在某些製造業的批次生產過程中，產品品質特性分布不均勻是一個常見的問題。例如在烘烤製程中，可能由於加熱器裝載位置上的差異，導致每盤產品內的元件受熱程度不一，並造成產品在該盤空間分布上良率不一致的情形發生。而過往雖然已有許多學者們提出最大化批次產品均勻度的方法，但僅有少數著重於品質特性在空間上變異程度的差異。此一空間上的變異資訊不僅能使工程師更易於辨別變異來源，更能用來建構預測模型並在品質改善中提供更細部準確的變異資訊。

因此，本研究期望藉由元件在空間資訊上的紀錄，分析其批次產品內元件間的空間相關性並與製程變數連結，來找出最佳製程可控因子水準的設定，以改善品質特性分布不均勻的情形。故在本研究中，首先以D最佳化準則求取在實驗資源限制下的最佳設計矩陣，接著藉由空間相關性的計算找出在某批次上相鄰元件間彼此的變異程度。此外，為更符合實務，將同時考慮多項期望達成的品質目標並考量噪音因子對於均勻度的可能影響。最後，以最佳的因子水準設定進行驗證實驗，並透過實例分析，發現能降低整體批次元件的變異程度並改善多品質特性下的均勻度。本研究對於整體批次產品均勻度的改善能應用於不同領域當中，並期望能夠提供給決策者作為品質改善的參考。

Product non-uniformity has been a common issue in batch processing. Baking process is an example of this. A heater in an oven can be set in different location so components in a plate may not absorb the same amount of energy. This uneven distribution of quality characteristics may cause defects and produce nonconformity products. Although many studies have been done on maximizing the overall uniformity, few has focused on the spatial effect within a batch. With the information of spatial correlation between components, engineers can identify sources of variation and make prediction more precisely in the process of quality improvement.

Therefore, this study aims to find spatial correlation between components in a batch and link to process variables so that a non-uniformity problem can be alleviated by setting values of control factors. In this study, we first apply D-criteria to find an optimal design matrix under constraints of experimental resources and then capture a correlation structure within plates of product components. Additionally, multiple response goals and possible noise effects are taken into consideration to meet practical demands. Finally, in the case study we compare the uniformity performance using the optimal setting and the setting under the current operating condition. The result finds an overall variance reduction for three quality responses so that the product uniformity is improved. The experiment is applicable in different fields as a reference for quality improvement.

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