In life testing, censoring is frequently employed to reduce the amount of time required. Two types of censoring are typically used in practice. One is called Type I censoring, under which the life test is terminated at the predetermined time, and the other Type II censoring, under which the life test is terminated as soon as a fixed number of failures occur. In this thesis, the relative efficiency of the two censoring methods are compared when the lifetime is exponentially distributed. If the primary concern is to estimate the mean lifetime, we suggest a procedure for selecting a censoring method based upon the mean square error of the maximum likelihood estimator, expected number of failures, and expected completion time. When the purpose of the lifetest is for reliability acceptance sampling, we compare the two censoring methods in terms of the power, expected number of failures, and expected completion time. We found that the two censoring methods are similar in terms of power. If the true mean lifetime is close to the value specified by H., then Type I censoring is preferred to Type II censoring in terms of the expected number of failures and expected completion time. If the true mean lifetime is close to the value specified by $H_1$, the reverse is true.
