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In the reliability analysis of large structures, usually only a very small sample can be tested. Hence, the expected time to first failure and possibly the expected value of the time interval between the first and the second failures are much more significant measures than the mean time to failure or any related measure of the central tendency of the distribution of times to failure. In the present report, general expressions for these expected values and associated variances are derived and numerical computations are carried out using three types of distribution of the time to failure; (1) the logarithmic normal distribution (2) the gamma distribution and (3) the third asymptotic distribution of extreme (smallest) values. The results are presented in the form of diagrams.