| Abstract: | 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 we 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, we establish a vector Markov process and hence transfer the problem to the solution of a system of integrodifferential equations. We can then obtain explicit formulas for the steady-state system availability and failure frequency, respectively. In concluding this article we make some conjectures on series systems and point out future research opportunities. © 1996 John Wiley & Sons, Inc. |
