研究设备的视情预防维修与备件订购策略的联合优化问题。在分析设备劣化与备件库存联合状态转换的基础上,给出了联合状态的稳态概率密度函数的显式表达式和数值求解方法。基于此联合概率密度函数,推导连续劣化的设备受备件库存状态影响的维修概率和备件的订购和持有概率,建立以设备的检测周期、备件订购阈值、预防维修阈值为决策变量,同时考虑维修和备件相关成本的长期平均费用率模型。通过数值试验验证了联合概率密度函数推导的正确性和所建立的模型的有效性。灵敏度分析结果表明维修成本和备件成本之间存在一定的权衡,只有将二者联合优化才能取得设备的全局最优联合策略。以氢气合成装置传输管道的变薄劣化为例验证了模型的实用性。
A jointly condition-based preventive maintenance and spare parts provisioning policy is discussed for equipment maintenance. Based on analysis of all possible transitions of the joint state of equipment and its spare parts inventory, the explicit expression of stationary joint probability density function is derived and its numerical solution is deduced. On the basis of the joint probability density function, the maintenance probabilities of the equipment with the influence of spare parts inventory and the ordering and holding probabilities of its spare parts are derived. Then the expected long-run cost rate model is formulated for the joint policy using the renewal process, taking into account the costs incurred for performing maintenance and managing the spare parts inventory. A numerical experiment is carried out to identify the optimal values for the parameters of the policy, including the inspection interval, the ordering threshold, and the preventive maintenance threshold. The experiment results verify that the derivation of the joint probability density function is correct and the established model is effective. The results of the sensitivity analysis show that a trade-off exists between the maintenance related costs and the inventory related costs, and joint optimization of preventive maintenance and spare parts provisioning policy can ensure a global optimal policy. A practical case is provided to verify the effectiveness of the proposed method.