由於現今科技的發達，產品的效能都比以往提高了許多。對製造商而言，產品壽命的檢測是關鍵工作之一。在工業統計領域，我們常應用加速壽命檢定的方式來檢測我們的產品。通常在加速檢定的領域當中，最常被人所運用的是產品壽命與壓力間呈現一個對數線性的關係。然而，在本文中，我們提出一個含有隨機誤差項的合理假設，目的是為了修正上述古典假設下可能會受到其他不確定的因素如溫度、溼度、電壓穩定度等等因素(許多是難以控制的)而影響實際的結果。在這個新的架構下，我們運用了在平方損失函數下貝氏估計法、最小平方法、邊際最大概似法當作本研究的分析方法 In modern technology, lifetimes of the products have been improved significantly so that life of a product has been much longer than ever before. In order to shorten times of experiments, accelerated life test(ALT) is usually applied for life testing. It is well-known and also most of the research in such area follow that the relationship between lifetime and stress is log-linear. However, in many occasions, due to incontrollable situations such as temperature, humidity, stability of electric voltage etc., such log-linear relationship is violated. Accordingly, in this paper we propose a new model with random error term for the relationship between lifetime and stress. A Bayesian approach under squared loss and some maximum likelihood principal for marginal density are proposed and studied.