隨著製造系統逐漸朝向自動化與多製程並行發展，如何在有限人力條件下有效處理多張管制圖的異常警報，成為品質管理中的重要課題。傳統統計製程管制雖能即時偵測製程異常，但多著重於單一管制圖之設計與參數設定，對於多張管制圖同時監控下的警報派工與人力限制問題，相關探討仍相對有限。當多張管制圖相繼或同時發出警訊時，工程師必須在有限資源下決定處理優先順序；若僅依先到先處理或經驗判斷，可能造成高成本異常延誤處理，進而增加停機損失、品質損失與整體營運成本。本研究結合統計製程管制與半馬可夫決策過程，建立一套可描述多張管制圖警報處理派工的數學模型，以有限人力條件下之總成本最小化為目標。模型假設各管制圖之異常到達時間與處理時間皆服從指數分配，並將系統狀態定義為各管制圖之正常或異常情形，以及工程師目前之工作狀態。決策行動包含等待或指派工程師處理特定異常管制圖，並於異常發生或處理完成時觸發決策，形成事件驅動式決策架構。在成本設計上，本研究同時考量異常持續造成之停機成本、處理成本與生產品質損失成本，以反映實際製造現場中警報處理決策對系統績效之影響。為求得最適處理策略，本研究採用有限期動態規劃與反推演算法，計算各狀態下之期望成本與對應最適行動。進一步透過蒙地卡羅模擬，將本研究提出之動態規劃策略與先到先處理策略進行比較。模擬結果顯示，在多張管制圖共享有限工程師資源的情境下，動態規劃策略能有效降低平均總成本，且在多數模擬情況下優於先到先處理策略。此結果說明，當不同管制圖具有不同停機成本、處理成本與品質損失成本時，若能根據系統狀態進行派工決策，將有助於避免高成本異常被延誤處理，並提升整體警報處理效率。本研究將多張管制圖監控、有限人力限制與異常處理排程整合於半馬可夫決策架構中，擴展半馬可夫決策過程模型於品質管理與多任務排程領域之應用。研究成果可作為製造現場在工程師人力受限情境下進行警報處理排序與派工決策之參考。未來研究可進一步納入實際產線資料、管制圖間相依性，以及強化學習方法，以提升模型於大規模與即時決策系統中的應用性。

This study develops a decision-making model for dispatching alarm handling of multiple control charts under limited manpower. In practical production systems, several control charts may be monitored at the same time, while the number of engineers available to inspect and handle abnormal processes is limited. When multiple alarms occur simultaneously.An inappropriate handling sequence may increase waiting time, downtime, and total operating cost.
To address this problem, this study formulates the alarm-handling process as a Semi-Markov Decision Process. The system state represents the condition of each controlchart and the working status of the engineers. The available actions include waiting or assigning the engineer to handle a specific abnormal control chart. Based on the proposed model, dynamic programming is applied to determine the optimal actionpolicy over a finite planning horizon.
The numerical results show that the proposed policy can reduce total cost compared with the first-come, first-served rule, especially when engineering manpower is insufficient. This indicates that considering system states, event timing, and cost differences among control charts is important for effective alarm-handling decisions.

林勁宇(2017）。腦中風患者慢性病危險因子與失智之半馬可夫鏈建模與關聯分析(碩士論文)。國立臺灣科技大學工業管理系。
張凱鈞(2019）。受限於短期人力短缺下之X-bar 管制圖之適應性經濟設計（碩士論文)。國立成功大學工業與資訊管理學系。
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