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Using the data for upper record values, the interval estimation for the scale parameter of two-parameter exponential distribution is presented. In addition, two methods for the joint confidence region of two parameters are proposed. In terms of confidence region area, the simulation comparison of two methods of the confidence region is performed in this paper. The criterion of minimum confidence region area is used to obtain the optimal method of the confidence region. To illustrate our proposed interval estimation methods, one biometrical example is used and the corresponding confidence interval length and confidence region area are also calculated. Our research topic is related to the asymmetrical probability distributions and applications across disciplines.