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研究生： Shalemu Sharew Hailemariam
Shalemu Sharew Hailemariam
論文名稱： 應用常態與非常態資料之抽樣計畫於食品業
Sampling Plans for Normal and Non-normal Data in the Food Industry
指導教授： 王福琨
Fu-Kwun Wang
口試委員: 徐世輝
Shey-Huei Sheu
劉庭祿
Tyng-Luh Liu
葉瑞徽
Ruey-Huei Yeh
歐陽超
Chao Ou-Yang
王福琨
Fu-Kwun Wang
學位類別： 博士
Doctor
系所名稱： 管理學院 - 工業管理系
Department of Industrial Management
論文出版年： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 130
中文關鍵詞： 允收抽樣 、雙重允收標準 、獨立混和抽樣 、零膨脹負二項分配 、膨脹型柏拉圖分配
外文關鍵詞： Acceptance sampling, Dual acceptance criteria, Independent mixed sampling, Zero-inflated negative binomial, Inflated Pareto
相關次數： 點閱：352  下載：9 
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    • 允收抽樣一直是工業中廣泛運用的統計品質管制技術之一，當前的製造環境能夠大量批次的產品，在這個情況下，現存的單一抽樣計畫可能無法滿足生產者與消費者的需求，本論文提供了抽樣計畫的替代方案，像是專用單一屬性抽樣計畫、基於雙重允收標準的抽樣計畫和適用於常態與非常態分配的獨立混和抽樣分配， 研究目標計畫的執行並與現有計畫互相比較。本研究的績效指標包括樣本大小和抽樣計畫對於不符合單位之區分能力，針對零膨脹負二項分配，重新遞交了單一樣本計畫、重複性群組之抽樣計畫及多重依賴性之抽樣分配，而多重依賴性抽樣分配優於重新遞交之樣本計畫、重複性群組抽樣計畫和現存單一屬性之抽樣計畫，針對常態與膨脹型柏拉圖分配(Pareto distributions)，提出了基於雙重允收標準之抽樣分配，而此雙重允收標準之抽樣計畫優於單變量樣本計畫，具有邊際品質之獨立混合抽樣計畫優於沒有邊際品質及雙變量之抽樣計畫，而在擬議計畫中呈現良好的績效以確保滿足顧客的需求。此篇論文的說明案例是基於已發表論文和模擬資料所提供的真實數據，說明所提出的抽樣計畫的績效。

    Acceptance sampling has been one of the widely used statistical quality control techniques enabling to ensure quality of industrial products. Due to the production of large size of lots in the current manufacturing environments and the various distributions of quality attributes, the traditional attributes and variables sampling plans may not be suitable for satisfying producer and consumer requirements. This dissertation presents alternative sampling plans such as special purpose single sampling plans by attributes, sampling plans based on dual acceptance criteria and independent mixed sampling plans that are suitable for normal and non-normal distributions. The performance measures such as sample size and the discriminating power of sampling plans are used to compare the proposed sampling plans with existing sampling plans. Resubmitted single sampling, repetitive group sampling and multiple dependent state sampling plans have been proposed for zero-inflated negative binomial distribution. Multiple dependent state sampling plan outperforms the resubmitted sampling plan, repetitive group sampling plan and existing single attributes sampling plan. Sampling plans based on dual acceptance criteria are proposed for normal and inflated Pareto distributions. The sampling plans based on dual acceptance criteria performs better than single variables sampling plans. Independent mixed sampling plan with marginal quality shows better performance in terms of sample size and discriminating power compared with the one without marginal quality and double variables sampling plan. The proposed plans show better performance to ensure the satisfaction of producer and customer needs. Illustrative examples are provided to illustrate the performance of the proposed sampling plans.

    摘要 i Abstract ii Acknowledgment iii Table of contents iv List of figures vii List of tables viii Chapter One 1 Introduction 1 1.1. Background 1 1.2. Overview of the food industry 3 1.3. Statement of the problem 4 1.4. Objectives of the study 4 1.5. Organization of the dissertation 5 Chapter Two 6 Literature review 6 2.1. Overview of acceptance sampling plans 6 2.2. Classification of acceptance sampling plans 8 2.3. Sampling plans for microbiological study 9 2.3.1. Microbiological distributions 9 2.3.2. Microbiological sampling plans 11 2.4. Special purpose single sampling plans 12 2.5. Mixed sampling plans for normal and non-normal distributions 13 Chapter Three 16 Methodology 16 3.1. Statistical models and sampling plans 16 3.1.1. Description of the food quality measurement data 16 3.1.2. The statistical models 17 3.2. Attributes sampling plans for ZINB distribution 21 3.2.1. Single attributes sampling plan 21 3.2.2. The resubmitted single sampling plan 23 3.2.3. The repetitive group sampling plan 24 3.2.4. The multiple dependent state sampling plan 26 3.3. Review of sampling plans based on multiple acceptance criteria for normal distribution 27 3.3.1. Mixed sampling plans based on two stage sampling schemes 27 3.3.2. Acceptance probability based on three criteria with known variance 32 3.3.3. Acceptance probability based on dual criteria with unknown variance 33 3.4. Sampling plan based on dual acceptance criteria for normal distribution 34 3.4.1. Existing sampling plans 34 3.4.2. Proposed sampling plan based on dual acceptance criteria 35 3.5. Sampling plans based on dual acceptance criteria for inflated Pareto distribution 37 3.5.1. Existing single sampling plans 37 3.5.2. Proposed sampling plan based on dual acceptance criteria 39 3.6. Independent mixed sampling plans for inflated Pareto distribution 40 3.6.1. Existing double variables sampling plan 43 3.6.2. Proposed sampling plans 44 Chapter Four 49 Results and discussion 49 4.1. Performance evaluation of sampling plans 49 4.1.1. Single sampling plan for zero-inflated negative binomial distribution 50 4.1.2. Sampling plan based on dual acceptance criteria for normal distribution 59 4.1.3. Sampling plan based on dual acceptance criteria for inflated Pareto distribution 61 4.1.4. Performance comparison of independent mixed sampling plan for inflated Pareto data 64 4.2. Illustrative examples 70 Chapter Five 75 Conclusions and future study 75 5.1. Conclusions 75 5.2. Applications 76 5.3. Future study 77 Appendices 78 Appendix IA. The R-code for computing the plan parameters of SS and RSS plans 78 Appendix IB. The R-code for computing the plan parameters of RGS plan 79 Appendix IC. The R-code for computing the plan parameters of MDS sampling plan 80 Appendix ID. The R-code for computing the OC curves of sampling plans under ZINB distribution 82 Appendix IIA. The R-code for computing the OC curves of sampling plans under normal distribution 83 Appendix IIB. The approximation method for computing the joint probability 86 Appendix IIC. The R-code for computing the joint probability 87 Appendix IID. The R-code for computing the plan parameters of sampling plans for inflated Pareto 88 Appendix IIE. The R-code for computing the OC curves of sampling plans under inflated Pareto distribution 104 Appendix IIIA. The R code for computing the plan parameters double sampling plan by variables 105 Appendix IIIB. The R-code for computing plan parameters independent mixed sampling plans under inflated Pareto distribution 106 Appendix IIIC. The R code for computing plan parameters of independent mixed plans with marginal quality under inflated Pareto distribution 108

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