Preventive maintenance for coherent systems considering postponed replacement

One primary objective of reliability engineering is to achieve optimal maintenance of technical systems, which ensures they remain in good operating condition. This paper proposes an age-based preventive optimal maintenance policy for $n$-component coherent systems. Under this proposed strategy, the system begins operating at $t=0$ and undergoes preventative maintenance (PM) at a time $T_p$. If the system fails before $T_p$, it will be replaced with a new one. If the system is still functioning at time $T_p$, an assessment is made based on the number of failed components to determine whether the system should be replaced or allowed to continue operating. If the number of failures at $T_p$ is below a predetermined threshold $m$, the PM time $T_p$ is postponed and a new PM time $T_N$ will be scheduled, and the system continues operating in the interval $(T_p,T_N)$. Otherwise, the entire system is preventively replaced at $T_p$ with a new one. In this scenario, we use a cost function to determine the optimal values of decision variables $T_p$, $T_N$, and $m$. To examine the effectiveness of our proposed model, we analyze some examples of coherent systems using graphical and numerical methods.