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摘要: 为了有效解决同时具有随机失效与退化失效的拉式生产系统的维护问题，提出了基于状态的双阶段预防性维护（Preventive maintenance，PM）策略.首先，根据设备的退化状态、生产端状态以及库存容量构建了系统的状态空间，并利用马尔科夫链描述系统的状态转移.之后，分别以最小化失效率和最大化产出速率为目标，建立了考虑检测周期、看板数量以及预防性维护阈值的综合预防性维护模型.针对设备随役龄增加而故障频发的特点，引入失效率递增因子.最后，给出了最小化失效率和最大化产出速率两种目标下的求解算法，并对决策变量做了敏感性分析.数值实例与现有方案的对比表明了所建模型和算法的有效性.Abstract: To solve the preventive maintenance (PM) problem for a pull production system with both degradation failure and random failure, a two-stage conditional preventive maintenance strategy is proposed. First, the system's state space is built according to the machine's degradation state, the production system's state and the amounts of products in buffers; the state transition matrix is constructed using Markov chain. Then, a joint preventive maintenance and production control optimization model with the goal of minimizing the failure probability and maximizing the throughput rate is built, which takes the inspection period, amounts of Kanban and PM threshold into account simultaneously. Meanwhile, the failure rate increasing factor is introduced into the modeling of the degradation process of machine. Finally, an algorithm for solving the model is proposed, and its sensitivity analysis for key parameters is conducted. Numerical experiments and contrast experiment with the current strategy have verified the effectiveness and efficiency of the proposed model.
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Key words:
- Pull system /
- preventive maintenance (PM) /
- Kanban /
- Markov chain /
- genetic algorithm
1) 本文责任编委 胡昌华 -
图 5 看板数量与检测频率对失效率的作用
Fig. 5 Effect of Kanban$'$s quantity and inspection frequency on ROF
图 6 看板数量与检测频率对可用度的作用
Fig. 6 Effect of Kanban$'$s quantity and inspection frequency on availability
表 1 符号及含义
Table 1 Symbols and definitions
符号 定义 $i$ 退化阶段序号 $j$ 生产端状态 $d$ 退化总阶段 $k$ 库存区产品数量 $K$ 看板最优量(决策量) $ins$ 最优检测速率(决策量) $b_1$ & $b_2$ 阈值(决策量) $\lambda_d$ 退化速率 $\lambda_i$ 阶段$i$的失效速率 $\lambda_a$ 订单到达速率 $\lambda_p$ 订单完成速率 $1/{\lambda _{\rm{ins}}}$ 检测平均间隔期 $1/\mu_{ins}$ 检测平均用时 $1/\mu_r$ 小修平均用时 $1/\mu_{upm}$ UPM平均用时 $1/\mu_{ppm}$ PPM平均用时 $1/\mu_{up}$ 更换平均用时 $UB$ & $LB$ 数值上(下)限 
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表 2 实验参数
Table 2 Experiment parameters
变量 值 实际值 $\lambda_a$ 1.0 接单能力平均100单/天 $\lambda_p$ 1.4 生产能力平均140单/天 $\lambda_d$ 0.02 平均50天退化一个程度 $\lambda_0$ 0.005 初始状态失效间隔期200天 $d$ 8 退化分为8个阶段 $\mu_{ins}$ 0.8 检测平均用时1.25 h $\mu_{r}$ 0.25 小修平均用时4 h $\mu_{upm}$ 1 非完美维护平均用时1 h $\mu_{ppm}$ 0.5 完美维护平均用时2 h $\mu_{up}$ 0.2 更换平均用时5 h
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表 3 $\lambda_a=1.0 $时结果对比
Table 3 Comparison of results when $\lambda_a=1.0$
$\lambda_p$ $ROF$ $K, \lambda_{ins}, b_1, b_2$
$K, \lambda_{ins}, b$$THR$ $K, \lambda_{ins}, b_1, b_2$
$K, \lambda_{ins}, b$${\bf 1.0}$ ${\bf 0.0370} $ ${\bf 6, 0.074, 2, 4} $ ${\bf 0.87} $ ${\bf 10, 0.043, 2, 5}$ $0.0393 $ $7, 0.082, 3 $ $0.82 $ $11, 0.103, 5 $ ${\bf 1.2}$ ${\bf 0.0395} $ ${\bf 10, 0.179, 2, 6} $ ${\bf 0.960 } $ ${\bf 11, 0.149, 3, 5} $ $0.0402 $ $10, 0.152, 4 $ $0.94 $ $11, 0.124, 2 $ ${\bf 1.4}$ ${\bf 0.0339} $ ${\bf 6, 0.074, 2, 4} $ ${\bf 1.001} $ ${\bf 20, 0.035, 6, 7}$ $0.0351 $ $7, 0.081, 3 $ $1.201 $ $19, 0.042, 4 $ ${\bf 1.6}$ ${\bf 0.0297} $ ${\bf 5, 0.151, 2, 6} $ ${\bf 1.202} $ ${\bf 20, 0.018, 5, 8} $ $0.0321 $ $6, 0.181, 1 $ $1.187 $ $21, 0.032, 3 $
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