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This paper addresses the assessment of simple system availability when there is concern about (a) time-dependence, so demands for system performance are not necessarily when the system is in steady-state,' as is often assumed, and when (b) information about system failures and repairs is in the form of observed data so questions of statistical influence arise. The methods and models involved lean towards the semi-parametric or non-parametric; in particular we employ the empirical Laplace transform in the time-dependent scenarios of interest. The authors propose analytically simple approximations to time-dependent system behavior, and assess the effects of model specification (up and down time dependence) upon rates of approach to a long-run steady state as the latter are estimated from available data (assumed to be a random sample).