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系統識別號 U0002-1307202009521400
中文論文名稱 Gompertz分配產品在逐步型I區間設限下之壽命績效指標之最佳抽樣設計
英文論文名稱 Sampling design for the lifetime performance index of Gompertz lifetime distribution under progressive type I interval censoring
校院名稱 淡江大學
系所名稱(中) 大數據分析與商業智慧碩士學位學程
系所名稱(英) Master's Program In Big Data Analytics and Business Intelligence
學年度 108
學期 2
出版年 109
研究生中文姓名 謝怡君
研究生英文姓名 Yi-Jun Xie
學號 607890059
學位類別 碩士
語文別 中文
口試日期 2020-07-03
論文頁數 62頁
口試委員 指導教授-吳淑妃
委員-吳錦全
委員-王智立
中文關鍵字 製程能力指標  逐步型I區間設限  Gompertz分配  最大概似估計量  檢定程序  抽樣設計 
英文關鍵字 Censored sample  Gompertz distribution  Maximum likelihood estimator  Process capability index  Testing algorithmic procedure  Sampling Design 
學科別分類
中文摘要 在這個人工智能時代,科技的日新月異使產品生產技術更加精密複雜,消費者對產品品質要求也日趨嚴苛。製造商為了達到消費者所要求的品質水準,便設法提高產品的壽命以及製程良率,同時嚴格控管製造過程,避免造成不必要的浪費,以降低成本。藉此擴大市場競爭力並達到利潤最大化。
本研究假設產品壽命服從Gompertz分配時,當規格下限L已知,在逐步型I區間設限下,基於使用壽命績效指標之最大概似估計量做為檢定統計量,所建構出的假設檢定程序下,為了達到給定的檢定力水準以及最小的總實驗成本,建構出的最佳抽樣設計。最後,利用一個模擬與一個數值實例來說明這個檢定程序下樣本設計的使用,以檢驗此製程是否有能力。
英文摘要 In this artificial intelligence era, the constantly changing of technology makes production techniques become sophisticated and complicated. Therefore, manufacturers are dedicated to improving the quality of products by increasing the lifetime in order to achieve the quality standards demanded by consumers. Meanwhile, to increase market competitiveness and profits, the process of product manufacturing is strictly controlled to avoid unnecessary waste, and so as to reduce costs.
Based on the hypothesis testing procedure using the maximum likelihood estimator as testing statistic, the sampling design is determined and the related values are tabulated for practical use to reach the given power level or minimize the total experimental cost under progressive type I interval censoring. At last, one practical example and one simulation example are given to illustrate the use of this sampling design for the testing procedure to determine whether the process is capable.
論文目次 目錄
目錄 I
表目錄 III
圖目錄 V
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻探討 3
1.2.1 製程能力指標之發展 3
1.2.2 設限型式 6
1.3 本文架構 8
第二章 壽命績效指標的檢定程序介紹 10
2.1 產品的壽命績效指標C_L 10
2.2 壽命績效指標的假設檢定 14
第三章 可靠度抽樣設計 18
3.1 在固定的觀測區間個數和總觀測時間下,樣本數大小之決定 18
3.2 在固定的總觀測時間下,最佳觀測區間個數與樣本數大小之決定 23
3.3 當總觀測時間為不固定時,最佳觀測區間個數、觀測區間時間以及樣本數之決定 31
第四章 模擬與數值實例分析 40
4.1 數值實例 40
4.2 模擬範例 45
第五章 結論與未來研究 51
5.1 結論 51
5.2 未來研究 52
參考文獻 53


表目錄
表2.1 壽命績效指標C_L值對應之製程良率P_r 13
表4.1 被餵食未飽和飲食的老鼠,未罹患腫瘤天數(單位:200天) 40
