Computation of instant system availability and its applications.

The instant system availability $$S_\tau (t)$$ of a repairable system with the renewal equation was studied. The starting point monotonicity of $$S_\tau (t)$$ was proved and the upper bound of $$S_\tau (t)$$ is also derived. It was found that the interval of instant system availability monotonically decreases. In addition, we provide examples that validate the analytically derived properties of $$S_\tau (t)$$ based on the Lognormal, Gamma and Weibull distributions and the results show that the value of T is slightly smaller than its value defined in Theorem 2. The procedure of using a bathtub as application for this article is also discussed. [ABSTRACT FROM AUTHOR]