Asymptotic and finite sample behavior of the time on test estimator under random censorship when lifetimes are not Exponetial

The robustness of the time on test estimator of mean life is studied in both asymptotic and finite sample situations under random censorship. The estimator is shown t o be asymptotically normal and generally in consistent , unless the life time sare exponential . The limiting value of the estimator depends on both the life time and censorship distributions . A simulations tudy of finite sample behavior shows that biases a reslight under exponentiality and serious if exponentia lity is viol at ed . The finite sample behavior is not well described by the limiting normal distribution . Jackknifing produces a useful variance estimate, but is of little value in bias correction.