| Abstract: | 在可靠度和壽命試驗中, 我們通常對加諸於實驗的產品之極端或變化的應力要素如溫度,電壓,負載所造成壽命的影響感到有興趣. 逐步應力試驗是加速壽命試驗的一特別情況, 允許我們在試驗的特定時間增加要素強度以較依循正常執行的情況下更為快速而取得有關實驗產品之壽命分配的訊息. 本計劃乃針對來自lognormal 分配的(1) 型I 設限資料, (2) 型I 混合設限資料, (3) 型II 混合設限資料, (4) 一般化型I 和型II混合設限資料, 對簡單逐步應力模式做參數的推論. 由於資料是有所設限, 所以參數的最大概似估計值未必存在. 我們將討論參數的條件最大概似估計值, 並且導出其條件動差生成函數. 我們也希望推導出參數的條件最大概似估計值的機率分配與其他重要統計特性. 最後, 我們會利用實際方法,極限方法,或者靴環法來建立參數的信賴區間. 蒙地卡羅模擬與實際資料應用的結果將會一一整理報告. In reliability and life-testing experiments, we are often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows us to increase the stress levels at fixed times during the experiment in order to obtain the information on the parameters of the life distributions more quickly than under the normal operating conditions. In this project, we consider the simple step-stress model from the lognormal distribution when the available data are (1) Type-I censoring, (2) Type-I hybrid censoring, (3) Type-II hybrid censoring, (4) generalized Type-I and Type-II hybrid censoring. Due to the schemes of censoring, the maximum likelihood estimators (MLEs) of the unknown parameters do not always exist. We shall discuss the conditional MLEs, and derive their conditional moment generating functions. We will also derive the exact conditional distributions of the MLEs and then discuss their properties. We further discuss the exact method of constructing confidence intervals for the unknown parameters as well as the asymptotic method and the bootstrap methods. Monte Carlo simulation results and some illustrative examples will be presented, respectively. |
