A Bivariate Maintenance Policy for Multi-State Repairable Systems With Monotone Process

This paper proposes a sequential failure limit maintenance policy for a repairable system. The objective system is assumed to have
$k+1$
states, including one working state and
$k$
failure states, and the multiple failure states are classified potentially by features such as failure severity or failure cause. The system deteriorates over time and will be replaced upon the
$N$
th failure. Corrective maintenance is performed immediately upon each of the first
$(N-1)$
failures. To avoid the costly failure, preventive maintenance actions will be performed as soon as the system's reliability drops to a critical threshold
$R$
. Both preventive maintenance and corrective maintenance are assumed to be imperfect. Increasing and decreasing geometric processes are introduced to characterize the efficiency of preventive maintenance and corrective maintenance. The objective is to derive an optimal maintenance policy
$(R^{\ast},N^{\ast})$
such that the long-run expected cost per unit time is minimized. The analytical expression of the cost rate function is derived, and the corresponding optimal maintenance policy can be determined numerically. A numerical example is given to illustrate the theoretical results and the maintaining procedure. The decision model shows its adaptability to different possible characteristics of the maintained system.