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Abstract
It is known that observations from any censored life (or competing risk) process can be described by a random censoring (or independent risk) model. On the other hand it is impossible to verify that the censoring is really random. A class of age-dependent censoring processes are defined and the class of corresponding subsurvival functions is described. Exponential life variables censored by independent variables can also be described by age-dependent censoring models if the censoring variable is DFR. The total time on test statistic consistently estimates the expected life of an exponential life variable under random right censoring. If the censoring is age-dependent, the Total Time on Test statistic will severly overestimate the expected life of the variable of interest. Care should be taken to motivate the application of the total time on test statistic in such situations.
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