近年來，製程能力指標被製造商廣泛用在品質監控方面，藉由指標值評估製程能力是否合乎水準。大多數的製程能力指標都是假設產品的品質特性具有常態分配；然而在實務上，產品的壽命並非服從常態分配，例如:柏拉圖分配、韋伯分配、浴缸型分配等等。在製造業中，製程能力指標常被用來評估產品品質是否達到所要求的水準，而壽命績效指標C_L就是評估工具之一，其中L為規格下界。在進行產品可靠度的分析及改善時，通常需要做產品的抽樣壽命實驗，希望能利用已觀測到的產品壽命資料來估計參數與評估產品品質是否達到所要求的水準。本文考慮以逐步第一失敗設限計畫，利用柏拉圖壽命分配取得的設限樣本觀測值，探討具有柏拉圖壽命分配之產品的壽命績效指標，並對壽命績效指標做統計推論。                   
    本文主要以服從柏拉圖壽命分配的逐步第一失敗設限樣本，來建構壽命績效指標C_L之最大概似估計量(MLE)，進而利用C_L之MLE求得壽命績效指標C_L之信賴區間，同時發展一檢定程序以評估產品之壽命是否達到所要求的水準，再針對壽命績效指標的檢定力及信賴區間進行蒙地卡羅模擬。最後，透過實例分析，說明各種程序與方法的運用，以提供製造商評估產品的壽命是否達到所要求的水準。
 表單編號：ATRX–Q03–001–FM030–01

In recent years, many process capability indices (PCIs) have been widely used in quality monitoring by many manufacturing industries. Most PCIs asuume that the quality characteristic has a normal distribution. However, the lifetime of many products frequently possesses non-normal distribution, such as Pareto, Weibull or Bathtub-shape distribution etc. Process capability indices are often used to assess whether the product quality to meet the required level, and the lifetime performance index   is the tools  to evaluate the performance indicators, where L is the lower specification limit. During the analysis and improvement of product’s reliability, we usually need to do sampling test. We can take advantage of the product life who has been observed characteristic to estimate parameters and to assess whether the product quality to meet the required level. In this article, we consider the progressive first-failure-censored plan using the censored sample observations from Pareto distribution to explore the statistical inference for the lifetime performance index of products.
   This research constructs a maximum likelihood estimator (MLE) of   based on the progressive first-failure-censored sample from the Paereto distribution. The MLE of  is then utilized to develop the confidence interval in the condition of known L and the hypothesis testing procedure to determine whether the lifetime performance of products adhere to the required level. And using the Monte Carlo simulation to study lifetime performance index power and confidence level. Finally, we use the numerical examples to illustrate how to apply the proposed method to analyze the performance index to assess the product's life to meet the required level.  
表單編號：ATRX–Q03–001–FM031–01

目錄.......................................................Ⅰ 
表目錄.....................................................Ⅲ
圖目錄.....................................................Ⅶ  


第一章 緒論.................................................1
  1.1 前言.................................................1
  1.2 研究動機與目的.........................................1
  1.3 本文架構..............................................2  
第二章 文獻探討..............................................3
  2.1 設限型態..............................................3
  2.2 製程能力指標..........................................4
  2.3 分配介紹..............................................5 
第三章 利用逐步第一失敗設限樣本評估具有柏拉圖分配之產品的壽
      命績效指標............................................8
  3.1 產品的壽命績效指標與合格率..............................8
  3.2 參數的最大概似估計量..................................10
  3.3 壽命績效指標 之估計量.................................11
  3.4 壽命績效指標 的檢定程序................................12
  3.5 壽命績效指標 之檢定力函數..............................14
  3.6 壽命績效指標 之檢定力的真值與蒙地卡羅模擬值之比較.........15
  3.7 壽命績效指標 之信賴區間................................17
  3.8 壽命績效指標 之信賴水準的蒙地卡羅模擬....................19
  3.9 數值範例.............................................20
第四章 結論與未來研究方向....................................51
  4.1 結論................................................51
參考文獻...................................................52
附錄......................................................55
 

