineering changes. The second is a parametric function analysis, which allows, for instance, the identification of bottlenecks, e.g., components of a technical system that are part of several processes (i.e., they are involved in the fulfilment of a large number of functions and, hence, failure of these function carriers is likely to have a severe impact on the system). Design improvements that address these bottlenecks can lead to systems that are more robust and fault-tolerant. The final approach is a function change effect analysis, which allows, for instance, to assess the consequences of an engineering change of one or more function on other functions. An assessment of the consequences of such changes can be an important tool to develop system-specific redesign strategies. It is important to note that other analysis approaches would be possible. This section of the paper will concentrate on the function path analysis. This analysis adopts some ideas of the Failure Modes and Effects Analysis (FMEA) (see, e.g., [PERSON] [58]). In an FMEA, three components are multiplied in order to calculate the risk in form or a risk priority number (RPN):  
Severity (S): the severity indicates the effect of a certain failure on the systems customer; it is described on a 10-point scale from 1 (no effect) to 10 (hazardous effect). Occurrence (O): the occurrence indicates the probability of a certain failure; it is described on a 10-point scale from 1 (failure unlikely, no failure history) to 10 (failure almost certain). Detection (D): the detection indicates the probability to detect the failure before it has an effect (during all phases including conception, design, testing, production, end-of-line-testing, and operation (even by the customer him-/herself)); it is described in a 10-point scale from 1 (proven detection methods already available in the concept stage) to 10 (no known detection method available). For the development of the function path analysis, there is also the Failure Modes, Effects and Criticality Analysis (FMECA) ([59], respectively MIL-STD-1629A). In this analysis, the criticality is calculated by multiplying the item unreliability, the mode ratio of unreliability and the probability of loss for each failure mode of a certain component, and by summing up the criticality of a failure mode of this component. This allows the identification of critical components--the function path analysis aims at a more abstract level of the design process and aims to identify critical or risky functions. It is proposed to add an analysis to the function model in the engineering framework that analyses three entities, as follows. An assessment is made of how important the process of a certain function (see process flow view in Figure 4) for the fulfilment of the overall system function; this assessment is described as severity (S) on a 10-point scale from 1 (not at all important for the overall system functionality) to 10 (absolutely essential for the overall system functionality). An assessment is made of how probable it is that a circumstance in which a certain process can fail is detected before the failure occurs; this assessment is described as detection (D) on a 10-point scale from 1 (the possibility of failure will definitely be detected before the occurrence) to 10 (no detection method for the possibility of failure exists).