# Contextual Explanations for Decision Support in Predictive Maintenance
## 4 Experiments
### Data Set  
The data set used in the experiments is based on the data reported in [11]. The initial data set consists of the measurements recorded for a coal crusher operating at the boiler of the power plant. The crusher, named NW-10, was equipped with two sensors C122 and C123 located on the opposite sides of the rotating shaft. The data collected by the sensors include three attributes: maximum and root mean square (RMS) value of vibration, and temperature. The measurement values were recorded every 10 s between 13 July 2019 and 30 March 2021. During this period, two machine failures requiring servicing operations were reported.  
For the purpose of the analysis, the measurement values were aggregated within a time window of 8 h, which corresponds to the length of the shift. The aggregation resulted in a data set consisting of 717 examples that covered the period from the beginning of the measurements until the second machine failure. Two distinct approaches to aggregation were applied, which resulted in two different data representations. The first representation, hereinafter referred to as Basic, was calculated as a mean value of each attribute value within the time window. Therefore, Basic representation consists of six attributes, which correspond to the three measurements recorded by each of the two sensors (C122 and C123). The second representation, hereinafter referred to as Extended, was calculated by means of the tsfresh [36] library. This Python package offers methods for calculating a large number of time series characteristics. For each attribute of the data set, the following 15 statistical and time-based characteristics were calculated and taken as derived attributes: sum, median, mean, standard deviation, variance, root mean square, maximum, absolute maximum, minimum, intercept of the regression line, slope of the regression line, standard error of the estimated slope (gradient), assuming normality of the residuum, R value of the regression line, non-directional \(p\)-value for a test whose null hypothesis is that the slope is zero, using the Wald test with \(t\) distribution of the test statistic. Thus, the Extended representation consists of 90 attributes.  
Figure 2 presents the values of the vibration-based attributes calculated for the Basic representation. In addition to the data characteristics, the figure presents when the failures took place in the form of dashed vertical lines. Looking at Figure 1, it can be noticed that around example 220 the characteristics of the measurements recorded by sensor C123 changed. Specifically, the values of VibrRMS_123 and VibrMax_123 decreased noticeably. This change occurs more than two months prior to Failure 1 and it can be interpreted as an indication of an impending failure, in a post hoc analysis. Similarly, it can be noticed that around example 600 the characteristics of the measurements recorded by sensor C122 changed. Specifically, the values of VibrRMS_122 and VibrMax_122 decreased noticeably. This change occurs almost one-and-a-half months prior to Failure 2 and it can be interpreted as an indication of an impending failure, in a post hoc analysis.  
Figure 2: Values of the selected attributes (representing vibrations [mg]) of crusher data set, machine failures are marked by red dashed vertical lines.