Optimal (T,N,n) preventive replacement first policy for a parallel system

A (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 T, the time when the system successively completes N jobs or the time when the system suffers the n-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 N and n exhibit favorable convexity characteristics. This indicates that we can uniquely determine the optimal N and n under the principle of minimizing the mean cost rate. Furthermore, we find that the mean cost rate cannot be minimized as T 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 T-, N- and n- 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.