系統識別號 | U0002-1807201817231800 |
---|---|
DOI | 10.6846/TKU.2018.00525 |
論文名稱(中文) | Weibull分配產品的壽命績效指標在逐 步型Ι區間下之檢定程序的檢定力分析 |
論文名稱(英文) | The power analysis of the testing procedure for the lifetime performance index of products with Weibull distribution under progressive type I interval censoring |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 統計學系應用統計學碩士班 |
系所名稱(英文) | Department of Statistics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 106 |
學期 | 2 |
出版年 | 107 |
研究生(中文) | 吳奇翰 |
研究生(英文) | Chi-Han Wu |
學號 | 605650141 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2018-07-04 |
論文頁數 | 71頁 |
口試委員 |
指導教授
-
吳淑妃
委員 - 王智立 委員 - 吳錦全 |
關鍵字(中) |
逐步型I 區間設限 Weibull 分配 最大概似估計量 拔靴法 製程能力指標 檢定程序 |
關鍵字(英) |
progressive type I interval censoring Weibull distribution maximum likelihood estimator bootstrap process capability index testing procedure |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
近年來,隨著科技的進步,許多電子資訊產品像是平板、智慧型手機等等越來越普及,而消費者對這類產品除了價格要低,品質也要求越高,因此如何提升產品製程的能力是品管上很重要的工作。目前,已經發展了許多方法評估產品的品質能力,而製程能力指標(process capability indices, PCIs) 已經被廣泛地應用在評估製程的績效,進而提升產品品質及製程能力。 本研究假設產品壽命服從Weibull分配時,在逐步型I區間設限下,計算出壽命績效指標CL之最大概似估計量並求其漸近分配。在規格下限L已知的情況下,使用此估計量及兩種拔靴法發展三個檢定程序以判定壽命績效指標是否達到預期的要求水準。最後,用一個數值例子和一個模擬例子說明如何使用本研究所提出的檢定程序。 |
英文摘要 |
In recent years, with the advancement of science and technology, many electronic information products such as tablets, smart phones, etc. have become more and more popular, and consumers are demanding more and more quality in addition to the price, so how to improve The ability to manufacture products is an important part of quality control. At present, many methods have been developed to evaluate the quality capabilities of products. Process capability indices (PCIs) have been widely used to evaluate the performance of processes and improve product quality and process capability. This research is focusing on the lifetime of products following the Weibull distribution. The maximum likelihood estimator is used to estimate the lifetime performance index (CL) based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator and two kinds of bootstrap methods to develop three kinds of hypothesis testing algorithmic procedure in the condition of known lower specification limit L. Finally, we give one practical example and one simulation example to illustrate the use of the proposed testing algorithmic procedure to determine whether the process is capable. |
第三語言摘要 | |
論文目次 |
目錄 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 設限形式.......................5 1.3 本文架構.............................7 第二章 Weibull分配壽命績效指標與其估計.....8 2.1 產品的壽命績效指標CL..................10 2.2 壽命績效指標的估計量..................13 第三章 壽命績效指標的檢定演算程序與檢定力...18 3.1 壽命績效指標的檢定演算程序.............18 3.2樣本大小之決定.........................23 3.3 檢定力模擬之分析......................27 3.4 點估計...............................35 第四章 模擬與數值實例分析..................36 4.1 數值範例.............................36 4.2 模擬範例.............................42 第五章 結論與未來研究.....................46 5.1 結論.................................46 5.2 未來研究.............................47 參考文獻.................................48 附錄.....................................50 表目錄 附表1 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60、80 ,設限樣本數m=20、30、40及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.01下,檢定力函數h(c1)在c1=0.8(0.02)0.92,0.93,0.99的數值.................50 附表2 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60、80,設限樣本數m=20、30、40及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.05下,檢定力函數h(c1)在c1=0.8(0.02)0.92,0.93,0.99的數值..................51 附表3 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60、80,設限樣本數m=20、30、40及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.05下,檢定力函數h(c1)在c1=0.8(0.02)0.92,0.93,0.99的數值..................52 附表4.