## 2 Definitions and Background
### Condition-Based Maintenance  
Condition monitoring of control valves is used as running example to illustrate the need for a data quality metric measuring data set completeness. In order to give some background, the following paragraphs introduce the concept of condition-based maintenance and discuss different approaches. Maintenance describe all actions that are taken to retain or restore the function of a component, device or system [23]. Different strategies can be pursued to achieve this goal. Condition-based maintenance replaces other maintenance strategies as corrective and time-based preventive maintenance. While latter performs maintenance measures after the breakdown of an equipment or preventively in advance to any deterioration, condition-based maintenance aims at taking action situation- and needs-based [23]. As a prerequisite, the condition of the equipment needs to be monitored. In order to do so, diagnostics and prognostics are the key elements [24]. Detecting faults of an equipment (fault detection), identifying the source of the fault (fault isolation) and specifying the severity of fault (fault identification) are included in diagnostics. In contrast, prognostics aims at predicting the  
Figure 2: Data quality assessment process. The main contribution of this paper is highlighted. occurrence of faults or the remaining useful life. Based on the diagnostics and prognostics, measures to retain or restore the function of the monitored component can be taken. Different approaches can perform diagnosis. They can be differentiated into model-based and model-free approaches (cf. Figure 3). Model-based approaches depend on the development of models describing the input and output dependencies of the monitored equipment [25]. The difference between the modeled and the actual output indicates the condition of the system. Physical modeling 1 aims to provide physical models in the form of mathematical equations. This requires expert knowledge, which is difficult in highly complex systems. Besides, model-free approaches can be differentiated into signal-based 2 and data-driven. Signal-based approaches do not model the input and output dependencies, but analyze the signal characteristics in order to detect faulty behavior. Limit checking or trend analysis are simple examples. Moreover, a variety of further characteristics, also in frequency-domain, is available to check for unfavorable behavior of the signals. In contrast to model-based and signal-based approaches, data-driven approaches aim at identifying features for fault diagnosis based on historic data and ML algorithms without expert knowledge. Therefore, data-driven approaches are also referred to as empirical approaches [26]. The machine learning algorithms for fault diagnosis can be differentiated further into classification 3 and novelty detection methods 4. Based on the sensor and actuator data the algorithm classifies different faults or distinguishes between normal and abnormal behavior without knowing the specific fault types, respectively. A disadvantage of these approaches is the requirement of well-sampled massive data. Hybrid approaches aims at combining model-based and model-free approaches to utilize the advantages of both. Data-driven modeling 5 describes the modeling of the input-output-relations based on historic data. The complex physical dependencies can be learned based on sensor and actuator data instead of being modeled by human experts based on physical characteristics. This facilitates model-based condition monitoring significantly. Furthermore, the complexity of the data-driven model is reduced by using the available expert knowledge regarding input features. This paper takes a data-driven modelling approach 5 to monitor the condition of control valves. This combines the advantages of model-based and model-free approaches. However, it is still required, that a well-sample training data set is available.