## 4 Findings--An Initial Model for Zero Defect Manufacturing
### Generic Framework for a Model of ZDM  
Combining operational and maintenance aspect into one framework has been promoted by [29]. It actually means that the system is studied from the perspective that the operation affects degradation and vice versa. The idea is to use this system theoretic approach also in ZDM. In order to systematically study the system behavior, the real-life context of a system as depicted in Figure 3 needs to be considered. There, the real-life system is affected by Manipulated Variables (MV) and Disturbance Variables (DV). The latter are exogenous effects that might be known through measurements, sometimes only on a qualitative level, or not known at all. The system then generates measurable outputs that need to adhere to certain specifications denoted Controlled Variables (CV) and other measurable outputs denoted Process Variables (PV). Moreover, internal system states, not necessarily measurable, are also categorized as PVs. Combining domain knowledge with data-driven modeling enables a more complete understanding of the system behavior and therefore aids in extending domain knowledge. Similarly, domain knowledge reflected by first-principle models can enrich data-driven modeling through the generation of synthetic data. In this way the usual use for simulation, monitoring and subsequent analytics is complemented. Figure 3: Principal sketch for a system in a real-life context. Figure 2: Understanding a system’s behavior on the basis of domain knowledge and data. To conclude, the most effective way of determining a model for the system is achieved by combining data-driven and first-principle models in conjunction. Henceforth, the term system model will be used. While system models enable the systematic design, operation, optimization, monitoring and control of a system, the validity is a critical aspect when relying on the models. In Figure 4, the system model is shown in a real-life context, where it is used in parallel with the real-life system. All variables denoted by \(\hat{\bullet}\) represent the estimate of the actual value of a variable. The estimate might be the result of a filtering, smoothing or calculation, and might include qualitative judgements. For the MVs \(u\) it is assumed that those are known and thus no estimate is needed. Thus, DVs are denoted as \(d\) and \(\hat{d}\), PVs are denoted as \(x\) and \(\hat{x}\), and CVs are denoted as \(y\) and \(\hat{y}\). In the context of ZDM, the production process represented by the system model is affected by the following domain aspects:  
* The wear and tear of different machine components and parts from a mechanical perspective need to be captured by specific condition-related states in the model. * Empiric data: rules-of-thumb via observations and experience (which often is undocumented) need to be captured by specific parameters that reflect these aspects. * Facts and data from production results need to be captured in the outputs generated by the model. * Underlying understanding of the input qualities, production process, process parameters and output qualities need to be captured in the parameters of the model. Related questions to the above bullets are: the length of production campaigns or series and how much time passes between the campaigns or series. As the production pace and length of campaigns render wear and tear it is necessary to have a model where both condition- and time-based maintenance are present. Additional external parameters, such as scheduling and re-scheduling of production and maintenance, should be part of a future, more advanced, model. An important aspect that needs to be considered is also the operational context of the production process. Most production processes can be understood as discrete production stages that only interact through the product flow within the production chain, while the individual stages in a production process do have a continuous behavior with a high level of interaction between the product and the dynamics of the production stage.