連續製造可透過高頻感測器與即時製程資料支援品質監測與控制，但關鍵品質屬性常因離線或產線旁檢測成本、破壞性取樣與量測延遲，而呈現低頻、稀疏且不規則的觀測型態。高頻製程特徵與低頻品質量測並存的多頻率資料結構，使傳統監督式學習模型往往必須仰賴聚合、重取樣或插補進行特徵--標籤對齊，因而可能壓縮或忽略品質狀態隨時間演化的動態特性。本研究以商業規模連續藥片製造資料為實證對象，聚焦於壓製階段之平均硬度。相較於平均重量與平均厚度，平均硬度雖多數仍落於規格範圍內，卻呈現較明顯的規格內漂移與較高的不穩定性，更能反映低頻品質監測的挑戰。為處理製程訊號與品質量測之間的時間解析度不一致，本研究將平均硬度視為隨時間演化的潛在品質狀態，並以狀態空間模型與 Kalman filter 建立品質狀態估計架構；研究中比較完整高頻資料與量測對齊簡化資料兩種資料設定，並檢驗 deterministic constant、local level model、local linear deterministic trend 與 local linear trend 等不同狀態空間模型。

實證結果顯示，在量測對齊簡化資料下，local level model 取得最低 AIC（499.785）與測試集 MSE（0.279），優於固定水準模型與較複雜的趨勢模型，表示平均硬度的基準水準並非固定不變，而是會隨時間漂移；將其建模為可由品質量測更新的潛在狀態，較能符合本研究資料結構。在製程變數方面，compression cycle fill depth 與 ejection force tablet 為最主要且穩定的正向解釋變數，pre-compression force 則具有次要但仍具統計支持的關聯；相對地，壓製環境溫度與濕度並未提供足夠證據顯示其為平均硬度變化的主要來源。與 Random Forest Regression 及 LSTM 相比，local level model 亦具有較佳測試集表現；Random Forest 的測試集 MSE 為 0.571，LSTM 雖能納入完整高頻製程序列，其測試集 MSE 仍為 0.529。結果指出，完整高頻資料與較複雜模型並不必然提升低頻品質預測能力；在品質標籤稀疏的情境下，清楚的特徵--品質對齊方式與符合資料結構的狀態估計模型，較能兼顧預測表現與結果解釋。Local level model 因此可作為連續製造中平均硬度品質監測的基礎模型，並可延伸至非線性狀態空間模型、多品質屬性監測與線上更新機制。

Continuous manufacturing uses real-time process data and frequent sensor measurements to support quality monitoring and control. However, critical quality attributes are often observed at low frequency, sparsely, and irregularly because of off-line or at-line testing costs, destructive sampling, and measurement delays. This multi-rate data structure, in which high-frequency process features coexist with low-frequency quality measurements, often forces conventional supervised learning models to rely on aggregation, resampling, or imputation for feature--label alignment, which may compress or overlook the dynamic evolution of product quality. This study uses commercial-scale continuous tablet manufacturing data and focuses on average hardness in the compression stage. Compared with average weight and average thickness, average hardness remains mostly within specification but shows more pronounced in-spec drift and higher instability, making it a suitable target for studying low-frequency quality monitoring. To address the mismatch in temporal resolution between process signals and quality measurements, this study treats average hardness as a latent quality state that evolves over time and develops a state estimation framework based on state-space models and the Kalman filter. The analysis compares full high-frequency data with measurement-aligned simplified data, and evaluates deterministic constant, local level model, local linear deterministic trend, and local linear trend specifications.

The empirical results show that, under the measurement-aligned simplified data setting, the local level model achieves the lowest AIC of 499.785 and test MSE of 0.279, outperforming both the fixed-level model and more complex trend models. This finding indicates that the baseline level of average hardness is not fixed but drifts over time; modeling it as a latent state updated by quality measurements better matches the data structure in this study. Among the process variables, compression cycle fill depth and ejection force tablet are the most important and stable positive explanatory variables, while pre-compression force shows a secondary but statistically supported association. In contrast, press temperature and humidity do not provide sufficient evidence as major sources of average hardness variation. Compared with Random Forest Regression and LSTM, the local level model also achieves better test performance: the Random Forest model has a test MSE of 0.571, and the LSTM model, despite using full high-frequency process sequences, has a test MSE of 0.529. These results suggest that full high-frequency data and more complex models do not necessarily improve low-frequency quality prediction. When quality labels are sparse, clear feature--quality alignment and a state estimation model consistent with the data structure can better balance predictive performance and interpretability. The local level model can therefore serve as a baseline model for monitoring average hardness in continuous manufacturing, with potential extensions to nonlinear state-space models, multi-attribute quality monitoring, and online updating mechanisms.

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