This paper deals with the problem of a single sampling plan withpolynomial loss for the exponential distribution based on uniformlydistributed random censored data. A Bayes sampling plan is derivedunder various schemes of censoring time. We focus on a quadratic lossand an unit time cost is also considered in the loss. Some optimalBayes solutions are tabulated and some numerical comparisons of risksbetween the proposed plan and that of Lam and Choy(1995) under specialloss are also made. It is shown that their optimal solutions are notBayes in the usual sense.