In this thesis, a Bayesian accelerated life testing model for the scale parameter of Weibull distirbution with the inverse power law is proposed. We assume that the prior information of the scale parameter is given in the form of gamma distribution and shape and power parameters are constants. Maximum likelihood and least squares methods are used for estimating the life distribution at use condition from the failure data under acclerated condition. Monte Carlo study is made for perfomance comparison of the above two methods.