Life Estimation after Testing for Early Failures

Life estimation based on ordered observations from the exponential distribution is considered for the case when several early failures may be present. The method proposed here requires a preliminary statistical test to decide whether the suspected observations are indeed early failures. The role of the suspected observations (early failures) in the subsequent estimation problem is based on the result of this test. The proposed estimator has, under certain conditions, smaller mean square error than that of the minimum variance unbiased estimator, and its bias remains small.