Burr XII分配之型I設限資料的逐步部分加速測試：MLE在小樣本的估計效率

Step Partially Accelerated Life Tests for Burr XII Distribution with Type I Censored Data:MLE Performance in Small Sample

劉家成(Chia-Cheng Liu)

指導教授 ： 陳景祥

淡江大學/管理學院/統計學系碩士班/碩士(2012年)

https://doi.org/10.6846/TKU.2012.00308

摘要

隨著產品可靠性的提升, 在一般條件下的壽命試驗會花費很多時間, 進而耗掉很多成本, 唯一的辦法就是降低樣本個數, 此外要短時間內得到產品的資料也相當困難。為了確保實驗單位能加速失效進而縮短實驗時間, 加速壽命測試經常被用來做為進行壽命實驗的主要架構, 但在一些狀況下,失效模型的加速因子參數是未知狀況下, 特別是當試驗對象為新產品時, 部分加速壽命測試則是另一個很好的選擇。
在小樣本下, 本文研究考慮逐步應力部分加速壽命測試方法, 並選擇以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。分配及加速因子的參數估計值皆是經由推導的聯立方程式計算求得, 除了參數估計外, 本文也同時推導近似變異數且計算參數的信賴區間以比較估計量的實際表現。

關鍵字

部分加速壽命測試 ； 加速因子 ； Burr XII分配 ； 最大概似估計 ； 型I設限資料

並列摘要

The lifetime of products under normal conditions endures a long period of time because of high reliability of products. Reducing the sample size is the only way to solve this problem. It is difficult to obtain information about the lifetime of products under normal conditions. In order to assure rapid failure and then shorten the testing period, accelerated life test (ALT) is commonly used to obtain information about the lifetime of products quickly. In some cases, the failure model relating the lifetime of products and the stress are not known or cannot be assumed, especially for the new products. So step-stress partially accelerated life tests are the optional choice.
This article considers step-stress partially accelerated life tests for small samples under Burr XII distribution. We use maximum likelihood method to estimate the distribution parameters and acceleration factor. The estimates are obtained by solving two nonlinear equations simultaneously. In addition, we also perform simulation of the asymptotic variance and confidence intervals of the parameters to evaluate the empirical performances of our estimators.

並列關鍵字

Partially accelerated life test ； Acceleration factor ； Burr XII distribution ； Maximum Likelihood Estimation ； Type I censored data

參考文獻

[3] Abdel-Ghaly, A.A., Attia, A.F. and Abdel-Ghani, M.M. (2002).The Maximum Likelihood Estimates in Step Partially Accelerated life Tests for the Weibull Parameters in Censored Data. Commincation in Statistics-Theory

[5] Abdel-Ghaly, A.A., El-Khodary, E.H. and Ismail, A.A. (2003). Estimation and Optimal Design in Step Partially Accelerated life Tests for the Compound Pareto distribution using Type II Censoring. Proceeding of the 15st Annual Conference on Statistics and Computer Modeling in Human

[6] Abdel-Ghani, M.M. (2004). The Estimation Problem of the Log Logistic Parameters in Step Partially Accelerated Life Tests using Type I Censored Data The National Review of Social Sciences, 41(2): 1-19.

[7] Abd-Elfattah, A.M., Soliman, A.H. and Nassr, S.G. (2008) . Estimation in Step-Stress Partially Accelerated Life Tests for the Burr Type XII distribution Using Type I censoring. Statistically Methodology,5(6): 502-514.

[8] Abdel-Ghaly, A.A., Attia, A.F. and Abdel-Ghani, M.M. (1996). The Maximum Likelihood Estimates in Step Partially Accelerated Life Tests for the Weibull Parameters in Censored Data. Communication in Statistics -Theory and Methods, 31(4), 551-573.