臺灣博碩士論文加值系統

自1956年Duncan發表X-bar經濟設計管制圖後，許多學者受此啟發，針對不同管制圖進行經濟設計的相關研究。經濟設計為調整管制圖的三個重要決策變數：抽樣間隔長度、樣本大小及管制界限以獲得最低之總成本。若將這些決策變數由定值改為會隨前一次製程觀測資料進行變動，便稱為適應性管制圖。然而，傳統的管制圖或經濟設計管制圖均以長期的架構建構管制圖，他們的決策變數在決定後便不再變動，短期內若有大幅度的調整便有大機率會使成本上升，但在某些特殊情況，如短期的人力之配置下，便可能會透過調整決策變數來因應人力在短期的變化。近幾年開始有學者將管制圖的經濟設計融入人力配置的概念，藉由事前優化監控管制圖所需的人力以更進一步達到成本的降低。然而，過去的經濟設計管制圖多是針對單張管制圖進行監控，但在實際工廠運作中通常是多種不同製程同時運行，因此必須考量同時監控多張管制圖的情況。本研究建構一套可同時調整抽樣間隔長度、管制界限及警戒界限的方法，不但更具彈性，成本減少及偵測變異的效率也較傳統的管制圖高。當短期內監控管制圖之人力有限且須同時監控多張管制圖，為避免在人力不足時產生過多的警報導致人力無法負荷，此時抽樣間隔長度、管制界限及警戒界限便需因應人力做出適當的調整。因此，本研究主要目的為考量短期時間且工程師人力受限下，如何因人數調整最適當的抽樣間隔長度、管制界限及警戒界限之組合，以使總成本最小化。最後，透過實際案例驗證本研究數學模型之正確性，也確實發現隨著工程師人數減少，管制界限與警戒界限適當的放寬及抽樣間隔長度適當的增加確實有助於降低成本，並利用敏感度分析發現對成本函數影響較明顯之參數。

Economic design of control charts have drawn a great number of researchers’ attention since Duncan first proposed the economic design of X-bar control charts in 1956. We call it economic design when we adjust three important decision variables in the control chart: sampling interval length, sample size and control limits in order to minimize the total cost. However, we call it adaptive control chart if these three decision variables varied based on the value of the preceding sample statistics. Wu et al. merge the concept of deploying manpower in the statistical process control scheme for the purpose of minimizing the expected total cost. The concept of constructing traditional or economic control chart is from a long-term perspective, and both of their decision variables were decided at the beginning. If we change decision variables at will, cost will rise in the short term. Our research develop a methodology for adjusting sampling interval length, warning limits and control limits simultaneously, subject to short-term manpower shortage for monitoring multiple control charts. The purpose of our research is to find the best combination of sampling interval length, warning limits and control limits by minimizing total cost per unit time. We modify Bai and Lee cost function for adaptive economic design and added in the M/M/c queueing model for manpower construction. The results show that expected total cost per unit time can be lowered by adjusting the combination of control limits, warning limits and sampling interval length appropriately. Sensitivity analysis is presented to evaluate how the parameters influence the total cost per unit time.

摘要……………………………………………………………………………………I
目錄…………………………………………………………………………………...X
表目錄………………………………………………………………………………XII
圖目錄……………………………………………………………………………...XIII
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 3
1.3 研究目的 4
1.4 研究流程 5
第二章 文獻回顧 6
2.1 修華特管制圖 6
2.1.1 計數值管制圖 9
2.1.2 計量值管制圖 10
2.2 適應性管制圖 11
2.2.1 適應性修華特管制圖 11
2.2.2 適應性累積和管制圖 14
2.2.3 適應性指數加權移動平均管制圖 15
2.3 經濟設計 16
2.3.1 單個可歸屬原因之經濟設計 17
2.3.2 多個可歸屬原因之經濟設計 19
2.3.3 聯合管制圖之經濟設計 20
2.3.4 變動管制圖之經濟設計 21
2.3.5 累積和管制圖之經濟設計 24
2.3.6 指數加權移動平均管制圖之經濟設計 25
2.4 人力限制 26
第三章 僅考慮管制界限之X-bar管制圖之適應性設計 28
3.1 研究問題描述 28
3.2 研究假設 29
3.3 符號定義 30
3.4 研究模型建構 31
3.5 小結 34
第四章 同時考慮管制界限、警戒界限與抽樣間隔長度之X-bar管制圖適應性經濟設計………………………………………..……………………………37
4.1 研究問題描述 37
4.2 研究假設 40
4.3 符號定義 41
4.4 研究模型建構 43
4.5 決策變數求解 51
4.6 小結 53
第五章 數值驗證與敏感度分析 54
5.1 案例討論 54
5.2 敏感度分析 57
5.2.1 成本分析 57
第六章 結論與建議 64
6.1 研究貢獻 64
6.2 未來研究方向 65
第七章 參考文獻 66

中文文獻：
卓怡如 (2018). 短期內受限於人力資源下X-bar管制圖之管制界限設定 國立成功大學碩士論文
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