On Estimation Of Mean Life In The Presence Of An Outlier

Life estimation based on an ordered sample from the exponential distribution is considered in the following situations: 1. The first failure occurs at a very early stage of the experiment and is suspected to be an ``early failure´´. 2. The last failure is suspected to come from a population with a higher mean than the rest of the sample. Three estimates of mean life are investigated: sample mean, trimmed mean, and a Winsorized mean. For small samples and in the presence of an early failure, the sample mean is biased but has smaller mean square error than the other two estimates. However, when the last observation has a higher mean than the rest of sample, the sample mean loses its superiority.