| 摘要: | 本計劃提出一個新的逐步型I混合設限策略. 此策略不但可使壽命檢測實驗於固定時間中止, 也比已知的逐步型I混合設限策略提供更有效的訊息. 本計劃將首先針對Weibull分配在逐步型I混合設限策略下作參數的點估計和區間估計. 在點估計的討論中, 本計劃將分別用最大概似估計及貝式估計. 而貝式估計將使用Lindley (1980) and Tierney and Kandane (1986)逼近法以及馬可夫鏈模擬法來分析. 然後, 本計劃將根據最大概似估計的變異及共變異矩陣之Trace和行列式, 還有Fisher訊息矩陣之Trace來討論最佳的逐步型I混合設限策略及其敏感度檢測. 另外, 也會根據 Zhang and Meeker (2005)和Gupta and Kundu (2006)討論的訊息準則作貝式壽命檢測計劃的分析, 並觀察這兩種最佳的逐步型I混合設限策略(非貝式與貝式)的差異. 最後, 本計劃將根據Chen et al. (2007)提出的二次損失函數討論在四種混合設限策略下指數分配之最佳抽樣計劃. 本計劃將分別推導出在各種混合設限策略下貝式風險的具體公式, 並且利用數值方法取得最佳貝式抽樣計劃, 並檢驗其穩定性.
In this project, we propose an adaptive Type-I progressive hybrid censoring scheme (adaptive Type-I PHCS), which assures the termination of the life-testing experiment at a fixed time T and result in highly efficient methods as compared with the Type-I PHCS. We will first discuss the maximum likelihood estimation and Bayesian estimation for the two-parameter Weibull distribution under adaptive Type-I progressively hybrid censored scheme. The Bayes estimates of unknown parameters are obtained by using the approximation forms of Lindley (1980) and Tierney and Kandane (1986) as well as Markov Chain Monte Carlo technique. Next, we plan to investigate the optimal adaptive progressive hybrid censoring plans subject to (i) minimization of the trace of the variance-covariance matrix of the MLEs, (ii) minimization of the determinant of the variance-covariance matrix of the MLEs, and (iii) maximization of the trace of the Fisher information matrix. We also plan to examine the sensitivity of the optimal censoring plan by determining the change in efficiency of censoring plans departing a little from the optimal one. Another possible way to choose the optimum censoring scheme among possible different schemes is to define the information measure for a particular sampling scheme, which is the inverse of the asymptotic variance of the 100p-th quantile estimator obtained using the adaptive progressive hybrid censoring scheme. We shall investigate the Bayesian life testing plan subject to this information measure. A comparison between these two approaches shall be also made. Finally, we shall extend the results of Lin et al. (2008b) to develop the sampling plans for the exponential distribution under the adaptive Type-I and Type-II progressive hybrid censoring schemes, and Type-I and Type-II progressive hybrid censoring schemes discuss in Childs et al. (2008), respectively, when a general quadratic loss function proposed by Chen et al. (2007) is used. The explicit expressions of the Bayes risk of a sampling plan under the selected progressive hybrid censoring schemes shall be established. We shall also conduct some numerical comparisons between the proposed optimal sampling plans and perform the study of the robustness. |
