品質計劃與管制：以管制圖監控製程為例

Abstract

本研究旨在比較 Xbar-R、Xbar-S 及 I-MR 三種管制圖在不同製程條件下之性能，並分析其在統計製程管制之適用性及應用價值。透過結合課堂所學及Minitab模擬實驗數據，探討三種管制圖在誤判率、敏感度及成本效益方面表現，並根據不同樣本數及製程變異情境進行比較。 研究結果顯示，Xbar-R 管制圖在成本效益方面表現最佳，適用於一般穩定製程品質監控；Xbar-S 管制圖雖成本較高，但其對製程穩定度判斷更為準確，適用於變異較大製程環境；I-MR 管制圖則適合用於需要即時反應之快速變化製程，雖然誤判風險較高，卻在單次製程監控具有一定應用價值。 綜合分析結果，本研究提出不同管制圖在各種情境下最佳應用建議。Xbar-S 管制圖在降低誤判風險及提高製程管制準確度方面具有較高效果，尤其適用於變異較大或對品質管制要求較高之環境。

This study aims to compare the performance of Xbar-R, Xbar-S, and I-MR control charts under different process conditions, and analyze their applicability and value in Statistical Process Control (SPC) .By combining classroom learning with Minitab simulation experiments, the study explores the performance of the three control charts in terms of false alarm rates, sensitivity, and cost-effectiveness, and compares them based on different sample sizes and process variation scenarios. The results show that the Xbar-R control chart performs best in cost-effectiveness and is suitable for quality monitoring in generally stable processes; the Xbar-S control chart, though more costly, offers more accurate process stability assessment and is suitable for processes with greater variation; the I-MR control chart is suitable for processes requiring immediate response to rapid changes, although it has a higher risk of false alarms, it still holds some application value for monitoring single processes. Based on the analysis, the study provides recommendations for the best application of different control charts under various scenarios. The Xbar-S control chart demonstrates higher effectiveness in reducing false alarm risk and improving process control accuracy, making it particularly suitable for environments with greater variation or higher demands for quality control.