指數型設限資料的貝氏計量值抽樣計畫

Bayesian Variable Sampling Plans for the Exponential Distribution Based on Censored Samples

黃彥龍(Yen-Lung Huang)

指導教授 ： 林千代

淡江大學/理學院/數學學系博士班/博士(2010年)

https://doi.org/10.6846/TKU.2010.01119

摘要

本論文首先提出一個新的修正逐步混合型I設限計畫。然後，我們根據 Childs et al. (2003) 和 Childs et al. (2008) 的結果推導出指數型I設限和修正的逐步混合型I及型II設限資料下之最大概似估計值的分配。利用不同設限資料下所得之最大概似估計值的分配，我們分別針對簡單和一般性的損失函數建立抽樣計畫之貝氏風險函數，再應用 Lam (1994) 的離散分割法或模擬退火演算法找出最佳的抽樣計畫。最後，我們呈現一些數據及比較來驗證本論文所提出的方法之有效性及穩定性。

關鍵字

貝氏風險 ； 離散分割法 ； 最大概似估計法 ； 普通的混合設限 ； (修正) 逐步混合設限 ； 模擬退火演算法

並列摘要

In this dissertation, we propose a new adaptive Type-I progressive hybrid censoring scheme. We follow the work of Childs et al. (2003) and Childs et al. (2008) to derive the exact distributions of the maximum likelihood estimator of the mean lifetime of an exponential distribution under Type-I censoring and both types of adaptive progressive hybrid censoring schemes. Based on the distributions of maximum likelihood estimator, we obtain the explicit expressions for the Bayes risks of sampling plans when a simple or general loss function is used. The discretization method of Lam (1994) and the simulated annealing algorithm are then used to determine the optimal sampling plans under different censoring schemes. Some numerical examples and comparisons are presented to illustrate the effectiveness of the proposed method.

並列關鍵字

Bayes risk ； Discretization method ； Maximum likelihood estimation ； Ordinary hybrid censoring ； (Adaptive) Progressive hybrid censoring ； Simulated annealing algorithm

參考文獻

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Balakrishnan, N., Childs, A. and Chandrasekar, B. (2002).An efficient computational method for moments of order statistics under progressive censoring. Statistics and Probability Letters 60, 359--365.

Chandrasekar, B., Childs, A. and Balakrishnan, N. (2004). Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring. Naval Research Logistics 51, 994--1004.

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