In a number of life-testing experiments, there exist situations where the monitoring breaks down for a temporary period of time. In such cases, some parts of the ordered observations, for example the middle ones, are censored and the only outcomes available for analysis consist of the lower and upper order statistics. Therefore, the experimenter may not gain the complete information on failure times for all experimental units. So, the accuracy of some statistical inferences may be decreases. In this paper, the effect of reconstructing missing order statistics on the performance of the maximum likelihood estimator (MLE) of the mean of the exponential distribution is investigated. To illustrate the proposed procedure in the paper, a real example is presented and using a simulation study, it will be shown that the reconstructing missing order statistics improves the estimation of the parameter of interest.