﻿ 带失效的拉式生产系统预防性维护建模
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 自动化学报  2018, Vol. 44 Issue (6): 1045-1052 PDF

1. 同济大学机械与能源工程学院 上海 201804

Preventive Maintenance Modeling of Pull System With Failures
ZHOU Bing-Hai1, LIU Zi-Long1
1. School of Mechanical Engineering, Tongji University, Shanghai 201804
Manuscript received : November 14, 2016, accepted: February 6, 2017.
Foundation Item: Supported by National Natural Science Foundation of China (71471135)
Corresponding author. ZHOU Bing-Hai  Professor at the School of Mechanical Engineering, Tongji University. His research interest covers modeling, scheduling, simulation, and control in integration of manufacturing systems, reliability and preventive maintenance model for systems. Corresponding author of this paper
Recommended by Associate Editor HU Chang-Hua
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.
Key words: Pull system     preventive maintenance (PM)     Kanban     Markov chain     genetic algorithm

1 问题描述

 图 1 拉式生产系统 Figure 1 Pull production system

 \begin{align} &F(s, fd) =\notag\\ &\quad\ \begin{cases} (i + 1, j, k), & i \in [0, d - 1], ~j = 0, \\&k \in [0, K - 1] \\[1.5mm] (i + 1, j - 2, k), & i = d, ~j = 0, \\& k \in [0, K - 1] \end{cases} \end{align} (5)

$fs$事件使$j$由0转换为$-1,$表示为

 \begin{align} F(s, fs) =&\ (i, j - 1, k), \notag\\ &\ i \in [0, d], ~j = 0, ~ k \in [0, K - 1] \end{align} (6)

 \begin{align} F(s, upm) =&\ (i - 1, j - 2, k), \nonumber\\ &\ i \in [{b_1}, {b_2} - 1], ~j = 2, ~k \in [0, K] \end{align} (10)

$ppm$事件使系统"修复如新", $i$回归到状态0, 平均时长为$1/\mu_{ppm}$, 即

 \begin{align} F(s, ppm) =&\ (0, j - 3, k), \notag\\ &\ i \in [{b_2}, d], ~ j = 3, ~k \in [0, K] \end{align} (11)

7) 更新($up$).退化阶段处于$d+1$时, 则要进行更新操作.由于设备只有在加工时才会退化, 所以$k$值最大为$K-1$. $up$事件同样可使系统"修复如新", 所用时长为$1/\mu_{up}$, 即

 \begin{align} F(s, up) =&\ (0, j + 2, k), \notag\\ &\ i = d + 1, ~j = - 2, ~ k \in [0, K - 1] \end{align} (12)

 图 2 系统状态转移图 Figure 2 System state transition diagram
2.3 状态空间

 \begin{align} Q=\left[ \begin{matrix} {{q}_{11}}&{{q}_{12}}&\ldots &{{q}_{1m}} \\ {{q}_{21}}&{{q}_{22}}&\ldots &{{q}_{2m}} \\ \vdots &\vdots &\ddots &\vdots \\ {{q}_{m1}}&{{q}_{m2}}&\ldots &{{q}_{mm}} \\ \end{matrix} \right] \end{align} (13)

 \begin{align} \pi \times Q=0, \quad \text{s}\text{.t}\text{.}~\sum\limits_{n=1}^{m}{{{\pi }_{{{s}_{n}}}}}=1 \end{align} (14)

 \begin{align} AVA= \sum\limits_{k = 0}^K {\sum\limits_{i = 0}^d {{\pi _{i, 0, k}}} } \end{align} (15)

 \begin{align} UTI = \sum\limits_{k = 0}^K {\sum\limits_{i = 0}^d {{\pi _{i, 0, k}}} } - \sum\limits_{i = 0}^d {{\pi _{i, 0, K}}} \end{align} (16)

 \begin{align} THR = {\lambda _p} \times \left(\sum\limits_{k = 0}^K {\sum\limits_{i =0}^d {{\pi _{i, 0, k}}} } - \sum\limits_{i = 0}^d {{\pi _{i, 0, K}}} \right) \end{align} (17)

