## 3 Related Work in the Area of the Data Quality Dimension Completeness
Beside the metrics concerning the values of the variables, also metrics evaluating the amount of data of each variable is reasonable. The completeness concerning the amount of data is reduced if the valve's stroke is gathered for 2 h even though the use case requires 3 h. Record Level:
* Task-independent: Two different viewpoints are introduced for the record level. The first viewpoint considers and assess each record individually. This completeness is calculated based on the empty items in one record in relation to the number of variables. The record \(t_{6}\) (example (4) in Figure 5) has a Weak Tuple Completeness [34] and Record Completeness [37] of 0.5 since one of the two sensor signals is missing. The strong tuple completeness [34] evaluates the completeness of the record t\({}_{6}\) as 0, since it is not complete. The second viewpoint observes how many records with missing values are contained in the data set [37]. In Figure 5, the Empty Records in a Data File [37] is 0.57 (5). * Task-dependent: On record level, only one task-dependent attribute is introduced [37] concerning the amount of data rather than the content. The quotient of number of records within a data set and expected number of records describes the Data File Completeness [37]. Like the variable level, this completeness is reduced if the entire data set contains data of 2 h even though 3 h are required. A consideration regarding a metric to assess task-dependent completeness on record level concerning the content is not introduced yet. It is not evaluated if the records show all the combinations of values that are expected. Schema level:
* Task-independent: No attribute is introduced since it is not reasonable. If the schema is complete and contains all the relevant variables, can only be evaluated based on the expectations of the use case. * Task-dependent: This attribute is evaluated based on the comparison of available and expected variables. If the condition monitoring of control valves requires a sensor for vibration, a data set containing only stroke, pressure and pressure difference is not complete. Consequently, the Schema completeness [16] and Conceptual Data Model Completeness [37] is reduced. Furthermore, the Conceptual Data Model Attribute Completeness [37] considers the format of the variables. If vibration is measured with a vibration velocity transducer providing values in mm/s; however, the values of an accelerometer in m-s\({}^{-2}\) is required and the completeness is reduced. These metrics cover a wide range of attributes for completeness. Besides the literature defining metrics for completeness, further research is performed using and evaluating the introduced metrics for sensor and actuator data. For example, [PERSON] et al., 2016 [41] use task-independent record completeness to assess the data quality of sensor data from drilling rigs. However, on record level, the task-dependent attribute is limited to concerns regarding the amount of data. The content, in particular the combinations of variable values in the records, is not considered even though [PERSON] and [PERSON] 1996 [11] already observed that completeness is a question of \"data combinations rather than just [...] null values\" [11]. On variable level, it is observed whether all possible values are covered by the data. The stroke of control valves should contain values from fully closed (stroke = 0%) to fully opened (stroke = 100%). However, none of the introduced completeness metrics is concerned whether the stroke values appear with different combinations of the other variables, e.g., pressure. The task-dependent completeness on record level still is a research gap. Closing the gap, this paper introduces the concept of data set completeness. Data set completeness examines the combinations of variables in a multi-dimensional data set of sensor and actuator data. The proposed metric for data set completeness indicates whether the data set is complete and balanced regarding the different combinations of variable values.