近年來，隨著科技技術的發展與進步，產品品質好壞成了企業競爭及生存之關鍵。為確保其品質符合顧客所需，品質檢驗為品質把關之必要程序。驗收抽樣計畫在品質控管領域中扮演相當重要之統計工具，其目的為滿足生產者及消費者所要求的品質水準及可承受之風險下，提供給買賣雙方一個決策法則以判定該貨批應被接收或拒絕。然而，傳統型驗收抽樣策略大多針對產品良率，評估該產品特性是否符合消費者所需之規格，卻忽略了當品質特性偏離目標值時也會帶來額外的品質損失，故田口博士建議以二次品質損失函數衡量產品品質。另一方面，近幾年也有學者提出，針對過去送驗貨批之檢驗結果納入判決當前貨批考量之抽樣策略。亦即，當前貨批是否該被接收或拒絕，係根據當前抽樣品質狀況以及過去送驗貨批之歷史資料。經證實，此策略相較於傳統型驗收抽樣計畫，更能有效地節省抽樣成本。因此，本論文設計架構主要分為兩大部分：基於損失概念之製程能力指標，分別以傳統單次及重複群集驗收抽樣計畫為基底，發展出多重相依狀態以及改良型重複群集驗收抽樣策略。其次，基於不同品質水準及風險要求組合下，以最小化抽樣樣本數條件為目標，建構其非線性最佳化數學模型以求得計畫參數值，並將結果彙整成表格供使用者參考。接著，本研究除了針對兩驗收抽樣計畫進行分析與評估之外，也與傳統型驗收抽樣計畫進行比較與探討。最後，藉由兩個實例案例作為說明，以驗證本研究實作之有效性及可行性。

Nowadays, due to the advanced technical application, majority of companies have become focusing on “quality” to improve their productivity and international competitiveness. Quality inspection is a crucial stage of quality control to ensure the conformity of the production to the consumer’s specifications. Acceptance sampling plan, a major statistical tool in quality control, provides producers and consumers a decision rule for sentencing whether the lot meets their requirements or not. However, traditional sampling inspections have only put an emphasized on the product defective rate, they ignore the fact that the additional cost is incurred when the quality characteristic of a product moves away from the target value. Therefore, Dr. Taguchi presented the concept of quadratic quality loss function for measuring the loss of the profit. On the other hand, a new sampling strategy that utilizes the disposition of prior lot records for lot sentencing has been proposed recently. Namely, a decision to accept or reject the submitted lot depends not only on the evidences obtained from the current lot but also the results obtained from the previous batches. Its distinguishing characteristic can reduce dramatically the required sample size for inspection to provide the same protection with traditional sampling plans. For above reasons, the major attempt for this dissertation involves two parts: purpose the multiple dependent state sampling plan and the modified-repetitive group sampling plan based on the loss-based process capability indices. The mathematical problem of the proposed plan is also formulated in which the objective function is minimizing the required sample size (or average sample number). The tables for plan parameters of the developed plans are determined by solving the nonlinear optimization problem under various required quality levels and allowable risks. The behaviors of the proposed plans are investigated and compared with traditional sampling plans. Besides, two application cases are presented to illustrate the use of the proposed plans. Some concluding remarks are also provided for addressing their effectiveness and feasibility.

致謝 I
摘要 II
Abstract III
List of Contents IV
List of Tables VI
List of Figures VII
Chapter 1. Introduction 1
1.1 Background and Motivation 1
1.2 Research Objectives 3
1.3 Organization 3
Chapter 2. Literature Review 4
2.1 Acceptance Sampling Plan 4
2.2 Process Capability Indices 6
2.2.1 Process capability index with Cpm and its estimation and distribution 7
2.2.2 Process capability index with Cpmk and its estimation and distribution 9
Chapter 3. Variables Multiple Dependent State Sampling Plan Based on Process Capability Indices 11
3.1 Introduction 11
3.2 Variables Multiple Dependent State Sampling Plan with Cpm 13
3.2.1 The probability of acceptance and OC functions 13
3.2.2 The designed plan parameters 15
3.2.3 Analysis and discussion of the plan 17
3.3 Variables Multiple Dependent State Sampling Plan with Cpmk 22
3.3.1 The probability of acceptance and OC functions 22
3.3.2 The designed plan parameters 24
3.3.3 Analysis and discussion of the plan 24
Chapter 4. Variables Modified-Repetitive Group Sampling Plan Based on Process Capability Indices 30
4.1 Introduction 30
4.2 Variables Modified-Repetitive Group Sampling Plan with Cpm 31
4.2.1 The probability of acceptance and OC functions 31
4.2.2 The designed plan parameters 37
4.2.3 Analysis and discussion of the plan 38
4.3 Variables Modified-Repetitive Group Sampling Plan with Cpmk 44
4.3.1 The probability of acceptance and OC functions 44
4.3.2 The designed plan parameters 47
4.3.3 Analysis and discussion of the plan 48
Chapter 5. Application Examples 54
5.1 Examples - Polyvinyl Chloride 54
5.1.1 Application example of the proposed Cpm -MDSS plan 54
5.1.2 Application example of the proposed Cpm -MRGS plan 55
5.2 Example 2 - Surface Mount Technology 56
5.2.1 Application example of the proposed Cpmk -MDSS plan 57
5.2.2 Application example of the proposed Cpmk -MRGS plan 58
Chapter 6. Conclusions and Future Works 60
6.1 Conclusions 60
6.2 Future Works 61
References 62

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