Estimation of process capability indices for high-dimensional data
针对高维制造环境中的多变量过程能力指数估计问题，提出一种改进的自适应阈值方法，确保估计的可靠性和有界性，并通过模拟和半导体案例验证其准确性。
In high-dimensional manufacturing environments, quality assessment must account for multiple correlated characteristics, posing significant challenges for multivariate process capability indices (MPCIs). This study focuses on identifying and improving MPCIs suitable for such settings. Among several candidates, volume-ratio-based indices are found to retain interpretability and sensitivity under high dimensionality. However, their practical applicability is hindered by instability in covariance matrix estimation. To address this issue, a modified adaptive thresholding approach is developed, incorporating a positive-definiteness constraint to ensure reliable and bounded MPCI estimation. Theoretical analysis establishes the consistency of the proposed estimator. We further develop interval estimation procedures for high-dimensional MPCIs and evaluate their coverage and length properties via bootstrap-based and asymptotic approaches. In addition, we propose a diagnostic variable-ranking strategy to identify and prioritise the characteristics most responsible for capability degradation, providing actionable guidance for process improvement. Simulation studies across various sample sizes, sparsity levels, and dimensions confirm the superior accuracy of the proposed framework over existing methods. A semiconductor manufacturing case study further demonstrates its practical relevance for high-dimensional process capability analysis.