Abstract:

In manufacturing systems， practitioners rely on sampling inspection to detect real-time changes within the system. However， due to the large number of categories （variables） that need inspection and the limited availability of inspection resources such as human labor or instruments， only a subset of categories can be inspected at each time point. As a result， only partial observations of the defective numbers for each category can be obtained. To enable a prompt system change detection， it requires not only a powerful change detection scheme that can deal with partially observable data， but also an adaptive variable selection strategy to identify which set of variables to be observed for the next time point such that the change information can be reserved maximally. The challenge of online change detection is addressed for high-dimensional data streams following a binomial distribution， based on a partially sampling inspection process. First， high-dimensional data is decomposed into smooth normal signals and sparse abnormal signals. The normal signals are represented as a linear combination of basis functions multiplied by corresponding coefficients， capturing the correlations between variables. The anomalous parameter is modeled using a spike-slab distribution and variational Bayesian inference is employed to estimate the distribution parameters. Next， a likelihood ratio test is constructed as the detection statistic for detecting system changes. Furthermore， combinatorial multi-armed bandit （CMAB） algorithms are leveraged by treating the test statistics as the reward function. Specifically， a variable selection policy based on Thompson sampling is proposed， enabling the selection of the most anomalous categories for inspection at each time point and minimizing change detection delay. Through experimental evaluations， the results highlight its potential to improve the efficiency and accuracy of defect detection in manufacturing systems while considering the constraints of limited inspection resources.

Key words: online learning, partial observations, sampling inspection, binomial distribution, sparse change