製程監控中的管制圖穩定性分析

Abstract

本研究聚焦於製造過程品質管理中之異常檢測與製造過程穩定性問題，旨在針對不同生產場景中的樣本數與成本條件，選擇適合的管制圖工具，以達到異常檢測的準確性與製程穩定性的最佳平衡。研究對X̄&R管制圖、X̄&S管制圖與I&MR管制圖進行深入比較，分析其在不同應用情境中的優劣勢，並探討如何根據製程需求選擇合適之工具以提升品質管理效率。期望透過樣本數及管制圖的選擇，以提升製程穩定性並降低生產異常帶來的損失。 Process Stability Simulation是個專為統計製程管制主題所設計的網站，主要用於比較與分析常見管制圖之表現。該網站由授課老師設計並提供，結合實際數據模擬與操作，為學生提供完整的學習環境。在網站中，使用者可以自訂樣本數與樣本組數，隨機生成模擬數據，以進行分析與比較，並觀察數據在管制圖上的分布與變化，且聚焦於兩個重要的SPC階段：Phase 1與Phase 2。Phase 1是製程穩定性分析的開始，目的是透過數據建構初始管制界限，確認製程是否處於穩定狀態。在此階段，使用者需確保製程穩定。Phase 2為預測製程是否穩定，將Phase 1所確立的管制界限以檢測新數據是否仍維持穩定。在Process Stability Simulation網站中，Phase 2整合Minitab的分析結果，讓使用者根據數據表現選擇是否認定製程穩定，並進一步模擬不同決策對成本的影響。 X̄&R管制圖在樣本數為6時，以$4,500最低總成本實現無誤判之製程控制，展現最佳穩定性與成本效益；X̄&S管制圖在樣本數為11時同樣無誤判，總成本略高為$8,250，但仍屬穩定可靠之選擇。而I&MR管制圖因僅依賴單一樣本數據點，在Phase II出現多次誤判，導致總成本高達$48,750，顯著高於其他兩者。綜上所述，X̄&R管制圖在適中樣本數條件下是降低誤判風險與成本的最優選擇，而I&MR管制圖在誤判風險較高的製程條件下應避免使用。

This study focuses on anomaly detection and process stability issues in manufacturing quality management. It aims to select suitable control chart tools based on sample size and cost conditions in various production scenarios to achieve an optimal balance between anomaly detection accuracy and process stability. The research conducts an in-depth comparison of X̄&R, X̄&S, and I&MR control charts, analyzing their strengths and weaknesses in different application contexts. It further explores how to choose the appropriate tools according to process requirements to enhance quality management efficiency. By selecting the appropriate sample size and control charts, this study aims to improve process stability and reduce losses caused by production anomalies. Process Stability Simulation is a website designed specifically for statistical process control topics. It is mainly used to compare and analyze the performance of common control charts. The website is designed and provided by the instructor, and combines actual data simulation and operation to provide students with a complete learning environment. On the website, users can customize the number of samples and sample groups, randomly generate simulated data for analysis and comparison, and observe the distribution and changes of the data on the control chart, focusing on two important SPC stages: Phase 1 and Phase 2. Phase 1 is the beginning of process stability analysis. The purpose is to construct initial control limits through data and confirm whether the process is in a stable state. At this stage, users need to ensure that the process is stable. In order to predict whether the process is stable, Phase 2 uses the control limits established in Phase 1 to detect whether the new data is still stable. In the Process Stability Simulation website, Phase 2 integrates Minitab's analysis results, allowing users to choose whether to deny process stability based on data performance, and further simulate the impact of different decisions on costs. The X̄&R control chart achieved process control without errors at a sample size of 6, with the lowest total cost of $4,500, demonstrating optimal stability and cost-effectiveness. The X̄&S control chart also achieved error-free results at a sample size of 11, with a slightly higher total cost of $8,250, but remained a stable and reliable option. In contrast, the I&MR control chart, relying solely on single data points, experienced multiple errors in Phase II, leading to a total cost of $48,750, significantly higher than the other two. In summary, the X̄&R control chart is the optimal choice for reducing error risks and costs under moderate sample size conditions, while the I&MR control chart should be avoided in processes with high error risk.