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研究生:高偉庭
論文名稱:在Weibull分配的型II右設限樣本下望小型製程能力指標之評估
論文名稱(外文):Assessing the smaller-the-better lifetime performance index of Weibull products under type II right censored samples
指導教授:吳忠武吳忠武引用關係
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:100
語文別:中文
中文關鍵詞:望小型製程能力指標Weibull分配最大概似估計量型II右設限樣本
外文關鍵詞:smaller-the-better process capability indicesweibul distributionmaximum likelihood estimatortype II right censored samples
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製造業或服務業常利用製程能力指標(Process capability indices;PCIs)來評估產品品質是否達到所要求的水準。以往大多數製程能力指標都以產品的品質特性為常態分配作為前提假設,事實並非如此,許多產品品質特性往往來自於其他分配,例如:Exponential分配、Rayleigh分配、Gamma分配或Weibull分配等等,因此本文針對品質特性具有偏斜、非負和厚尾的分配,提出望小型製程能力指標Cma,其中具有上規格界限(Upper specification limit)。此外,在壽命試驗中常因時間限制以及人力、物力和成本的考量而無法取得完整的樣本資料,使得必須使用設限樣本資料,所以本研究主要在探討產品品質特性來自雙參數Weibull分配且具有高度偏斜(亦即,偏態系數 )之型 右設限樣本,來建構Cmaw之最大概似估計量(maximum likelihood estimator, MLE),且使用此估計量在已知的上規格界限 和顯著水準 下,發展出一套對 之假設檢定程序新的假設檢定來評估產品績效。因此,它也可以提供廠商方便評估產品績效是否達到所要求的水準。
The service or manufacturing industry are generally employed the process capability indices (PCIs) to ensure whether product quality satisfy the required level. Most process capability indices assumed that the product quality characteristic comes from normal distribution. However, it is not a reasonable assumption. Actually, the lifetime of products may usually come from an Exponential distribution, Rayleighl distribution, Gamma distribution, weibull distribution, etc. Now, we studied the smaller-the-better process capability indices Cma when quality characteristic of interest has a skewed, zero-bound distribution with a long tail towards large values and there is an upper specification limit. In addition, tests of product lifetime experiments often due to time limitation as well as manpower, material resources and cost considerations had not collected the complete observations, makes it imperative to use a censored sample data. Therefore, this study was to investigate the quality characteristics from the two-parameter Weibull distribution is highly skewed under type right censored in the condition of know Upper Specification Limit. Hence, we propose the maximum likelihood estimator of Cmaw to develop a novel hypothesis testing procedure under given significance level . Therefore, it can also provide manufacturers facilitate the assessment of product quality to reach the required standard.
中文摘要........................................... I
英文摘要........................................... II
誌謝辭............................................. III
目錄............................................... V
圖表目錄........................................... VI
表格目錄........................................... VII
第一章 緒論........................................ 1
1-1 研究動機與背景............................. 1
1-2 本文架構................................... 2
第二章 文獻探討.................................... 4
2-1 品質特性文獻探討........................... 4
2-2 製程能力指標文獻探討....................... 5
2-3 設限資料文獻探討........................... 7
第三章 製程能力指標估計與檢定...................... 9
3-1 製程能力指標之Weibull分配................. 9
3-2 製程能力指標之不合格率..................... 12
3-3 型 右設限樣本之最大概似估計................ 13
3-4 製程能力指標之假設檢定..................... 17
3-5 製程能力指標之模擬修正項k值................ 18
3-6 製程能力指標之檢定力....................... 29
第四章 實際範例.................................... 33
樣本數與設限數相同............................. 33
樣本數與設限數不相同........................... 35
第五章 結論與未來研究.............................. 39
5-1 結論....................................... 39
5-2 未來研究................................... 40
文獻參考........................................... 42
附錄A-1............................................ 44
附錄A-2............................................ 47

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