附表 1 當形狀參數k=4.47、規格下限L=0.05、總觀測時間T=0.5、型II誤差β=0.25,0.2,0.15、觀測次數m=5(1)8、逐步設限移除率p=0.05(0.025)0.1時,在顯著水準α=0.01、目標值C_0=0.8和實際值C_1=0.825(0.025)0.95下,所需要的最小樣本數,以及其對應臨界 56
附表 2 當形狀參數k=4.47、規格下限L=0.05、總觀測時間T=0.5、型II誤差β=0.25,0.2,0.15、觀測次數m=5(1)8、逐步設限移除率p=0.05(0.025)0.1時,在顯著水準α=0.05、目標值C_0=0.8和實際值C_1=0.825(0.025)0.95下,所需要的最小樣本數,以及其對應臨界 57
附表 3 當形狀參數k=4.47、規格下限L=0.05、總觀測時間T=0.5、型II誤差β=0.25,0.2,0.15、觀測次數m=5(1)8、逐步設限移除率p=0.05(0.025)0.1時,在顯著水準α=0.1、目標值C_0=0.8和實際值C_1=0.825(0.025)0.95下,所需要的最小樣本數,以及其對應臨界 58
附表 4 當形狀參數k=4.47、規格下限L=0.05、總觀測時間T=0.5、觀測次數上界m_0=20、逐步設限移除率p=0.05(0.025)0.1時,在目標值C_0=0.8和實際值C_1=0.825,0.850下,所推薦的最佳觀測區間個數、樣本數,以及其對應之總成本與臨界值 59
附表 5 當形狀參數k=4.47、規格下限L=0.05、總觀測時間T=0.5、觀測次數上界m_0=20、逐步設限移除率p=0.05(0.025)0.1時,在目標值C_0=0.8和實際值C_1=0.875,0.90下,所推薦的最佳觀測區間個數、樣本數,以及其對應之總成本與臨界值 60
附表 6 當形狀參數k=4.47、規格下限L=0.05、觀測次數上界m_0=20、逐步設限移除率p=0.05(0.025)0.1時,在目標值C_0=0.8和實際值C_1=0.825,0.850下,所推薦的最佳觀測區間個數、觀測區間時間、樣本數,以及其對應之總成本與臨界值 61
附表 7 當形狀參數k=4.47、規格下限L=0.05、觀測次數上界m_0=20、逐步設限移除率p=0.05(0.025)0.1時,在目標值C_0=0.8和實際值C_1=0.875,0.90下,所推薦的最佳觀測區間個數、觀測區間時間、樣本數,以及其對應之總成本與臨界值 62


圖目錄
圖1.1 逐步型I區間設限 7
圖3.1.1 當α=0.05、m=5及p=0.05下,不同的檢定力1-β=0.75,0.8,0.85時,所需的最小樣本數n 21
圖3.1.2 當α=0.05、β=0.2及p=0.05下,不同的觀察次數m=5,6,7,8時,所需的最小樣本數n 21
圖3.1.3 當α=0.05、β=0.2及m=5下,不同的逐步設限移除率p=0.05,0.075,0.1時,所需的最小樣本數n 22
圖3.1.4 當β=0.2、m=5及p=0.05下,不同的顯著水準α=0.01,0.05,0.1時,所需的最小樣本數n 22
圖3.2.1 當β=0.25 ,α=0.01 ,p=0.05 ,c_1=0.825 ,m_0=20時,觀測區間個數與其相對應的總成本曲線 25
圖3.2.2 當β=0.15 ,α=0.1 ,p=0.1 ,c_1=0.9 ,m_0=20時,觀測區間個數與其相對應的總成本曲線 25
圖3.2.3 當α=0.05及p=0.05下,不同的檢定力1-β=0.75,0.8,0.85時,所需的最小觀測區間個數m 27
圖3.2.4 當α=0.05及β=0.2下,不同的逐步設限移除率p=0.05,0.075,0.1時,所需的最小觀測區間個數m 28
圖3.2.5 當β=0.2及p=0.05下,不同的顯著水準α=0.01,0.5,0.1時,所需的最小觀測區間個數m 28
圖3.2.6 當α=0.05及p=0.05下,不同的檢定力1-β=0.75,0.8,0.85時,所達的最小總成本TC* 30
圖3.2.7 當α=0.05及β=0.2下,不同的逐步設限移除率p=0.05,0.075,0.1時,所達的最小總成本TC* 30
圖3.2.8 當β=0.2及p=0.05下,不同的顯著水準α=0.01,0.5,0.1時,所達的最小總成本TC* 31
圖3.3.1 當β=0.25 ,α=0.01 ,p=0.05 ,c_1=0.825 ,m_0=20時,觀測區間個數與其相對應的總成本曲線 33
圖3.3.2 當β=0.15 ,α=0.1 ,p=0.1 ,c_1=0.9 ,m_0=20時,觀測區間個數與其相對應的總成本曲線 33
圖3.3.3 當α=0.01及p=0.05下,不同的檢定力1-β=0.75,0.8,0.85時,所需的最小觀測區間個數m 35
圖3.3.4 當α=0.01及β=0.2下,不同的逐步設限移除率p=0.05,0.075,0.1時,所需的最小觀測區間個數m 36
圖3.3.5 當β=0.2及p=0.05下,不同的顯著水準α=0.01,0.05,0.1時,所需的最小觀測區間個數m 36
圖3.3.6 當α=0.01及p=0.05下,不同的檢定力1-β=0.75,0.8,0.85時,所達的最小總成本TC** 38
圖3.3.7 當α=0.01及β=0.2下,不同的逐步設限移除率p=0.05,0.075,0.1時,所達的最小總成本TC** 38
圖3.3.8 當β=0.2及p=0.05下,不同的顯著水準α=0.01,0.05,0.1時,所達的最小總成本TC** 39
圖4.1 不同k下之p值 42
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