Estimation in a Random Censoring Model with Incomplete Information: Exponential Lifetime Distribution

Analysis of methods and simulation results for estimating the exponential mean lifetime in a random censoring model with incomplete information are presented. The instant of an item#x2019;s failure is observed if it occurs before a randomly chosen inspection time and the failure was signalled. Otherwise, the experiment is terminated at the instant of inspection during which the true state of the item is discovered. The maximum likelihood method (MLM) is used to obtain point and interval estimates for item mean lifetime, for the exponential model. It is demonstrated, using Monte Carlo simulation, that MLM provides positively biased estimates for the mean lifetime and that the large sample approximation to the log-likelihood ratio produces rather accurate confidence intervals. The quality of the estimates is very little influenced by the value of the probability of failure-to-signal. Properties of the Fisher information in the censored sample are investigated theoretically and numerically.