一般傳統的設限試驗都是在實驗最後才能移除存活元件，然而在實務上，我們有時需要在實驗進行中提早移除部份存活元件，此類型的試驗稱之為逐步設限。除此之外，因為成本或實驗操作上的限制，某些壽命試驗只能在固定時點觀察元件故障與否，以此方式所收集到的資料稱為分群資料。本篇論文我們將逐步型一設限與分群資料結合，
以逐步型一區間設限方法收集指數壽命分配下元件的壽命資料做相關的參數估計，並討論以下兩個主題：

在可靠度的壽命試驗中，收集越多關於產品的資訊對我們評估產品可靠度越有幫助。然而，為了得到更多關於產品的壽命資訊，往往需要增加實驗成本，而實驗成本常會影響整個實驗的規模。為了同時兼顧評估產品可靠度的精確度與實驗成本的大小，我們給定實驗成本與實驗預算限制，以非線性混合整數規劃方法，找出使得最大概似估計量的漸近變異數最小且不超過實驗預算限制的實驗配置，並舉例做敏感度分析。

抽樣檢查是品質管制問題中主要研究的議題，如何決定壽命實驗的配置與允收臨界值將會影響整個抽樣實驗的結果，我們將在給定生產者風險與消費者風險下，建立一允收抽樣計畫使得整個實驗總成本小，並做數值的模擬分析與討論。

In traditional censoring schemes, surviving units can only be removed at the end of the life tests. However, in some practical situations, one has to remove surviving units at the points other than the final termination point. A life test of this type is called progressive censoring. Besides, in some life tests, we can only record whether a test unit fails in an interval instead of measuring failure time exactly. Hence, the test units are inspected intermittently.  This type of inspection is called interval censoring. In this thesis, we combine progressive censoring and interval censoring to develop a progressive type-I interval-censoring scheme. We will focus on two designing problems of progressive type-I interval-censoring life test with exponential failure time distribution.

The first problem is how to design an appropriate life test that would result in the optimal estimation of the mean life. Simply put, more test units, more test time, and more number of inspections will generate more information, which improves the precision of estimates. However, one practical problem arising from designing a life test is the restricted budget of experiment.  The size of budget always affects the decisions of number of test units, number of inspections and length of inspection intervals and hence, affects the precision of estimation. In this study, we will use the nonlinear mixed integer programming to obtain the optimal settings of a progressive type-I interval-censored life test by minimizing the asymptotic variance of mean life under the constraint that the total experimental cost does not exceed a pre-determined budget. An example is discussed to illustrate the proposed method and sensitivity analysis is also studied.

The second problem is to establish the acceptance sampling plans with cost consideration.  We will construct acceptance sampling plans which have the minimum experimental cost under given consumer's and producer's risks. Some numerical examples and studies are performed to illustrate the proposed approach.

目錄
1 緒論...........................................................................................................................1
  1.1 研究目的與動機..................................................................................................1
  1.2 文獻探討..............................................................................................................4
  1.3 本文架構............................................................................................................. 6
2 逐步型一區間設限........................................................................................................7
  2.1 實驗方式............................................................................................................. 7
  2.2 參數估計..............................................................................................................8
3 逐步型一區間設限在成本限制下的最佳設計..............................................................13 
  3.1 成本限制下的最佳設計................................................................................... 13
  3.2 數值實例............................................................................................................15
  3.3 敏感度分析........................................................................................................17
    3.3.1 壽命分配參數對最佳解的影響...................................................................17
    3.3.2 移除比例對最佳解的影響...........................................................................19
    3.3.3 成本參數對最佳解的影響...........................................................................19
  3.4 總實驗時間限制下的最佳設計........................................................................23
4 逐步型一區間設限在成本限制下的允收抽樣計畫                                             25
  4.1 允收抽樣計畫....................................................................................................25
  4.2 成本限制下的允收抽樣計畫..................................................................................27
  4.3 數值分析............................................................................................................29
  4.4 固定總實驗時間下的允收抽樣計畫........................................................................30
5 結論  ....................................................................................................................36 
參考文獻                                                                                                                    38

表格目錄
3.1 逐步型一區間設限樣本......................................................................................16
3.2 不同的theta與p下最佳的(n,k,tau)組合................................................................18
3.3 不同成本參數組合下的最佳(n,k,tau)設計，theta=4.9326與p=0.05.........................20
3.4 不同成本參數組合下的最佳(n,k,tau)設計，theta=4.9326與p=0.1..........................21
3.5 不同成本參數組合下的最佳(n,k,tau)設計，theta=4.9326與p=0.25.........................22
4.1 使總成本最小的允收臨界c值與實驗配置(n,k,tau)，alpha=0.05，beta=0.05............31
4.2 使總成本最小的允收臨界c值與實驗配置(n,k,tau)，alpha=0.05，beta=0.1..............32
4.3 使總成本最小的允收臨界c值與實驗配置(n,k,tau)，alpha=0.1，beta=0.05..............33
4.4 使總成本最小的允收臨界c值與實驗配置(n,k,tau)，alpha=0.1，beta=0.1................34

圖形目錄
2.1 逐步型一區間設限計畫........................................................................................8

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