有鑑於客戶期望值、產品複雜性和全球競爭的提升，產品品質對企業營業績效有愈來愈顯著的影響。近年來企業積極投資於品質成本，以確保並維持高品質的生產過程，並以準確、精密的方式生產出具卓越品質的產品。鑑定及評估成本，包括對材料進行進料檢驗、實驗室內的產品測試、生產過程中的性能評估以及最終檢查（100％檢查/抽樣計畫），亦是品質成本的一環。因此，近年來已有許多創新的測試與驗收的程序被開發出來，尤其是在計量的驗收抽樣計畫方面，以提高檢效率、可靠性和適應性。其中，多重抽樣計畫（Multiple Sampling Plan, MSP）是單次抽樣計畫（Single Sampling Plan, SSP）和雙重抽樣計畫（Double Sampling Plan, DSP）的擴展，已被證明是有效的抽樣計畫策略。然而，由於判定貨批須同時考量當次抽樣樣本與前一次樣本的檢驗結果，使得MSP的作業操作特性（Operational Characteristics, OC）函數難以構建。因此，在此論文中，我們提出了一種改良方法，透過設計和開發可彈性調整的MSP模型，假設各階段的多重抽樣結果為獨立，稱為階段獨立多重抽樣計畫（Stage-Independent MSP, SIMSP）。論文中除推導出SIMSP的OC函數，並透過最小化平均抽樣樣本數（Average Sample Number, ASN）及設定一組可容忍風險和品量水準的限制式來設計優化的數學模型，來求解計畫的參數。此外，我們分析了SIMSP的行為，並將其性能與傳統抽樣計畫，在相同條件下進行性能的比較，以證明SIMSP能有效且具鑑別度的貨批判定優勢，能在同樣條件下透過相對較少的檢驗樣本數來做出貨批貨允收判定。再者，我們透過案例分析以展現SIMSP在實際應用中的可行性，並設計及開發一套圖形化的使用者操作介面供執行者參考應用。

Due to increasing customer expectations, product complexity, and global competition, the long-term success of an industry is now significantly influenced by quality strategies. Consequently, the industry invests in quality costs to ensure and maintain a high-quality production process that delivers precise and accurate products with a robust level of quality. The appraisal cost, which includes activities such as inspecting incoming materials, conducting product testing in laboratories, monitoring the production process, performing performance evaluations, and carrying out final inspections (including both 100% inspection and sampling inspection), constitutes a critical component of the overall quality expenses. Numerous innovations in testing and inspection procedures, particularly in the realm of sampling plans, have been developed recently to enhance efficiency (reducing mandatory sample sizes), reliability, and adaptability to various contexts. Multiple Sampling Plans (MSP) serve as an extension of Single Sampling Plans (SSP) and Double Sampling Plans (DSP), offering a successful approach for determining whether a lot meets acceptable risk levels for both consumers and producers. However, constructing the Operational Characteristics (OC) function for MSP is challenging due to its reliance on previous sample outcomes to evaluate the current sample. To address this issue, this dissertation presents a modified approach that designs and develops a variable inspection model within the MSP framework, promoting independence between stages and integrating process capability indices. This novel approach is termed the Stage-Independent Multiple Sampling Plan (SIMSP). The SIMSP is designed through an optimization mathematical formula that minimizes the Average Sample Number (ASN) while adhering to specified tolerable risk and quality level constraints to obtain efficient plan parameters. The reliability of SIMSP is assessed by deriving the OC curve. The behavior and performance of SIMSP are analyzed and compared to that of conventional sampling plans under identical conditions to demonstrate the superior effectiveness and reliability of SIMSP in lot assessment. Furthermore, illustrative cases are examined to showcase the practical feasibility of SIMSP through a user-friendly graphical interface. The results reveal that SIMSP provides comparable protection for both business partners while significantly reducing costs by inspecting fewer samples over the long term and requiring smaller sample sizes than existing lot disposition plans.

摘要 iii
Abstract iv
List of contents v
List of figures vii
List of tables ix
Chapter 1. Introduction 1
1.1 Background and Motivation 1
1.2 Research Objectives 3
1.3 Structure of Writing 4
Chapter 2. Literature Review 5
2.1 Acceptance Sampling Plan 5
2.2 Process Capability Indices (PCIs) 8
2.2.1 Process capability index with Cpk, the estimation, and distribution 10
2.2.2 Process capability index with Cpm, the estimation, and distribution 11
2.2.3 Process capability index with Cpmk, the estimation, and distribution 12
Chapter 3. The Development of Variables Stage-Independent Multiple Sampling Plan (SIMSP) using Process Capability Indices 15
3.1 Introduction 15
3.2 Variables Stage-Independent Multiple Sampling Plan Based on Cpk 16
3.2.1 The probability of acceptance and OC functions 16
3.2.2 The designed plan parameter 19
3.2.3 Analysis and discussion 20
3.3 Variables Stage-Independent Multiple Sampling Plan Based on Cpm 31
3.3.1 The probability of acceptance and OC functions 31
3.3.2 The designed plan parameter 34
3.3.3 Analysis and discussion 35
3.4 Variables Stage-Independent Multiple Sampling Plan Based on Cpmk 45
3.4.1 The probability of acceptance and OC functions 45
3.4.2 The designed plan parameter 48
3.4.3 Analysis and discussion 49
3.5 Concluding remarks 60
Chapter 4. Example Verification 62
4.1 Example using Cpk-SIMSP 62
4.2 Example using Cpm-SIMSP 66
4.3 Example using Cpmk-SIMSP 70
Chapter 5. Conclusions and Future Research 75
5.1 Conclusions 75
5.2 Future Research 77
References 78

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