Kernel-based multivariate statistical process control (K-MSPC) extends classical monitoring to nonlinear industrial processes. Its performance depends critically on kernel parameters such as lengthscales and variance terms. In current practice these parameters are typically selected by heuristics or deterministic optimisation, and then treated as fixed, despite being inferred from finite and noisy data. This can lead to overconfident control limits and unstable alarm behaviour when the kernel choice is uncertain. This work proposes a probabilistic K-MSPC framework that quantifies and propagates kernel parameter uncertainty to the monitoring statistics. The approach follows a two-stage workflow: (i) deterministic kernel calibration using supervised or unsupervised models, and (ii) Bayesian inference of kernel parameters via Markov chain Monte Carlo. Posterior samples are propagated through kernel Principal Component Analysis to produce probabilistic $T^2$ and squarred prediction error control charts, together with uncertainty-aware contribution plots. The framework is evaluated on the Tennessee Eastman Process benchmark. Results show that posterior-mean monitoring often improves fault detection compared to deterministic prior-mean charts for the squared exponential kernel, while credible bands remain narrow in-control and widen under faults, reflecting amplified epistemic uncertainty in abnormal regimes. The automatic relevance determination kernel reduces posterior uncertainty and yields performance close to the deterministic baseline, whereas unsupervised calibration produces wider posterior bands but still robust fault detection.

翻译：基于核的多变量统计过程控制将经典监控扩展至非线性工业过程。其性能关键取决于长度尺度和方差项等核参数。当前实践中，这些参数通常通过启发式方法或确定性优化选取，随后被视为固定值，尽管它们是从有限且有噪声的数据中推断得出。当核选择存在不确定性时，这可能导致控制限过于自信以及报警行为不稳定。本研究提出一种概率性核多变量统计过程控制框架，该框架量化核参数不确定性并将其传播至监控统计量。该方法遵循两阶段工作流程：（i）使用监督或无监督模型进行确定性核校准，以及（ii）通过马尔可夫链蒙特卡洛方法对核参数进行贝叶斯推断。后验样本通过核主成分分析传播，生成概率性$T^2$和平方预测误差控制图，以及基于不确定性感知的贡献图。该框架在田纳西伊士曼过程基准上进行了评估。结果表明，对于平方指数核，与确定性先验均值图相比，后验均值监控通常能改善故障检测，同时可信带在受控状态下保持狭窄，并在故障条件下变宽，反映出异常状态下认知不确定性的放大。自动相关性确定核减少了后验不确定性，并产生接近确定性基线的性能，而无监督校准产生更宽的后验带，但仍能实现稳健的故障检测。