Optimal (<italic>T</italic>,<italic>N</italic>,<italic>n</italic>) preventive replacement first policy for a parallel system.

AbstractA (T,N,n) preventive replacement first (PRF) policy is proposed in this article to investigate a parallel system with two independent parts where the secondary part is in a cold-standby state initially. Before the system fails completely, a preventive replacement is carried out at the planned time <italic>T</italic>, the time when the system successively completes <italic>N</italic> jobs or the time when the system suffers the <italic>n</italic>-th type-I failure, whichever occurs first. The system deteriorates stochastically, and it may experience two types of failures: type-I (repairable or minor) failure and type-II (non repairable or catastrophic) failure. When the system suffers a type-II failure, it’s correctively replaced. This model is widely applied in real-life scenarios, especially in the aviation industry. Under the single-parameter optimization scenario, both cost-minimal <italic>N</italic> and <italic>n</italic> exhibit favorable convexity characteristics. This indicates that we can uniquely determine the optimal <italic>N</italic> and <italic>n</italic> under the principle of minimizing the mean cost rate. Furthermore, we find that the mean cost rate cannot be minimized as <italic>T</italic> is less than a certain threshold, which implies that the planned time of the preventive replacement should not be implemented too early. In addition, the optimal multi-dimensional replacement policy that minimizes the mean cost rate can be uniquely obtained by theoretical or numerical analysis. Our proposed model provides a versatile formulation for analyzing a large variety of replacement policies. Compared with previous literature, the PRF policy adopted in this article integrates <italic>T</italic>-, <italic>N</italic>- and <italic>n</italic>- control policies, making it more comprehensive. It’s of practical significance for relevant enterprises to make decisions, assisting them in minimizing the mean cost rate while enhancing system reliability. [ABSTRACT FROM AUTHOR]