 \begin{align} ROF = {\lambda _d} \times \sum\limits_{k = 0}^{K - 1} {{\pi_{d, 0, k}}} + \sum\limits_{k = 0}^{K - 1} {\sum\limits_{i = 0}^d {{\lambda _i} \times{\pi _{i, 0, k}}} } \end{align} (18)

 \begin{align} BUF =&\ \sum\limits_{k = 0}^K (k \times(\sum\limits_{i = 0}^d {({\pi _{i, 0, k}} + {\pi _{i, 1, k}})}\, +\nonumber\\&\ {\sum\limits_{i = {b_1} + 1}^{{b_2}} {{\pi _{i, 2, k}} + } } \sum\limits_{i = {b_2} + 1}^d {{\pi _{i, 3, k}}))}\, + \nonumber\\&\ \sum\limits_{k = 0}^{K - 1} {(k} {\pi _{d + 1, - 2, k}} + \sum\limits_{i = 0}^d {k{\pi _{i, - 1, k}}} ) \end{align} (19)

 \begin{align} & {\rm object}:\quad \min~ROF~~(\mbox{或}~\max~ THR) \notag \\ &{\rm s.t.}\qquad\quad~ THR \geq L{B_{{{\rm THR}}}}~~(\mbox{或}~ ROF \leq U{B_{\rm ROF}})\notag \\ & \qquad\qquad~~ 1 \leq K \leq U{B_K} \notag \\ & \qquad\qquad~~ 1 \leq {b_1} < {b_2}, ~\, 2 \leq {b_2} < d\notag \\ & \qquad\qquad~~ L{B_{{\lambda _{ins}}}} \leq {\lambda _{ins}} \leq U{B_{{\lambda _{ins}}}} \end{align} (20)
3 数值实验 3.1 求解方法

3.2 敏感性分析

 图 3 决策变量对系统的影响 Figure 3 Effects of decision variables on system

 图 4 失效率递增因子对可用度的影响 Figure 4 Effect of increase factor on availability
 图 5 看板数量与检测频率对失效率的作用 Figure 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 Figure 6 Effect of Kanban$'$s quantity and inspection frequency on availability
3.3 最佳维护策略