α=0.01,β=0.25情況下,不同的m及p的最小樣本數...53 附表5.α=0.01,β=0.2情況下,不同的m及p的最小樣本數....54 附表6.α=0.01,β=0.15情況下,不同的m及p的最小樣本數...55 附表7.α=0.05,β=0.25情況下,不同的m及p的最小樣本數...56 附表8.α=0.05,β=0.2情況下,不同的m及p的最小樣本數....57 附表9.α=0.05,β=0.15情況下,不同的m及p的最小樣本數...58 附表10.α=0.1,β=0.25情況下,不同的m及p的最小樣本數...59 附表11.α=0.1,β=0.2情況下,不同的m及p的最小樣本數....60 附表12.α=0.1,β=0.15情況下,不同的m及p的樣本數.......61 附表13 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60,設限樣本數m=20、30及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.01下,在c1=0.8(0.02)0.9,0.91,0.92,0.93 的數值下三種方法的模擬檢定力.........................62 附表14 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=80,設限樣本數m=30、40及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.01下,在c1=0.8(0.02)0.9,0.91,0.92,0.93 的數值下三種方法的模擬檢定力.........................63 附表15 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60,設限樣本數m=20、30及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.05下,在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值下三種方法的模擬檢定力.........................64 附表16 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=80,設限樣本數m=30、40及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.05下,在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值下三種方法的模擬檢定力.........................65 附表17 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60,設限樣本數m=20、30及逐步移除率p=0.01,0.05,0.075時,在目標值c0=0.8和顯著水準α=0.1下,在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值下三種方法的模擬檢定力.........................66 附表18 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=80,設限樣本數m=30、40及逐步移除率p=0.01,0.05,0.075時,在目標值 和顯著水準α=0.1下,在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值下三種方法的模擬檢定力...................................67 附表19 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60,設限樣本數m=20、30及逐步移除率p=0.01,0.05,0.075時,目標值為c0=0.8,顯著水準α=0.01下Bias在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值................68 附表20 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=80,設限樣本數m=30、40及逐步移除率p=0.01,0.05,0.075時,目標值為c0=0.8,顯著水準α=0.01下Bias在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值................69 附表21 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=60,設限樣本數m=20、30及逐步移除率p=0.01,0.05,0.075時,目標值為c0=0.8,顯著水準α=0.01下MSE在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值................70 附表22 當規格下限L=0.05,總觀測時間T=0.5,觀測樣本數n=80,設限樣本數m=30、40及逐步移除率p=0.01,0.05,0.075時,目標值為c0=0.8,顯著水準α=0.01下MSE在c1=0.8(0.02)0.9,0.91,0.92,0.93的數值................71 圖目錄 圖1.2.1逐步型I區間設限................................7 圖2.1 Weibull分配λ=1或2,不同β時的機率密度函數圖........9 圖2.2 Weibull分配λ=1或2,不同β時的失效率函數圖..........9 圖3.2.1 當α=0.01、1-β=0.75及m=30下,不同的逐步設限移除率p=0.01,0.05,0.075時所需的最小樣本數n...................25 圖3.2.2 當α=0.01、1-β=0.75及m=30下,不同的觀察次數m=20,30,40時所需的最小樣本數n..........................25 圖3.2.3 當α=0.01、m=30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.....................26 圖3.2.4 當1-β=0.75、m=30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.....................26 圖3.3.1 當α=0.05,m=30及p=0.01下,考慮不同的樣本數n=60、80時,三種方法的檢定力...................................31 圖3.3.2 當α=0.05,p=0.01及n=60下,考慮不同的觀察區間m=20,30時,三種方法的檢定力。.................................32 圖.3.3.3 當α=0.05,m=30及n=60下,考慮不同的預定逐步設限移除率p=0.01,0.05,0.075時,三種方法的檢定力................33 圖3.3.4 當m=30,n=60及p=0.01下,考慮不同的顯著水準α=0.01,0.05,0.1時,三種方法的檢定力....................34 圖4.1不同形狀參數 下之p-value..........................38 |
參考文獻 |
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