Root Cause Analysis under Reduced Information on a Manufacturing Line at Bosch

Description | In the age of Industry 4.0, mathematical models gain further importance to determine reasons for loss of production. In fact, manufacturing companies have manufacturing execution systems (MES) that allow engineers and managers to extract quantitative and real-time raw data. Nevertheless, their ultimate purpose is not only to identify and analyze production issues, to implement corrective actions, but also to predict possible harmful occurrences, in a preventive perspective.

This problem intends to merge techniques applied to probabilistic graph models with simple machine learning techniques to determine causes/factors that are associated with product testing failures, using real data from a production day of a manufacturing line at Bosch Termotecnologia.

A manufacturing line (ML) will be abstractly modeled by the so-called Queue Direct Graph (QDG) having nodes (the workstations), queues (waiting spaces) and tokens (the parts/products), whose graphical representation is given in the next figure, in parallel with the physical representation of the process.

We assume reduced information, meaning that it is only available a data set with the following fields:

Processed tokens in a ML at Bosch are tested for conformity on every node, and the testing results are recorded in the variable errorID. The last node executes an extended and complex set of test steps generating different types of errors, so errorID may have values in {0,1,2,…}. The remaining nodes can only generate two types of errors with values in {0,1}. For simplicity, errorID=0 means normal behavior and the errors of the last node will be called NOKs.

Tasks 1 (75% effort): For a given Bosch’s data set, understand and use Hidden Markov Chains to model the (probabilistic) associations between the nodes’ errors and the NOKs. By using the Viterbi’s algorithm, the sequence of expected nodeIDs (that are potentially the origin of the error issues) should be obtained when a sequence of NOKs is observed at the final node.

Tasks 2 (25 % effort): Implement a machine learning model (e.g., using decision trees) to predict if a token is going to fail the test at the last node.

Mathematical background | Basic programing in Python, basic probability theory, graph theory