本論文針對不同逐步設限資料(progressively censored data)探討在 log-gamma 和線性失敗率 (linear failure rate) 模式下的估計問題, 以及在韋伯(Weibull)和對數常態(log-normal)模式下的壽命檢測計劃。在形狀(shape)參數已知的情況下, 我們分別以牛頓法, EM 演算法和修正的 EM 演算法來計算逐步型 II 設限資料(progressively Type-II censored data)下log-gamma 分配之位置(location) 和尺度(scale)參數的最大概似估計值, 並利用條件法和蒙地卡羅法求取位置和尺度參數, 百分位數與可靠度函數的信賴區間。我們又分別利用傳統的貝氏推導方式和馬可夫鏈蒙地卡羅(Markov Chain Monte Carlo)法來求取廣義逐步型 II 設限資料(general progressively Type-II censored data)下線性失敗率分配參數的貝氏估計值和其預測值, 並使用不同先驗(prior)分配來探討這些估計值的敏感性分析(sensitivity analysis)。最後, 我們利用模擬退火演算法(simulated annealing algorithm)找出逐步區間設限計劃 (progressively interval censoring plan) 下雙參數韋伯和對數常態模式的最佳檢測時間(optimally spaced inspection times), 並比較四種不同最佳檢測時間所求得的參數最大概似估計值之漸近相對效率 (asymptotic relative efficiency)。 In this dissertation, we first discuss the estimations of parameters for log-gamma and linear failure rate distributions based on different kinds of progressively censored data. By assuming the shape parameter to be known, we apply three different methods -- Newton-Raphson method, the EM algorithm, and a new modified EM algorithm, to compute the maximum likelihood estimates of location and scale parameters of the log-gamma distribution based on progressively Type-II censored data. We also construct the conditional and unconditional confidence intervals for the location and scale parameters, the quantiles and the reliability function. Next, we employ the conventional Bayesian derivation and the Markov Chain Monte Carlo method to obtain the Bayesian estimates of parameters and predict the missing values and the future samples for the linear failure rate distribution based on the general progressively Type-II censored data. The sensitivity of these estimates to the modest changes in the prior is further examined. We then apply simulated annealing algorithm to determine the optimally spaced inspection times for the Weibull and log-normal distributions for any given progressive interval censoring plan. The comparison of the asymptotic relative efficiencies of the maximum likelihood estimates of the parameters under four different inspection schemes is made at the end.
