# Overlap in Automatic Root Cause Analysis in Manufacturing: An Information Theory-Based Approach
Overlap is a phenomenon that happens when, in two separate manufacturing steps, all products that go through a certain machine in one of the steps are all processed in another given machine in a later step. With the data generated by this phenomenon, it is very hard to distinguish the influence each machine has on the quality of the final product, especially if it is analyzed through classification algorithms. Overlap may happen due to stabilization in the manufacturing process. For example, if we have a process where products always flow from the same two machines in contiguous steps, as these have their times synchronized, as soon as the machine in the earlier step is finished, it is always the same machine in the later step that becomes available. Despite the example, this does not mean that overlap can only occur between machines that operate in contiguous steps. Attaining this sort of balance in the manufacturing process can be positive in terms of productivity and efficiency, but it becomes an issue during the analysis of the data generated from such a process. This contention between what is positive from a production perspective (that should be prioritised) and what is advantageous for diagnosis based on data analysis is relevant, as this signifies that overlap will occur regularly when performing diagnosis on data of the location type. It is important to mathematically measure overlap in order to correctly gauge its effect on the development of ARCA solutions. However, that measure needs to consider two aspects: (i) the direction of the association between factors (manufacturing process variables), and (ii) it needs to be able to recognize the effect of overlap between individual machines (further explanations can be found in Section 3). These aspects are not considered in [32]. The goal of this paper is to develop an ARCA solution that is able to locate the root cause of a problem in a manufacturing process, and that is robust to overlap. To do so, we propose an overlap measure that considers the aspects mentioned in the above paragraph. The measure is based on information theory, in particular, the use of a variant of mutual information named Positive Mutual Information (PMI), proposed in [33]. Building on top of this new measure, we introduce a new method that is used to handle RCA and identify the most probable root causes and is robust to overlap. A visualization tool is also proposed, making the task of identifying overlap and the root causes easier for practitioners. We validate the proposed approach in simulated data and real data from a case study in semiconductor manufacturing, which is a highly competitive sector [34]. The rest of the paper has the following structure. In Section 2, an overview of previous works relevant to this study is presented. First, a brief discussion about previous works of ARCA in manufacturing is presented. This is followed by a definition of the problem of overlap in Section 3. In Section 4, the proposed measure of overlap is described, in addition to the proposed method for RCA based on this measure. Sections 5.1 and 5.2 explain and show (respectively) the results of the experimental procedures used to validate the proposed methods. Section 6 discusses and summarises the results obtained in the previous section and discusses future research directions. Finally, we summarise our findings and present the main conclusions.