在型I混合設限定應力加速壽命試驗之對數位置尺度分配推論

Inference on Constant Stress Accelerated Life Tests under Log-Location-Scale Lifetime Distributions with Type-I Hybrid Censoring

李効諭(Hsiao-Yu Lee)

指導教授 ： 林千代

淡江大學/理學院/數學學系碩士班/碩士(2017年)

https://doi.org/10.6846/TKU.2017.00901

摘要

本論文延續Hsu（2014）的結果討論對數位置尺度壽命分配在型I混合設限定應力加速壽命試驗的點估計與區間估計。 由於使用最大概似法求得參數，經常不能獲得具體公式求解，因而必須改用數值演算法運算求得。因此，我們提出以近似最大概似估計法所求得的解，作為任何數值演算法的初始值，再進一步求得最大概似估計值。我們特別針對韋伯分配和對數常態分配比較最大概似估計值和近似最大概似估計值的偏差(bias)和均方誤差(mean squared error)。 此外，我們根據最大概似估計值討論四種區間估計:常態近似分配，概似比(likelihood ratio)，和兩個參數跋靴方法(parametric bootstrap methods)。最後，我們用兩個實際例子來說明我們的方法。

關鍵字

近似最大概似估計法 ； 預期費雪信息矩陣 ； 對數線性尺度應力 ； 最大概似估計法

並列摘要

In this thesis, we extend the work of Hsu (2014) to discuss the inference on constant stress accelerated life tests terminated by a hybrid Type-I censoring at the first stress level. The model is based on a general log-location-scale lifetime distribution with mean life which is a linear function of stress, along with constant scale. From the work of Hsu (2014), it is observed that the maximum likelihood estimates (MLEs) of the unknown parameters cannot be obtained in a closed form. We propose the approximate maximum likelihood estimates (AMLEs) and these can be used as initial estimates for any iterative procedure. We then evaluate the bias, and mean square error of these estimators; and provide asymptotic, likelihood ratio, and bootstrap confidence intervals for the parameters of the Weibull and lognormal distributions with the MLE. Finally,the results are illustrated with two examples.

並列關鍵字

Approximated maximum likelihood estimation ； expected Fisher information matrix ； log-linear scale stress relationship ； maximum likelihood method

參考文獻

Banerjee, A. and Kundu, D. (2008). Inference based on Type-II hybrid censored data from a Weibull distribution. IEEE Transactions on Reliability, 57, 369–378.

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