Correction for bias in maximum likelihood estimators of in a right–censored normal distribution

It is assumed that the logs of the time to failure in a life test follow a normal distribution. If the test is terminated after r of a sample of n items fail, the test is said to be censored. If the sample size is small and censoring severe, the usual maximum likelihood estimator of a is downwardly biased. Monte Carlo techniques and regression analysis were used to develop an empirical correction factor. Applying the correction factor to the maximum likelihood estimator yields an unbiased estimate of σ.