在精密製造中，品質管控是維持企業競爭力的核心。以半導體產業為例，傳統品質驗證高度仰賴實體量測，然而設備昂貴且耗時，不僅降低製造效率，更伴隨破壞性檢驗的風險。為突破此瓶頸，虛擬量測（Virtual Metrology, VM）技術應運而生。然而，現行方法多聚焦於點預測，忽略了結果的不確定性，且難以因應製程數據中普遍存在的時序自相關性、非高斯異質變異與概念漂移。
面對此困境，本研究開發一套結合相關修正交叉驗證之高斯過程潛在變數模型之虛擬量測監控框架。首先，透過相關修正交叉驗證機制精確診斷殘差之自相關結構並轉化為強先驗資訊修正傳統交叉驗證因相關干擾導致過度擬合，進而引發之預測區間覆蓋率偏差；其次，利用高斯過程潛在變數模型建構具異質變異性之非高斯噪聲模型，並配合雙重隨機採樣與經驗分位數法，精確量化系統不確定性以建構動態預測區間；同時導入基於相對皮爾森散度之雙視窗監控機制，主動識別全域與局部漂移並觸發模型重構。統計模擬與實例驗證結果顯示，本框架於不同壓力測試下與各目標水準之絕對誤差均能控制在 0.9% 以內，且能有效收斂區間寬度；而在刀具磨損與化學機械平坦化兩組工業競賽資料集應用中，結果顯示本研究提出之機制不僅能提供關鍵的預警前置時間，亦能針對異質與動態製程環境建構高度可靠且動態調適的預測區間。本研究成功兼顧了統計推論的嚴謹性與工業實務的實用價值

Quality assurance in precision manufacturing has long depended on physical measurement tools that impose significant cost and cycle-time penalties. Virtual Metrology (VM) offers a data-driven alternative, enabling real-time quality inference from process sensor signals. Despite its promise, most existing VM approaches are limited to point estimates and do not account for temporal autocorrelation, heteroscedastic non-Gaussian noise, or distributional shift over time.
This study proposes a VM framework that combines a Gaussian Process with Latent Covariate (GPLC) model and Correlation-Corrected Cross-Validation (CC-CV) to jointly address these limitations. CC-CV quantifies residual autocorrelation structure and translates it into informative priors, mitigating coverage distortion under correlated observations. Within an augmented input-latent space, GPLC with double stochastic posterior sampling produces calibrated prediction intervals that adapt to asymmetric and heavy-tailed error profiles. A complementary monitoring layer based on the Symmetric Pearson Divergence detects both gradual structural shifts and transient fluctuations, enabling timely adaptive model updates when drift is confirmed. Across simulation benchmarks, coverage converges reliably to nominal levels. On tool wear and chemical-mechanical planarization benchmarks, the framework delivers early warning capability, accurate point estimates, and well-calibrated intervals under process heterogeneity. The result is a statistically grounded yet practically deployable solution for smart manufacturing quality control.

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