近年來，製造業除追求品質提升與成本控制外，亦須面對現場人力短期變動所帶來之管理挑戰。傳統管制圖經濟設計多假設人力資源穩定充足，且管制界線與抽樣規則設定後維持不變；然而，實務上常因工程師臨時請假、排班調整或支援其他部門而產生短期人力不足。當多張管制圖同時監控製程且可用人力下降時，若仍沿用原有監控設計，可能造成警報累積、異常處理延遲與系統成本上升。本研究主要適用於高製程能力指標(Cpk)之製程情境。在此條件下，規格界線通常遠寬於管制界線，因此短期調整管制界線主要影響警報觸發頻率與異常偵測時點，而非直接改變產品是否符合規格之判定。基於此，本研究探討短期人力資源短缺下，多張適應性X-bar管制圖之經濟設計問題，並建構以半馬可夫決策過程為基礎之決策模型。模型以管制圖警報狀態與工程師處理狀態描述系統，透過事件驅動方式模擬異常到達、處理完成與狀態轉移，並將管制界線與抽樣頻率調整納入分析架構。本研究整合品質損失、停機、等待、降頻風險、警報、處理及未偵測到參數改變等成本，並採用有限期動態規劃求解最佳策略，再以事件驅動蒙地卡羅模擬評估不同管制界線組合之成本表現。數值分析結果顯示，當工程師人力低於正常配置時，最適監控設計不宜沿用所有管制圖皆採相同管制界線之傳統設定，而應依據各製程之成本結構與風險特性採取差異化配置。本研究可作為企業面對短期缺工時調整品質監控策略之決策依據。

In recent years, manufacturing firms have faced not only increasing demands for quality improvement and cost control but also managerial challenges arising from short-term fluctuations in on-site workforce availability. Conventional economic designs of control charts generally assume stable and sufficient staffing, with control limits and sampling rules remaining fixed after they are established. In practice, however, temporary workforce shortages may arise when engineers take unexpected leave, shifts are adjusted, or personnel are reassigned to support other departments. When multiple control charts are used to monitor processes simultaneously and the available workforce is reduced, retaining the original monitoring design may result in accumulated alarms, delayed responses to abnormalities, and increased system costs. This study is primarily intended for processes with high process capability indices (Cpk). Under such conditions, specification limits are typically much wider than control limits. Therefore, temporarily adjusting control limits mainly affects alarm frequencies and the timing of abnormality detection, rather than directly altering whether products conform to specifications. Accordingly, this study investigates the economic design of multiple adaptive $ar{X}$ control charts under short-term workforce shortages and develops a decision model based on a semi-Markov decision process. The model describes the system using the alarm status of the control charts and the service status of engineers. An event-driven framework is employed to represent alarm occurrences, repair completions, and state transitions, while adjustments to control limits and sampling frequencies are incorporated into the analysis. The proposed model integrates costs associated with quality loss, downtime, waiting, reduced-sampling risk, alarms, repairs, and undetected parameter changes. A finite-horizon dynamic programming approach is used to determine the optimal policy, and event-driven Monte Carlo simulation is conducted to evaluate the cost performance of different control-limit combinations. The numerical results indicate that, when the number of engineers falls below the normal staffing level, the optimal monitoring design should not necessarily retain the conventional setting in which all control charts use identical control limits. Instead, differentiated configurations should be adopted according to the cost structure and risk characteristics of individual processes. The proposed framework provides a decision-making basis for firms seeking to adjust quality-monitoring strategies during temporary workforce shortages.

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國立成功大學碩士論文
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