Availability analysis of a two-unit series system with a priority shut-off rule

This study shows that the steady-state availability of a two-unit series system, which operates under a one-direction shut-off rule with a preemptive repair priority for unit 1, depends only on the first-order system parameters. First the authors obtain both transient and steady-state system availability and failure frequency when the lifetime of Unit 1 is Erlang and the other distributions are general. When the lifetime of Unit 1 is general, the system process has no regenerative point. Using supplementary variables, the authors establish a vector Markov process and hence transfer the problem to the solution of a system of integrodifferential equations. They can then obtain explicit formulas for the steady-state system availability and failure frequency, respectively. In concluding this article the authors make some conjectures on series systems and point out future research opportunities.