## 3 Related Work in the Area of the Data Quality Dimension Completeness
**} & \multirow{2}{*}{**S**} & \multirow{2}{*}{**F.5**} \\ \cline{3-3} \cline{5-8} \multicolumn{1}{c}{**Author**} & & & & & & **Level** & \\ \cline{3-3} \cline{5-8} \multicolumn{1}{c}{**I**} & **V** & **R** & **S** & & & **Level** & **S** \\ \hline \multirow{3}{*}{[PERSON] 1996 [29]} & Attribute Compl. & X & & & & & **Indep. ** & \(\bigcirc\) \\  & Entity Compl. & & X & & & & **Dep. ** & \(\bigcirc\) \\ \cline{1-1} \cline{3-3} \cline{5-8} \cline{5  
In contrast, [PERSON] and [PERSON], as well as [PERSON] and [PERSON], describe completeness in a broader sense [11,15]. Completeness considers the \"breadth, depth and scope of information contained in the data\" [15]. It is concerned about \"data combinations rather than just null values\" [11]. Based on these qualitative fundamentals, much research appeared in recent years introducing metrics for completeness. To discuss and illustrate the application of the proposed metrics, the use case of condition monitoring of control valves and their sensor and actuator data is used as an example. Item level:  
* Task-independent: Several authors introduced an attribute concerning the task-independent completeness on item level, e.g., Value Completeness [34] or Data Item Completeness [30]. Besides their different names, the calculation of the metric is the same. The number of empty items (null values) in a data set is divided by the whole sum of items in the data set [28,30,33,34,35,35]. Sporadic missing values of sensors caused by, e.g., unstable wireless connection or sensor device outages such as limited battery life or environmental interferences [40], impact this completeness. The example (1) in Figure 5 shows task-independent completeness on item level of 0.79 (3 items out of 14 are NULL). * Task-dependent: No attribute is introduced. One specific item is either existing or not. It is not reasonable to evaluate task-dependent completeness on single items. Variable level:
* Task-independent: The task-independent attribute on variable level considers the empty items of one variable in relation to the number of available records [16,28,33,34,36,37]. The example (2) in Figure 5 illustrate this attribute which is called, among others, Column Completeness [16], Structural Completeness [36] or Attribute Completeness [37]. Even though several different names are introduced over time, the basic concept and the calculation is similar. However, Scannapieco and Batini 2004 further differentiate in a weak and a strong metric [34]. In contrast to the weak completeness (example (2) in Figure 5), the strong completeness is either 0 or 1 (0 for missing values in a variable and 1 for a complete variable). In Figure 5, the Strong Attribute Completeness is 0 for each variable. For sensor data, a window is defined, calculating the completeness value subsequently [38,39]. Based on a window of one minute, example (3) in Figure 5 reveals task-independent completeness on variable level of 0.67 for stroke and 0.83 for pressure in the first minute. Figure 5: Fictitious data set to illustrate the state-of-the-art metrics for the task-independent attributes on item, variable and record level. Task-dependent: For this attribute, the expectations concerning the values or the amount of data are considered, respectively [16; 28; 34; 36; 37]. Most metrics observe whether all expected values of a variable are included in the data or not. If the valve's stroke, which can vary from fully closed (stroke = 0%) to fully opened (stroke = 100%), only contains values between 60% and 90%, task-dependent completeness on variable level, e.g., Population Completeness [16] or Weak Relation Completeness [34], is reduced. The strong relation completeness [34] is 0 in this case. In contrast, the Content Completeness [36] refers to the precision of the data. If data does not contain as much information as required, e.g., only one decimal digit instead of the required three decimal digits, the completeness is reduced.