# Overlap in Automatic Root Cause Analysis in Manufacturing: An Information Theory-Based Approach
## 3 Problem Definition  
Overlap is a phenomenon specific to the problem of locating the root causes of problems in a manufacturing process. As products go through a sequence of manufacturing steps in a manufacturing process, in each of those steps, they are processed in a certain machine. A step-machine combination means that a product was processed in a certain machine in a certain step. This combination is also called a tuple. Figure 1 depicts such a manufacturing process, where a product goes through several steps, and is processed in a machine in each step. The squares with \(P_{i}\) illustrate products as they flow through a manufacturing process. In this depiction, Product 1 is in line to be processed before Step B, Product 2 is still being assembled/transformed in Machine M_3, and Product 3 was already processed and is currently being monitored. The problem's root cause is located in Step A, Machine M_1. At the end of the process, the product has its quality monitored, and it is defined as normal or problematic. If the number of products with problems increases sharply in a short period, it indicates that the process has a problem needing to be tackled, which requires RCA to determine its origin. The manufacturing process described above generates data similar to those shown in Table 1. Each row corresponds to a product, each column corresponds to a step, and each cell indicates the machine where that row's product was processed for that column's step. The \"Problem\" column represents the final quality of the product with respect to whether it  
Figure 1: A depiction of an example of a process that produces data that can be used to locate a root cause [32]. had a problem or not. We have chosen to use four instances in this table, as this provides enough variety of examples, but not enough complexity to prevent the comprehension of the conceptual example. The objective when trying to locate a root cause in this type of data is to determine the step-machine tuple that represents the location of the origin of the problem. However, this can become extremely hard if overlap is present. Overlap can be understood as a synchronization within the manufacturing problem that makes all products that pass through a given machine in a certain step also pass through another specific machine in a step further ahead in the process. In addition, all the products that pass through this later step have passed through the same machine in that previous step. This synchronization makes it extremely hard to differentiate how each of these machines influences the quality of the product. Note that the entire trace of step-machine tuples has to be analyzed, as the overlap may also occur between tuples of steps that are not contiguous. Figure 1 and Table 1 depict an example of overlap: the problem's origin is located in Step A--Machine M_1; however, all products that go through the root cause tuple also go through Step B--Machine M_3. In such a scenario, it is not possible to distinguish which of the tuples was the origin of the problem. Overlap is particularly problematic when trying to use classifiers to automatically extract root causes, as previous solutions in the literature have proposed. This arises due to the knowledge structures (e.g., decision trees, rules) being generated through the selection of the most representative factors, regularly discarding factors highly correlated with the representative ones, due to their supposed redundancy. The criterion used to identify redundant factors can lead to hiding factors that are the true root cause, giving more relevance to the representative factors. For example, when generating a Decision Tree (DT), using the information-gain criterion for splitting promotes the use of factors with more levels, although the root cause may be a factor with a smaller number of levels. In the example above, a DT based on information gain would select Step B-Machine M_3 as a root cause, discarding the true root cause (Step A-Machine M_1) and providing a wrong diagnosis.