4 结论

 1 Ji M, He Y, Cheng T C E. Single-machine scheduling with periodic maintenance to minimize makespan. Computers and Operations Research, 2007, 34(6): 1764-1770. DOI:10.1016/j.cor.2005.05.034 2 Lu S S, Tu Y C, Lu H T. Predictive condition-based maintenance for continuously deteriorating systems. Quality and Reliability Engineering International, 2007, 23(1): 71-81. DOI:10.1002/(ISSN)1099-1638 3 Pan E S, Liao W Z, Xi L F. Single-machine-based production scheduling model integrated preventive maintenance planning. The International Journal of Advanced Manufacturing Technology, 2010, 50(1-4): 365-375. DOI:10.1007/s00170-009-2514-9 4 Fitouhi M C, Nourelfath M. Integrating noncyclical preventive maintenance scheduling and production planning for a single machine. International Journal of Production Economics, 2012, 136(2): 344-351. DOI:10.1016/j.ijpe.2011.12.021 5 Nourelfath M, Fitouhi M C, Machani M. An integrated model for production and preventive maintenance planning in multi-state systems. IEEE Transactions on Reliability, 2010, 59(3): 496-506. DOI:10.1109/TR.2010.2056412 6 Brundage M P, Chang Q, Li Y, Arinez J, Xiao G X. Utilizing energy opportunity windows and energy profit bottlenecks to reduce energy consumption per part for a serial production line. In: Proceedings of the 2014 IEEE International Conference on Automation Science and Engineering. Taipei, China: IEEE, 2014. 461-466 7 Golmakani H R. Optimal age-based inspection scheme for condition-based maintenance using A* search algorithm. International Journal of Production Research, 2012, 50(23): 7068-7080. DOI:10.1080/00207543.2012.664793 8 Golmakani H R, Pouresmaeeli M. Optimal replacement policy for condition-based maintenance with non-decreasing failure cost and costly inspection. Journal of Quality in Maintenance Engineering, 2014, 20(1): 51-64. DOI:10.1108/JQME-12-2012-0044 9 Karamatsoukis C C, Kyriakidis E G. Optimal maintenance of two stochastically deteriorating machines with an intermediate buffer. European Journal of Operational Research, 2010, 207(1): 297-308. DOI:10.1016/j.ejor.2010.04.022 10 Lu Zhi-Qiang, Zhang Si-Yuan, Cui Wei-Wei. Integrating production scheduling and maintenance policy for robustness in flow shop problems. Acta Automatica Sinica, 2015, 41(5): 906-913.( 陆志强, 张思源, 崔维伟. 集成预防性维护和流水线调度的鲁棒性优化研究. 自动化学报, 2015, 41(5): 906-913.) 11 Gao Wen-Ke, Zhang Zhi-Sheng, Zhou Yi-Fan, Liu Yang, Liu Qi. Reliability modeling and maintenance policy for main and supplementary parallel system with failure interaction and imperfect detection. Acta Automatica Sinica, 2015, 41(12): 2100-2114.( 高文科, 张志胜, 周一帆, 刘飏, 刘祺. 存在故障相关及不完备检测的主辅并联系统可靠性建模与维修策略. 自动化学报, 2015, 41(12): 2100-2114.) 12 Lavoie P, Gharbi A, Kenné J P. A comparative study of pull control mechanisms for unreliable homogenous transfer lines. International Journal of Production Economics, 2010, 124(1): 241-251. DOI:10.1016/j.ijpe.2009.11.022 13 Khojasteh Y, Sato R. Selection of a pull production control system in multi-stage production processes. International Journal of Production Research, 2015, 53(14): 4363-4379. DOI:10.1080/00207543.2014.1001530 14 Thürer M, Stevenson M, Protzman C W. Card-based production control:a review of the control mechanisms underpinning Kanban, ConWIP, POLCA and COBACABANA systems. Production Planning and Control, 2016, 27(14): 1143-1157. 15 Xanthopoulos A S, Koulouriotis D E, Botsaris P N. Single-stage Kanban system with deterioration failures and condition-based preventive maintenance. Reliability Engineering and System Safety, 2015, 142: 111-122. DOI:10.1016/j.ress.2015.05.008 16 Ezema C N, Nonum E O, Umezinwa C N, Igwe J I. Optimal performance enhancement using JIT manufacturing system simulation model. International Journal of Technology and Systems, 2016, 1(1): 48-71. 17 Batra R, Nanda S, Singhal S, Singari R. Study of Lean Production System Using Value Stream Mapping in Manufacturing Sector and Subsequent Implementation in Tool Room. SAE Technical Papers, Delhi Technological University, India, 2016. 18 Qi Fa-Qun, Zhou Bing-Hai. Preventive maintenance policy of cluster tools based on Markov process. Journal of Shanghai Jiaotong University, 2014, 48(10): 1461-1467.( 綦法群, 周炳海. 基于Markov过程的集束型设备预防维护策略. 上海交通大学学报, 2014, 48(10): 1461-1467.) 19 Xia Tang-Bin, Zhou Xiao-Jun, Xi Li-Feng. Multi-attribute model for dynamic preventive maintenance decision with hybrid evolution factors. Journal of Shanghai Jiaotong University, 2009, 43(5): 821-824.( 夏唐斌, 周晓军, 奚立峰. 基于失效率调整因子的多目标动态预防性维护决策建模. 上海交通大学学报, 2009, 43(5): 821-824.) 20 Zhou B H, Liu Z L. Optimizing preventive maintenance:a deteriorating system with buffers. Industrial Management and Data Systems, 2016, 116(8): 1719-1740. DOI:10.1108/IMDS-01-2016-0026