基于随机系数回归模型的退化过程及维修策略

随机系数回归模型是一种描述设备退化过程的重要模型.在基本随机回归系数模型的基础上,运用加速失效时间模型,加入协变量的影响,对设备的退化过程进行建模分析.针对退化过程设置两类更新阈值,一类是预防性维修更新阈值,一类是故障更新阈值.当设备的运行状态被监测到达到或超过预防性更新阈值时,设备将被预防性维修更新,一个预防性更新周期完成;当设备的运行状态被监测到达到故障阈值时,设备将被故障更新,一个故障更新周期完成.运用更新回报定理,对两类更新周期内的单位时间期望维修费用建立模型,对模型求解可得设备的最优监测区间和最优预防性维修阈值.为进一步对所建立的模型进行验证,设计仿真过程求解最优值,并运用数值案例对所建立的模型和仿真过程进行计算.

Degradation process and maintenance planning based on random coefficient regression model

The random coefficient regression model is a very important model for describing the degradation process. This paper studies the degradation process based on the coefficient regression model, and the covariates are added in the process according to the accelerated failure time model. Two renewal thresholds are studied, one is preventive maintenance renewal threshold, and the other is failure renewal threshold. When the degradation process reaches or exceeds the preventive maintenance renewal threshold, the system should be renewed by preventive maintenance, and then a preventive maintenance renewal cycle is finished; when the degradation process reaches failure renewal threshold, the system should be renewed by replacement, and then a failure renewal cycle is finished. This paper develops the model of the expected cost per unit time in the renewal cycle using the renewal reword theory. A simulation algorithm is developed to verify the cost model. Numerical examples are studied to demonstrate the model and the simulation algorithm.