In this thesis, we examine a Bayesian single sampling plan for lot by lot sampling under Weibull lifetime istribution with known shape parameter; moreover it is assumed that the scale parameter is random and varies from lot to lot according to a predetermined prior distribution. If products are sold under a warranty policy and the size of test equipments is limited. A cost model is established which involves test cost, accept cost, and reject cost. An algorithm of finding the optimal sampling plans with minimizing the expected average cost per lot is provided, and sensitivity analyses for the parameters of the lifetime and prior distributions are conducted.