In data-processing standpoint, an efficient algorithm for identifying the minimum value among a set of measurements are record statistics. In this paper, point estimates are derived for the two parameters of the Exponential distribution based on record statistics with respect to the squared error and Linear-Exponential loss functions and then compared with together. The admissibility of some estimators is discussed. Optimal confidence intervals as well as uniformly most powerful test functions are derived for the two parameters of the Exponential distribution on the basis of such data. Since the assumption of known location parameter tend to be unreliable, we discussed how sensitive the procedure is to the known value of location parameter. We will consider the robustness of the test concerning the behavior of the significance level as well as power function when the location parameter is known. As an illustration, the times between consecutive telephone calls to a company\\\'s switchboard is analyzed using the proposed procedures. Also, some open problems are described.

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