Abstract: In this paper, we consider the problem of estimating location and scale parameter of an exponential distribution when location parameter space is restricted and the sample size is retained when censored on the right. We propose better estimators than the best affine estimators of location and scale parameters in unrestricated case with respect to the mean square error criterion. These estimators are also compared with respect to Pitman Nearness criterion and some paradoxical results are obtained. The theory developed is applied to the problem of estimating the location and scale parameters of two exponential distribution with the sample size is retained when censored on the right and with the prior imformation of location parameter are ordered