成本限制下之最適逐步型一分群試驗

在傳統的壽命試驗中，通常不允許在試驗中間移除存活之元件。但是，在實務上實驗者有時候必須於試驗中間移除部分的存活元件。因此，逐步設限便被用來處理這種型態的問題。此外，由於試驗操作上的限制，使得有些試驗無法連續地觀察受測試元件的狀況，而只能每隔一段時間來記錄這些元件是否發生故障，因此無法知道確切的故障時間，這種型態的資料稱為分群資料。再則由於科技的發達使得元件的可靠度不斷的提昇，所以在有限的試驗時間內可觀察到的故障元件個數便很少甚至等於零，因此加速壽命試驗的方法可讓實驗者提早獲得足夠的元件壽命資料。本論文首先將逐步設限和分群合併，提出逐步型一分群設限的試驗方式，探討在元件壽命為韋伯分配時，利用最大概似法推導出分配參數的估計及大樣本性質。然後將試驗成本列入考量，在有限的試驗預算下，以非線性混合整數規劃方法來找出最佳的試驗配置，並舉例子來闡述所提出的方法，以及探討分配和成本參數變動時的敏感度分析。此外，本論文也將逐步應力加速壽命試驗納入研究中，提出逐步型一分群設限逐步應力加速壽命試驗計畫，並探討韋伯壽命分配下，有關參數估計的問題。然後在總預算限制下，提出建立試驗最佳配置的方法，並舉數值例子及探討相關之敏感度分析。

關鍵字

加速壽命試驗；預算； D型最適性；費雪資訊矩陣；最大概似估計量；敏感度分析；逐步應力；韋伯分配

並列摘要

In traditional censoring life test,it is not allowed for surviving units to be removed from the test at points other than the final termination point.However, this allowance will be desirable for some experimenters.Therefore, a progressive censoring scheme is proposed to handle this problem.Besides, in practice, it is often impossible continuously to observe or inspect the testing process. 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. Data of this type are called grouped data.Moreover, with today's high technology, some life tests result in few or no failures in a short life testing time.One approach to solve this problem is to accelerate the life of units by increasing the levels of stress in order to obtain failures quickly.In this thesis, we first combine progressive censoring and grouped data to develop a progressive type-I group-censoring scheme.We will use the maximum likelihood method to derive parameter estimation under Weibull failure time distribution. Furthermore, we will use the nonlinear mixed integer programming to obtain the optimal settings of a progressive type-I group-censored life test by maximizing the terminant of Fisher's information 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.Finally, we will consider a step-stress accelerated life test with progressive type-I group-censoring scheme and derive the parameter estimation of Weibull distribution. The optimal design in presence of cost constraint is also investigated. A numerical example is studied to illustrate the proposed approach and sensitivity analysis is performed.

並列關鍵字

Accelerated life test ； Budget ； D-optimality ； Maximum likelihood estimation ； Sensitivity analysis ； Step stress ； Weibull distribution

參考文獻

Aggarwala, R. (2001).

Progressive interval censoring: some mathematical results with applications to inference,

Communications in Statistics -- Theory and Methods, 30, 1921-1935.

Optimum simple step-stress accelerated life tests for Weibull distribution and type I censoring,

Balakrishnan, N. and Aggarwala, R. (2000).

國際替代計量

成本限制下之最適逐步型一分群試驗

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