在當今競爭激烈的業界，暸解與提高品質對於企業成長和聲譽的提升扮演重要的角色。驗收抽樣計畫是一種被廣泛使用的統計品質管制技術，提供降低檢驗成本和減少產品損壞的方法，並同時確保消費者和生產者的品質要求及風險。隨著製造技術的進步，產品的不良率逐漸下降，也間接促進跳批抽樣計畫 (Skip-lot Sampling Plan, SkSP) 的發展，當連續批次有良好的品質時，僅檢驗提交批次的一個比例，以降低檢驗成本。近期學者提出之改良型兩階層跳批抽樣計畫 (SkSP-2L.1-R)為SkSP之延伸，其將重複遞交抽樣計畫的精神結合至兩階層跳批抽樣計畫，不但能更顯著地降低檢驗成本，亦提供生產者提高其產品品質之誘因。然而，大多數提出之SkSP是為計數型檢驗而設計，在不良率極低情況下，可能發生抽樣之不良品數為零，造成計算不良品比例之困難。
綜合上述，本研究旨在開發計量型SkSP-2L.1-R，其結合適用於具有單邊或雙邊規格之品質特性的良率指標。利用良率指標估計量之抽樣分配，推導出能執行計畫參數求解之數學模型，並提供常見品質規格與風險水準之計畫參數表。此外，將提出之計畫的成效與傳統抽樣計畫分別於平均樣本數與操作特性曲線方面進行比較。最後，基於所提出的計畫建構易於操作的圖形化使用者介面，提升使用者決策之效率。業界可根據其產品品質特性選擇使用單邊或雙邊規格良率指標之介面，並輸入其品質特性資料、合約訂定之規格界線及風險要求，系統將提供檢驗準則以供實務應用。介面之操作方法與其效益亦將在本文中透過實際案例進行展示及說明。

In today's highly competitive business environment, understanding and enhancing quality play a crucial role in facilitating business growth and establishing a favorable reputation. Acceptance sampling plans, widely utilized statistical quality control techniques, offer a means to reduce inspection costs and minimize product damage while ensuring satisfaction for both consumers and producers. As manufacturing technology advances, the fraction of defective products has decreased over time, driving the development of skip-lot sampling plans (SkSP). SkSP further reduces inspection efforts by selectively inspecting only a fraction of submitted lots when consecutive lots exhibit good quality. One recent extension of SkSP is the two-level skip-lot sampling reinspection plan (SkSP-2L.1-R), which incorporates the idea of resampling in a two-level skip-lot sampling plan. However, most proposed SkSPs are primarily designed for attributes inspection, which can pose challenges in computing the fraction of nonconforming items, especially when dealing with extremely low fractions of nonconforming items. Therefore, this thesis focuses on developing a variables-based SkSP-2L.1-R that integrates yield indices for quality characteristics with one-sided or two-sided requirements. The mathematical model for determining the plan parameters of the proposed plan is derived based on the sampling distributions of the estimated yield indices. Comprehensive tables of plan parameters under frequently used quality specifications and risk levels are provided. Furthermore, the performance of the proposed plan is compared with that of conventional sampling plans in terms of average sample number and operating characteristic curve. Finally, a user-friendly graphical user interface based on the proposed plan is constructed to expedite decision-making for practitioners. This interface allows the selection of one-sided or two-sided yield indices, enables data input for quality and risk conditions specified in the contract, and provides decision criteria for inspection in practical applications. The usability and effectiveness of the interface are also demonstrated through an example.

致謝.............................................................i
摘要............................................................ii
Abstract.......................................................iii
Table of Contents...............................................iv
List of Tables.................................................vii
List of Figures.................................................ix
Chapter 1 Introduction.....................................1
1.1 Research Background and Motivation.......................1
1.2 Research Objectives......................................4
1.3 Research Structure.......................................5
Chapter 2 Literature Review................................8
2.1 Process Capability Index.................................8
2.1.1 Process Precision Index Cp...............................9
2.1.2 Process Accuracy Index Ca................................9
2.1.3 One-sided Yield Index Cpu and Cpl.......................10
2.1.4 Two-sided Yield Index Spk...............................12
2.2 Acceptance Sampling Plan................................16
2.2.1 Basic Concepts of Acceptance Sampling Plan..............17
2.2.2 Evolution of Acceptance Sampling Plan...................18
2.2.3 Performance Measures of Acceptance Sampling Plan........19
2.3 Skip-lot Sampling Plan..................................22
2.3.1 SkSP-1..................................................23
2.3.2 SkSP-2..................................................24
2.3.3 SkSP-R..................................................25
2.3.4 SkSP-2L.................................................27
2.3.5 SkSP-2L.1-R.............................................29
Chapter 3 SkSP-2L.1-R Based on One-sided Yield Index......33
3.1 Operating Procedure.....................................33
3.2 Probability of Acceptance...............................36
3.3 Mathematical Model......................................37
3.4 Sensitivity Analysis....................................38
3.4.1 Sensitivity Analysis of Effect of i on ASN, n, and k....39
3.4.2 Sensitivity Analysis of Effect of j on ASN, n, and k....42
3.5 Tables of Plan Parameters...............................45
3.6 Comparison and Analysis.................................49
3.6.1 Operating Characteristic Curve (OC Curve)...............49
3.6.2 Average Sample Number (ASN).............................51
Chapter 4 SkSP-2L.1-R Based on Two-sided Yield Index......55
4.1 Operating Procedure.....................................55
4.2 Probability of Acceptance...............................57
4.3 Mathematical Model......................................58
4.4 Sensitivity Analysis....................................60
4.4.1 Sensitivity Analysis of Effect of i on ASN, n, and k....60
4.4.2 Sensitivity Analysis of Effect of j on ASN, n, and k....64
4.5 Tables of Plan Parameters...............................67
4.6 Comparison and Analysis.................................71
4.6.1 Operating Characteristic Curve (OC Curve)...............71
4.6.2 Average Sample Number (ASN).............................73
Chapter 5 GUI and Case Study..............................77
5.1 Industrial Application Example..........................78
5.2 GUI for Products with a Unilateral Specification Limit..79
5.3 GUI for Products with Bilateral Specification Limits....89
Chapter 6 Conclusion and Future Perspectives..............99
6.1 Conclusion..............................................99
6.2 Future Perspectives....................................100
References.....................................................101

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