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研究生: 趙宸得
Chao, Chen-De
論文名稱: 使用製程能力指標建構有限抽樣次數之重複抽樣計劃
Repetitive variable acceptance sampling plan with limited sampling times using capability index
指導教授: 胡政宏
Hu, Cheng-Hung
學位類別: 碩士
Master
系所名稱: 管理學院 - 工業與資訊管理學系
Department of Industrial and Information Management
論文出版年: 2021
畢業學年度: 109
語文別: 中文
論文頁數: 42
中文關鍵詞: 重複抽樣計劃製程能力指標平均樣本數
外文關鍵詞: Repetitive sampling plan, Process capability index, Average sample number
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  • 允收抽樣為品管領域應用十分廣泛的一項工具,可藉此提供生產或消費者判斷貨批品質水準是否滿足自身需求。而我們可根據數據型態的不同分為「計數型抽樣計劃(Attribute sampling plan)」及「計量型抽樣計劃(Variable sampling plan)」兩大類。而前者為根據良品或不良品數等離散型資料對其建立允收標準,若驗收之貨批不符合標準則予以拒收,反之則給予允收。後者主要針對數據為連續型資料如長度、重量或是本研究採用的製程能力指標值,在以其計算臨界值作為允收標準後再對貨批抽樣進而作出判定與否的決策。
    本研究之重點主要著重在欲改善重複群集抽樣可能會導致抽樣次數無窮多次的情況。傳統重複抽樣計劃的運作是在若抽樣出之樣本估計值在允收及拒收標準之間則對同一貨批進行重抽樣,直至能夠直接作出決策才停止。但此種狀況下,若供應商之製程能力較為中庸則有可能會進行太多次的重抽樣,其將會導致抽樣次數無限大,進而造成時間、人力等成本上的浪費。因此,本研究將會以最小化平均樣本數為目標,並設置一抽樣次數上限,若抽樣次數達到上限時將在當次抽樣直接作出決策,以避免上述情形的發生。而由於模式建構的複雜度,所以本次抽樣次數上限將先設置於兩次。
    而在研究後段將參考Yen et al. (2013)研究中的案例進行抽樣計劃的建構,過程中使用傳統搜尋演算法求解,並於建構完成後進行績效的分析。於研究最後,再以相同的環境條件下參考Yen et al. (2013)及Pearn & Wu (2006)等研究建構一傳統重複抽樣計劃及單次抽樣計劃,並將各抽樣計劃進行相互比較。
    而在最後的比較結果發現不論是否設置抽樣次數的上限,重複抽樣計劃在決策效率上明顯優於單次抽樣計劃。而兩種重複抽樣計劃則在不同的品質要求水平及抽樣風險下,決策效率則會有越來越接近的趨勢。

    Improving the problem which taking too many sampling times during repetitive group sampling (RGS) is the key-point of this research. Traditional RGS is keeping re-sampling until we can decide directly. The possible problem is taking too many times for re-sampling, then it will waste too many costs like time or labor. In this paper, our goal is "minimizing average sample number (ASN)", and setting the limitation of sampling times, the decision will be made directly in the current sampling when the sampling times reach the upper limit. Due to the complexity of the math model, the upper limit of sampling times will set on two times in this paper.
    However, we will refer to the case study about TFT-LCD of Yen et al. (2013) to construct the sampling plan, and find an optimal parameter set by searching method, also analyzing the efficiency after constructing the sampling plan. In last part of the research, we will compare three different sampling plans with the sample size and ASN and discuss which plan has better decision efficiency. Finally, we can find out the repetitive group sampling plan is always better than the single acceptance sampling plan no matter setting the limitation of sampling times, and the decision efficiency of two different repetitive sampling plan will get closer under the different quality levels and sampling risks.

    摘要 I SUMMARY II 誌謝 VIII 目錄 X 表目錄 XIII 圖目錄 XIV 第一章、緒論 1 1.1 研究背景 1 1.2 研究動機與目的 2 第二章、文獻探討 3 2.1 製程能力指標(Process capability index, PCI) 3 2.1.1 歷代重要製程能力指標 4 2.1.2 製程能力指標與製程良率的關係 4 2.1.3 僅有單邊規格界限的單邊製程能力指標 5 2.1.4 單邊製程能力指標估計式之抽樣分配 6 2.2 允收抽樣計劃(Acceptance sampling plan) 7 2.2.1 計數型抽樣計劃 8 2.2.2 計量型抽樣計劃 9 2.3 允收抽樣計劃之績效衡量 11 2.3.1 作業特性曲線(Operating characteristic curve, OC curve) 11 2.3.2 平均樣本數(Average sample number, ASN) 12 2.4 小結 12 第三章、有限抽樣次數之新式重複抽樣計劃 14 3.1 問題描述 14 3.2 抽樣計劃數學模式建構 16 3.2.1 參數符號設計 16 3.2.2 研究假設 17 3.2.3 m=2的計劃允收機率函數及平均樣本數函數 17 3.2.4 建構計劃參數之數學模式 18 3.3 模式求解 19 3.3.1 兩階段參數變化之關係 19 3.3.2 求得抽樣樣本數之上界 21 3.3.3 給定n1時,求得決策標準之上下界 22 3.3.4 搜尋演算法求解 23 第四章、案例與分析 25 4.1 設計一有限抽樣次數之重複抽樣計劃 25 4.2 個案討論 26 4.2.1 個案情境介紹 26 4.2.2 個案分析 27 4.2.3 抽樣計劃績效之評估 31 4.2.4 各式抽樣計劃績效比較 35 第五章、結論與未來展望 37 5.1 研究結論 37 5.2 未來展望 38 參考文獻 39

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