Sometimes, in reliability studies, neither the life of all failed units nor the number of units still functioning is known at any specific time due to problems such as administrative delays. Consequently, one might consider an estimate of the mean time to failure (MTTF) based only on known failure times of part of the units. An investigation is conducted into the bias and efficiency of such an estimator for either an exponential or a Weibull distribution. In the exponential case, exact expressions are obtained, and, for the Weibull case, a Monte Carlo simulation was used. The estimate of MTTF based on known lifetimes of failed units alone underestimates with smaller variance and higher mean squared error than does the estimate based on the total accumulated lifetime of both failed and surviving units. >