在產品壽命實驗的研究中，由於各種的原因，要取得完整的實驗單位失效的時間資訊經常是不太可能的，設限資料會經常在壽命實驗中出現。由於實驗有時並無法完全受到控制或因為實際的需要，因而導致某些實驗單位被迫中途移除，在這種情況下，型一及型二設限資料的型態並不適用這樣的實驗架構，此時樣本資料則是符合多重設限資料的型態。
隨著產品可靠性的提升，在一般條件下的壽命實驗會花費很多時間進而耗掉很多資源，此時要得到壽命實驗的資料也相對困難許多。為了確保實驗單位能加速失效進而縮短實驗時間，加速壽命測試方法經常被用來做為進行壽命實驗的主要架構，這是基於它能縮短實驗時間進而達到經濟效益的特點。加速壽命測試方法是在一些較高的環境應力(如高溫、高壓)的條件下測試產品，使產品提早失效。在加速壽命測試的實驗中，產品僅在較高環境應力的條件下進行測試，模型分配中的加速因子參數是假設為已知的，然而很多的狀況，加速因子參數經常是未知的，特別是當實驗對象為新產品時。在加速因子參數是未知的狀況下，部分加速壽命測試則是另一個很好的選擇，因為加速因子參數可以依據在部分加速壽命測試所蒐集的樣本資料估計得到，而不需要事先知道。
部分加速壽命測試又可細分為定應力、逐步應力或累進應力等方法，本研究則考慮定應力部分加速壽命測試以及逐步應力部分加速壽命測試這兩種方法。選擇以Burr XII分配做為壽命分配，使用最大概似估計法估計分配及加速因子的參數，而假設的樣本資料型態為多重設限樣本資料。使用的最大概似估計法又細分成兩種，第一種是以一般的概似函數為架構，分配的參數估計值及加速因子參數估計值則是經由解出由最大概似法所推導的聯立方程式而得，而解聯立方程式所使用的數值方法則是採用擬牛頓法中的BFGS演算法；第二種方法是考慮EM演算法，EM演算法則是在完全資料的概似函數的架構下進行參數估計。除了估計參數外，同時也推導近似變異數進而計算參數的信賴區間。
模擬的結果驗證了最大概似估計法在這樣的實驗結構下可以得到很好的結果，在定應力部分加速壽命測試的狀況下，相對於EM演算法參數估計的結果，使用BFGS演算法進行最大概似估計的結果較佳。然而，另一部分模擬的結果也顯示，在逐步應力部分加速壽命測試的狀況下，大多數的模擬組合中，EM演算法參數估計的結果則比BFGS演算法的結果佳，尤其在對 k 參數的估計有更佳的表現。

In many life testing and reliability studies, complete information on the failure times of all the experimental units may not be obtained for various reasons. Hence, censoring is very common in life testing experiments. Sometimes the experiments could not be under control completely because units may break accidentally. However, type I and type II censoring schemes do not allow for units to be removed from the test during the life testing duration. Multiple censoring schemes will be a good choice in this situation.
The lifetime of products under normal conditions endures a long period of time because of high reliability of products. So it is difficult to obtain information about the lifetime of products under normal conditions. In order to assure rapid failure and then to shorten the testing period, accelerated life test (ALT) is commonly used to obtain information about the lifetime of products quickly and economically under more severe operation conditions. In ALT, items are run only at stress conditions and the acceleration factor is assumed as a known value. However, sometimes the acceleration factor cannot be assumed as a known value especially when new products are on the testing. In this situation, partially accelerated life test (PALT) will be a good candidate to perform the life tests because the major assumption in PALT is that the stress is not known and cannot be assumed.
PALT can be carried out by various stress schemes, such as constant-stress PALT (CS-PALT), step-stress PALT (SS-PALT), or progressive-stress PALT (PS-PALT). In this study, CS-PALT and SS-PALT are considered. We consider the testing SS-PALT and CS-PALT for the Burr XII distribution. This dissertation considered two maximum likelihood estimation methods. One of the methods was based on observed-data likelihood function. The maximum likelihood estimates were obtained by using BFGS algorithm. The other was based on complete-data likelihood function. The maximum likelihood estimates were derived by using EM algorithm. Asymptotic variance and covariance matrix of the estimators were derived, and confidence intervals of the estimators were also obtained.
Simulation results show that the maximum likelihood estimation perform well in most cases in terms of relative absolute bias, mean bias and root mean square error. The maximum likelihood estimation with BFGS algorithm performs better than EM algorithm in most combinations of simulation conditions in CS-PALT. However, simulation results also show that the maximum likelihood estimation with the EM algorithm outperforms the BFGS algorithm in most cases in SS-PALT.

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