# Overlap in Automatic Root Cause Analysis in Manufacturing: An Information Theory-Based Approach
## 6 Discussion  
In this section, we discuss and summarise the results of the different experiments and how these combine to form coherent conclusions. In the Mockup experiments, the proposed PMI method was able to achieve a performance equal to the best solutions based on the previous overlap measure (CO) and a much better performance than the DT classifier. Through a comparative analysis of Figures 4 and 5, we can see that an increment in the amount of overlap leads to degradation in the performance of the classifier. This is evidence in favor of the argument presented in Section 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Moment** & **Begin** & **End** & **Overlap\({}_{PMI}\)** & **CO** & **PMI** & **DT** \\ \hline \(1\) & 60 & 240 & 0.96\% & COATFUSE & - & COATFUSE \\ \hline \(2\) & 312 & 360 & 4.74\% & PLATINGRDL & PLATINGRDL & PLATINGRDL \\ \hline \(3\) & 420 & 516 & 1.25\% & EXPOSEFUSE & EXPOSEFUSE & EXPOSEFUSE \\ \hline \(4\) & 516 & 660 & 1.67\% & EXPOSEFUSE & EXPOSEFUSE & EXPOSEFUSE \\ \hline \(5\) & 672 & 720 & 15.88\% & CUREFUSE & CUREFUSE & CUREFUSE \\ \hline \(6\) & 876 & 960 & 1.89\% & COATRDL & COATRDL & COATRDL \\ \hline \(7\) & 948 & 1656 & 0.67\% & EXOSERDL & - & EXPOSERDL \\ \hline \(8\) & 1656 & 1752 & 3.12\% & - & AOIDL1 & AOIDL2 \\ \hline \(9\) & 1860 & 1908 & 9.16\% & - & - & - \\ \hline _10_ & 2484 & 2592 & 1.50\% & - & PLATINGRDL & PLATINGRDL \\ \hline _11_ & 2580 & 3096 & 0.79\% & - & AOIDL2 & AOIDL2 \\ \hline _12_ & 3132 & 3240 & 1.45\% & - & - & CLEANTOPWLB \\ \hline _13_ & 3228 & 3432 & 0.74\% & AOIDL2 & AOIDL2 & AOIDL2 \\ \hline _14_ & 3456 & 3492 & 9.87\% & - & AOIDL2 & - \\ \hline _15_ & 3480 & 3888 & 0.66\% & - & - & - \\ \hline _16_ & 3888 & 3984 & 1.54\% & - & EXPOSERDL & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Table summarizing the problematic moments identified in the case study dataset, as well as the common root causes among the different algorithms proposed. In the experiments with the Stochastic simulation data, PMI achieved better performance than the other algorithms, as it put the true root causes in the same or higher rankings than the CO method. When applying the different algorithms to the real case study, the proposed method was found to be able to identify most root causes in common with other methods. An additional note on the experiments with the Stochastic simulation data is that, to enable the detection of tuples that overlapped with the Label, there was a need to lower the threshold (of Expression 5) to 0.8 for the first two datasets and 0.3 for the last dataset. As these datasets have greater levels of noise, this seems to indicate that the threshold needs to be adapted to the datasets at hand and that the noisier the dataset is, the lower the threshold needs to be to detect tuples overlapping with the label. The default threshold value of 0.9 was chosen so as to include instances with very high overlap but with some leeway for noise. The fact that we needed to lower the threshold in response to an increase in noise indicates that there is a reduction in the signal-to-noise ratio in terms of evidence of the presence of the root cause in the data. While overlap may be less evident due to the presence of noise, so is the root cause signal. From the results of all the experiments, we can clearly reach the conclusion that the proposed PMI algorithm has better performance than both the classifier solution and the CO algorithm. A relevant shortcoming of this work is that it was not possible to establish the root causes in the case study data, which hinders the validation in real data. This work would be improved if it was possible to access real data with the root causes identified. Another avenue for future work could be analyzing the effect of noise on the performance of the factor-ranking algorithms, as it is not clear what is causing the differences in the performance of the algorithms (although it is clear that they are resilient to overlap).