管制圖比較分析：不同應用場景下性能與適用性評估

Abstract

管制圖在製程監控中扮演關鍵角色，不同類型與樣本數設定將直接影響其對製程異常之敏感度及成本效益。選擇適合的管制圖以平衡誤判風險與監控成本，是製程品質管理中極需解決之問題；有鑑於此，本研究針對X ̅-R管制圖、X ̅-S管制圖與I-MR管制圖進行比較分析，並探討樣本數變化對其性能之影響，以提供製程管制最佳實務指引。首先，本研究透過課程老師所設計之製程穩定性模擬平台，得到實驗數據；其次，利用Minitab軟體分別構建X ̅-R、X ̅-S及I-MR管制圖，完成Phase I階段之製程穩定性分析並確定其上下管制界限。其次，於Phase II階段基於相同管制界限，對異常製程進行監控，記錄各個管制圖異常判定結果及誤判情況。接著，透過誤判次數與相關成本對三種管制圖進行性能評估，分析其在敏感度、穩定性及成本效益方面之差異。最後，選擇表現最佳之管制圖，結合不同樣本數設定進行深度分析，探討樣本數對監控精度與成本之影響。實驗結果顯示，三種管制圖在誤判風險與成本效益上展現顯著差異，樣本數的選擇進一步影響其性能表現。發現X ̅-R管制圖在監控效能與成本管制間表現出良好平衡，而I-MR管制圖因樣本數限制導致誤判風險增加，X ̅-S管制圖則在高敏感度下呈現較高成本。研究證實X ̅-R管制圖在樣本數適中時能有效平衡監控精度與成本效益，具備優越的實用性與應用價值。此結果為品質管理領域提供實踐參考，特別在製程穩定性與成本管制需求間，可作為制定監控策略之重要依據。

Control charts play a key role in process monitoring. Different types and sample number settings will directly affect its sensitivity to process abnormalities and cost-effectiveness. Selecting an appropriate control chart to balance the risk of misjudgment and monitoring costs is an issue that needs to be solved in process quality management; in view of this, this study focuses on X ̅-R control charts, X ̅-S control charts and I-MR controls Comparative analysis is performed on the graph and the impact of changes in sample number on its performance is discussed to provide best practice guidelines for process control. First, use Minitab software to construct X ̅-R, X ̅-S and I-MR control charts respectively to complete the process stability analysis of Phase I and determine its upper and lower control limits. Secondly, in the Phase II stage, the abnormal process is monitored based on the same control limits, and the abnormal determination results and misjudgments of each control chart are recorded. Then, the performance of the three control charts is evaluated through the number of misjudgments and related costs, and their differences in sensitivity, stability and cost-effectiveness are analyzed. Finally, the control chart with the best performance was selected, and an in-depth analysis was conducted based on different sample number settings to explore the impact of sample number on monitoring accuracy and cost. Experimental results show that the three control charts show significant differences in misjudgment risks and cost-effectiveness, and the choice of sample number further affects their performance. It was found that the X ̅-R control chart showed a good balance between monitoring performance and cost control, while the I-MR control chart increased the risk of misjudgment due to the limited sample number, and the X ̅-S control chart showed a higher risk under high sensitivity. cost. Research has confirmed that the X ̅-R control chart can effectively balance monitoring accuracy and cost-effectiveness when the number of samples is moderate, and has excellent practicability and application value. This result provides practical reference for the field of quality management, especially between process stability and cost control requirements, and can be used as an important basis for formulating monitoring strategies.