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.