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Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (7): 1298-1307    DOI: 10.3785/j.issn.1008-973X.2020.07.007
    
Optimum imperfect inspection and maintenance scheduling model considering delay time theory
Ge-hui LIU(),Shao-kuan CHEN*(),Hua JIN,Shuang LIU,Hong-qin PENG
MOT Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China
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Abstract  

The existing condition-based maintenance methods based on inspection activities were only suitable for short-term schedules and involved only imperfect inspection or maintenance. A long-term optimization model was proposed based on on-site features of system maintenance scheduling by incorporating deterioration process with both imperfect maintenance and inspection activities. The delay time theory was introduced to describe deterioration process of system with double contingencies from imperfect maintenance and inspection. The proposed recursive reliability model can accurately evaluate the deterioration rate and failure rate of system. A maintenance scheduling optimization model was applied to minimize the average cost by searching appropriate inspection cycles and replacement strategy. The reliability and availability constraints were considered to meet the requirement of maintenance. Case studies show that the proposed model can attain optimal inspection strategy with minimum system cost. The accuracy of inspection was crucial for the scheduling optimization model compared with age-based and reliability-based maintenance models. The proposed model with a high accuracy of inspection reached the minimum cost compared to models without inspections.



Key wordsdelay time model      preventive maintenance      imperfect maintenance      inspection cycle      reliability      maintenance cost     
Received: 02 July 2019      Published: 05 July 2020
CLC:  TB 114  
  TP 301  
Corresponding Authors: Shao-kuan CHEN     E-mail: 16114221@bjtu.edu.cn;shkchen@bjtu.edu.cn
Cite this article:

Ge-hui LIU,Shao-kuan CHEN,Hua JIN,Shuang LIU,Hong-qin PENG. Optimum imperfect inspection and maintenance scheduling model considering delay time theory. Journal of ZheJiang University (Engineering Science), 2020, 54(7): 1298-1307.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.07.007     OR     http://www.zjujournals.com/eng/Y2020/V54/I7/1298


基于延迟时间模型的不完全检修计划优化模型

针对现有基于检测的状态维修方法仅适用于短期维修计划,且通常单一地考虑不完全维修或不完全检测的问题,构建适合设备维修现场特征的长期维修计划优化模型,考虑检测与维修活动均不完全情况下的退化过程. 利用延迟时间模型描述退化过程,围绕双重不确定的检修活动,构建基于递推关系的可靠度模型,该模型可以有效表示系统退化速度和故障发生概率. 以单位时间系统费用最小为决策目标,引入可靠度、可用度等约束,建立检修计划优化模型,求解得到最佳检测周期和更换周期. 案例研究表明,利用提出的模型能够有效优化系统检修计划,节省维修成本. 通过与固定周期和固定可靠度阈值的维修策略进行对比,说明检测精度对于检测模型的优化效果具有显著影响,当检测精度属于较高水平时,检修模型明显优于其他维修模型.


关键词: 延迟时间模型,  预防性检修,  不完全检修,  检测周期,  可靠度,  维修费用 
Fig.1 Sketch map of defect detection
Fig.2 Sketch map of failure occurrence
Fig.3 Flow diagram of enumeration optimization algorithm
系统序号 检修参数 退化参数 参数验证
a r m1 l1?1 m2 l2 统计量实际值 统计量参照值 通过检验
1 0.05 0.68 1 0.003 5.347 6 126.344 0 18.364 18.548
2 0.02 1.00 1 0.011 1.857 1 124.111 0 16.465 16.748
3 0.05 0.78 1 0.020 5.678 7 112.360 3 20.936 21.954
4 0.05 0.57 1 0.006 3.063 3 180.541 0 15.475 16.748
5 0.05 0.87 1 0.011 5.639 2 99.360 3 18.325 18.548
Tab.1 Parameters of inspection and maintenance and deterioration process
系统序号 ci/元 cp/元 cr/元 cc/元 ti/h tp/h tr/h tc/h Rmin
1 100 280 1 800 4 000 1.5 3.0 6.0 20.0 0.94
2 80 400 1 600 3 500 0.5 1.0 2.5 25.0 0.94
3 50 150 840 2 750 0.5 1.5 4.5 8.0 0.93
4 100 320 2 150 7 200 2.0 4.0 10.0 15.0 0.92
5 120 500 1 670 9 000 1.5 3.5 6.5 10.0 0.94
Tab.2 Parameters of maintenance costs and reliability
系统 Tmax/d $\bar C$/(元·d?1 T/d τ L/d A Ga/%
1 134 24.27 41 11 451 0.997 66 0.02
2 66 18.84 24 30 720 0.998 61 0
3 93 14.55 27 27 729 0.998 56 0
4 144 40.44 42 7 294 0.996 12 0.06
5 88 34.38 30 23 690 0.996 65 0.01
Tab.3 Optimal solution of inspection model
Fig.4 Analysis of solution procedure
系统 检修策略(P1) 对比策略1:固定周期维修(P2) 对比策略2:固定可靠度阈值维修(P3)
$\bar C$/(元·d?1 T/d L/d ${\bar C_1}$/(元·d?1 Gc/% T1/d L1/d ${\bar C_2}$/(元·d?1 Gc/% R2 L2/d
1 24.27 41 451 21.81 ?10.14 90 450 19.73 ?18.71 0.990 512
2 18.84 24 720 39.89 +111.67 42 126 33.95 +80.14 0.984 152
3 14.55 27 729 16.81 +15.59 61 366 15.04 +3.39 0.988 370
4 40.44 42 294 32.24 ?20.28 92 368 28.80 ?28.77 0.986 477
5 34.38 30 690 37.58 +9.31 65 260 34.39 +0.01 0.984 263
Tab.4 Comparisons of different maintenance strategies
Fig.5 Influence of inspection accuracy on objective values and maintenance schedules
Fig.6 Influence of inspection accuracy on different maintenance strategies
Fig.7 Comparisons of objective values among different maintenance strategies
Fig.8 Variation of probability of preventive maintenance and expected number of failures
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