The thesis employs Bayesian decision theory to establish acceptance sampling plans for the Weibull lifetime distribution based upon progressively Type-II censored data. Assume that the shape parameter of the lifetime distribution is known, but the scale parameter is random and varies from lot to lot according to a predetermined prior distribution. A loss function involving sampling cost, test cost and decision loss is proposed to describe the Bayes risk. Moreover, an algorithm is suggested to determine the optimal sampling plans which minimize the expected average cost per lot. A sensitivity analysis study is conducted to evaluate the influences of the lot size, the censoring scheme and the parameter of the prior distribution on the proposed sampling plans.