在壽命分配參數的估計問題中，經常可自過去的實驗或經驗中知道參數的一些訊息，而貝氏方法即提供了結合過去訊息和現有資料來進行統計推論。本研究將考慮一種多用途的逐步型 II 設限方案，探討在此設限方案下壽命分配參數的估計問題。我們將推導分配參數的貝氏估計量和可靠區間，並同時推導出可靠度函數的貝氏估計量及可靠區間。此外，我們也將推導出未來觀察值的貝氏預測估計量及其最高事後密度區間。對於所提出的方法，我們將進行一些模擬上的比較，並透過實際的例子來闡述我們所得到的結果。 It is often the case that some information is available on the parameter of failure time distribution from previous experiments or analyses of failure time data. The Bayesian approach provides the methodology for incorporation of previous information with the current data. In this study, given a progressively type II censored sample from a Rayleigh distribution, Bayesian estimators and credible intervals will be obtained for the parameter and reliability function. We will also derive the Bayes predictive estimator and highest posterior density prediction interval for future observations. Some numerical examples will be presented for illustration, and some simulation study and comparisons will be performed.
