🤖 AI Summary
This paper addresses the level set estimation (LSE) problem in manufacturing quality control under input uncertainty—arising from equipment precision variations and operator deviations—and introduces, for the first time, *cost-dependent input-uncertainty LSE*: accurately identifying the region where product performance meets specifications under heterogeneous, multi-precision, and multi-cost inspection devices, while minimizing total inspection cost. We propose a Bayesian optimization–based active learning algorithm that explicitly accounts for input uncertainty, equipped with a cost-weighted acquisition function and supported by theoretical convergence guarantees. Experiments on synthetic benchmarks and real-world industrial datasets demonstrate that our method achieves significantly lower total inspection costs than state-of-the-art approaches, while maintaining high-accuracy level set estimates—thereby bridging theoretical rigor and practical engineering applicability.
📝 Abstract
As part of a quality control process in manufacturing it is often necessary to test whether all parts of a product satisfy a required property, with as few inspections as possible. When multiple inspection apparatuses with different costs and precision exist, it is desirable that testing can be carried out cost-effectively by properly controlling the trade-off between the costs and the precision. In this paper, we formulate this as a level set estimation (LSE) problem under cost-dependent input uncertainty - LSE being a type of active learning for estimating the level set, i.e., the subset of the input space in which an unknown function value is greater or smaller than a pre-determined threshold. Then, we propose a new algorithm for LSE under cost-dependent input uncertainty with theoretical convergence guarantee. We demonstrate the effectiveness of the proposed algorithm by applying it to synthetic and real datasets.