表目錄

表3.1  壽命績效指標與製程良率.................................9
表3.2  在顯著水準α=0.01、c^*=0.1(0.1)0.9及m=2(1)65下，產品壽命績  
效指標的臨界值.......................................23             
表3.3  在顯著水準α=0.05 、c^*=0.1(0.1)0.9及m=2(1)65下，產品壽績 
       效指標的臨界值 ............................ .........25
表3.4  在顯著水準α=0.01、目標值c^*=0.1、n=50、m=20、θ=0.8、k=3、 
       規格下界 L=0.02，以及不同的設限序列下，壽命績效指標的檢定力
       真實值P(c)與模擬平均值及MSE..........................27
表3.5  在顯著水準α=0.01、目標值c^*=0.1、n=50、m=20、θ=2、k=3、 
       規格下界L =0.02，以及不同的設限序列下，壽命績效指標的檢定力 
       真實值P(c)與模擬平均值及MSE..........................28
表3.6  在顯著水準α=0.01、目標值c^*=0.1、n=60、m=20、θ=0.8、k=3、  
       規格下界L =0.02，以及不同的設限序列下，壽命績效指標的檢定力
       真實值P(c)與模擬平均值及MSE..........................29
表3.7  在顯著水準α=0.01、目標值c^*=0.1、n=60、m=20、θ=2、k=3、 
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢定力   
       真實值P(c)與模擬平均值及MSE..........................30
表3.8  在顯著水準α=0.01、目標值c^*=0.1、n=50、m=20、θ=0.8、k=5、
       規格下界L =0.02，以及不同的設限序列下，壽命績效指標的檢定力      
       真實值P(c)與模擬平均值及MSE..........................31
表3.9  在顯著水準α=0.01、目標值c^*=0.1、n=50、m=20、θ=2、k=5、
       規格下界L =0.02，以及不同的設限序列下，壽命績效指標的檢定力 
       真實值P(c)與模擬平均值及MSE..........................32
表3.10 在顯著水準α=0.01、目標值c^*=0.1、n=60、m=20、θ=0.8、k=5、
       規格下界L =0.02，以及不同的設限序列下，壽命績效指標的檢定力  
       真實值P(c)與模擬平均值及MSE..........................33
表3.11 在顯著水準α=0.01、目標值c^*=0.1、n=60、m=20、θ=2、k=5、
       規格下界L =0.02，以及不同的設限序列下，壽命績效指標的檢
       定力真實值P(c)與模擬平均值 及MSE......................34
表3.12 在顯著水準α=0.01、目標值c^*=0.1、n=50、m=30、θ=0.8、k=3、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢定力  
       真實值P(c)與模擬平均值 及MSE.........................35
表3.13 在顯著水準α=0.01、目標值c^*=0.1、n=50、m=30、θ=2、k=3、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢定力
       真實值P(c)與模擬平均值及MSE..........................36
表3.14 在顯著水準α=0.01、目標值c^*=0.1、n=60、m=30、θ=0.8、k=3、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢
       定力真實值P(c)與模擬平均值 及MSE......................37
表3.15 在顯著水準α=0.01、目標值c^*=0.1、n=60、m=30、θ=2、k=3、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢
       定力真實值P(c)與模擬平均值及MSE.......................38
表3.16 在顯著水準α=0.01、目標值c^*=0.1、n=50、m=30、θ=0.8、k=5、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢定力
       真實值P(c)與模擬平均值及MSE..........................39
表3.17 在顯著水準α=0.01、目標值c^*=0.1、n=50、m=30、θ=2、k=5、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢定力
       真實值P(c)與模擬平均值及MSE..........................40
表3.18 在顯著水準α=0.01、目標值c^*=0.1、n=60、m=30、θ=0.8、k=5、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢定力
       真實值P(c)與模擬平均值 及MSE.........................41
表3.19 在顯著水準α=0.01、目標值c^*=0.1、n=60、m=30、θ=2、k=5、
       規格下界L=0.02，以及不同的設限序列下，壽命績效指標的檢定力
       真實值P(c)與模擬平均值 及MSE.........................42
表3.20 在顯著水準α=0.05, 0.01、 =50、參數值θ=0.7、目標值0.7和   
       規格下界L=0.02下，壽命績效指標之信賴水準模擬平均值與
       MSE................................................43      
表3.21 在顯著水準α=0.05, 0.01、 =50、參數值θ=2、目標值0.8和  
       規格下界L=0.02下，壽命績效指標之信賴水準模擬平均值與 
       MSE................................................44
表3.22 在顯著水準α=0.05 ,0.01、 =40、參數值θ=0.7、目標值0.7和
       規格下界L=0.02下，壽命績效指標之信賴水準模擬平均值與  
       MSE................................................45
表3.23 在顯著水準α=0.05, 0.01、 =40、參數值θ=2、目標值0.8和  
       規格下界L=0.02下，壽命績效指標之信賴水準模擬平均值與
       MSE................................................46

圖目錄

圖2.1  當θ=1時之柏拉圖分配的機率密度函數曲線....................6
圖2.2  當θ=2時之柏拉圖分配的機率密度函數曲線....................7
圖3.1  在顯著水準α=0.01、目標值c^*=0.1、n=50、m=20、θ=0.8、規格   
       下界L=0.02，逐步移下，壽命績效指標的檢定力真實值P(c)與模擬平  
       均值 之圖形.........................................47
圖3.2  在顯著水準α=0.01、目標值c^*=0.1、n=50、m=20、k=3、規格
       下界 L=0.02，逐步移除下，壽命績效指標的檢定力真實值P(c)與模
       擬平均值之圖形.......................................48
圖3.3  在顯著水準α=0.01、目標值c^*=0.1、n=50、θ=0.8、k=3、規格  
       下界 L=0.02，逐步移除下，壽命績效指標的檢定力真實值P(c)與
       模擬平均值之圖形.....................................49
圖3.4  在顯著水準α=0.01、目標值c^*=0.1、n=50、θ=0.8、m=20、k=3    
        、規格下界L=0.02，壽命績效指標的檢定力真實值P(c)與模擬 
         平均值 之圖形.....................................50

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