Condition-based switching and replacement policies for a two-unit warm standby redundant system subject to non-instantaneous switchover

Abstract

This study investigates condition-based switching and replacement policies for a two-unit warm standby redundant system subject to non-instantaneous switchover. The system consists of two identical units: one is operating unit, while the other is standby unit. Two units are under continuous monitoring and degradation described by Gamma processes. Both switching and replacement policies are based on the degradation level of the operating unit. The switching and replacement thresholds are decision variables decided by minimizing the long-run expected cost rate. We first setup the mathematical optimization model and then analyze the global optimal solution of replacement threshold, as well as the existence and uniqueness condition for the local optimal solution of switching threshold (STH). Finally, we find that the optimal replacement threshold is “the bigger the better”, but the optimal STH depends on some optimal conditions which can be easily computed. Numerical examples are provided to verify the policies, and the effects of non-instantaneous switchover and cost ratio on optimal STHs are numerically discussed.