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研究生: 周芳儀
Chou, Fang-I
論文名稱: 模糊歸屬函數在修正計數值抽樣檢驗計劃之應用
The modification of attribute acceptance sampling plan using fuzzy membership function
指導教授: 潘浙楠
Pan, Jen-Nan
學位類別: 碩士
Master
系所名稱: 管理學院 - 統計學系
Department of Statistics
論文出版年: 2004
畢業學年度: 92
語文別: 中文
論文頁數: 61
中文關鍵詞: 模糊檢定抽樣檢驗計劃模糊歸屬函數
外文關鍵詞: fuzzy hypothesis, acceptance sampling plan, fuzzy membership functions
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  •   工業界在進料或產品量產時,由於受到時間與人力的限制,必須藉由抽樣檢驗計畫隨機抽取一定數量之樣本,經過檢驗或測試後,根據其結果再依統計方法判定此批量是否達到允收的標準。
      
      本研究針對現行MIL-STD-105單次抽樣檢驗計劃的允收過程,以模糊檢定(Fuzzy hypothesis)的方式取代明確檢定(Crisp hypothesis,檢定H0: p AQL 與 H1: p > AQL),再依照現行抽樣檢驗計劃對生產者與消費者風險的定義,將生產者與消費者風險延伸至模糊檢定可適用之形式,並利用模糊歸屬函數建構模糊抽樣檢驗計劃,另進行該計劃與MIL-STD-105在降低生產者與消費者風險表現上之比較分析。

      Inspection for acceptance sampling plan is carried out at many stages in manufacturing. In many instances,sampling inspection is used because the cost of 100% inspection is prohibitive.

      In this thesis, a fuzzily formulated hypothesis is presented to replace the crisp hypothesis testing (H0: p AQL vs. H1: p > AQL) in order to modify the current MIL-STD-105 attribute acceptance sampling plan. In particular, we redefine the producer’s risk and the consumer’s risk instead of the probability of type I and type II errors, respectively.

      Then, the fuzzy membership functions are used to establish the fuzzy attribute acceptance sampling plan and their acceptance numbers, powers and OC curves are compared with those of MIL-STD-105 attribute acceptance sampling plan.

    第壹章 緒論 1 第一節 研究背景與動機 1 第二節 研究目的 2 第三節 研究架構與內容 2 第貳章 文獻之回顧與探討 4 第一節 統計抽樣檢驗計劃 4 2.1.1 相關符號定義 6 2.1.2 抽樣檢驗計劃簡史 12 2.1.3 抽樣檢驗計劃之種類 13 2.1.4 抽樣檢驗計劃之轉換 15 2.1.5 抽樣檢驗計劃與統計檢定 16 第二節 模糊集合理論 17 2.2.1 傳統集合論與模糊集合理論 17 2.2.2 傳統集合與歸屬函數 19 2.2.3 模糊補集 23 2.2.4 其他模糊集合之名詞介紹 24 2.2.5 模糊假設檢定 24 第參章 利用模糊歸屬函數修正MIL-STD-105抽樣檢驗計劃 27 第一節 研究步驟與流程 27 第二節 建構模糊假設檢定 30 3.2.1 模糊歸屬函數之建構 30 3.2.2 損失函數與懲罰函數 31 3.2.3 模糊生產者風險與模糊消費者風險 34 3.2.4 以梯形歸屬函數定義之懲罰函數 36 3.2.5 以S型歸屬函數定義之懲罰函數 38 第肆章 模糊計數值抽樣檢驗計劃與MIL-STD-105之比較分析 40 第一節 模糊計數值抽樣檢驗計劃以歸屬函數修正MIL-STD-105之情形 40 4.1.1 以梯形歸屬函數修正MIL-STD-105之模糊計數值抽樣檢驗計劃 40 4.1.2 以S型歸屬函數修正MIL-STD-105之模糊計數值抽樣檢驗計劃 42 4.1.3 梯形與S型模糊計數值抽樣檢驗計劃之比較 45 4.1.4 生產與消費雙方風險對等之模糊計數值抽樣檢驗計劃修正MIL-STD-105之情形 46 第二節 模糊計數值抽樣檢驗計劃之性質探討 47 4.2.1 不同歸屬函數對模糊計數值抽樣檢驗計劃之影響分析 47 4.2.2 模糊計數值抽樣檢驗計劃對生產者風險之敏感度分析 49 4.2.3 模糊生產者風險與模糊消費者風險對於允收數之敏感度分析 51 4.2.4 模糊生產者風險與模糊消費者風險對於檢驗樣本數之敏感度分析 51 第伍章 結論與建議 53 第一節 研究限制 53 第二節 結論 53 第三節 建議 54 附錄 55

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