东北大学学报(自然科学版) ›› 2025, Vol. 46 ›› Issue (7): 71-83.DOI: 10.12068/j.issn.1005-3026.2025.20240193
收稿日期:
2024-10-25
出版日期:
2025-07-15
发布日期:
2025-09-24
通讯作者:
蒋忠中
作者简介:
崔鹏浩(1990—),男,河北保定人,东北大学讲师,硕士生导师
基金资助:
Peng-hao CUI1, Qi-man ZHANG1, Zhong-zhong JIANG1(), Guo-jun SHENG2
Received:
2024-10-25
Online:
2025-07-15
Published:
2025-09-24
Contact:
Zhong-zhong JIANG
摘要:
装配线的产出性能不仅受到机器不可靠性和缓冲空间有限性的影响,还受到线边零件库存的制约.针对考虑线边零件库存的多阶段装配线,研究了其解析建模与性能评估问题.首先,对于单阶段装配线,基于马尔可夫链求得了单阶段装配线系统状态的稳态概率分布.其次,对于两阶段装配线,将单阶段子系统等效为具有1个工作状态和1个故障状态的机器,基于马尔可夫链建立性能评估模型,通过模型求解得到产出率等性能指标的闭集表达式.再次,对于多阶段装配线,提出了聚合方法对主要性能指标进行近似评估.进一步地,通过数值实验验证了性能评估方法的准确性.最后,基于所提出的性能评估方法,通过数值实验分析了多阶段装配线的可逆性及单调性等系统性质.
中图分类号:
崔鹏浩, 张祺曼, 蒋忠中, 盛国军. 考虑线边零件库存的多阶段装配线解析建模与性能评估[J]. 东北大学学报(自然科学版), 2025, 46(7): 71-83.
Peng-hao CUI, Qi-man ZHANG, Zhong-zhong JIANG, Guo-jun SHENG. Analytical Modeling and Performance Evaluation of Multi-stage Assembly Lines with Line-Side Buffers[J]. Journal of Northeastern University(Natural Science), 2025, 46(7): 71-83.
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
0.786 2 | 0.747 4 | 0.727 4 | 0.717 3 | 0.710 3 | 0.705 9 | |
0.784 4 | 0.746 4 | 0.724 7 | 0.712 9 | 0.704 3 | 0.698 6 | |
0.27 | 0.92 | 1.26 | 1.50 | 1.70 | 1.82 |
表1 产出率(Ppr)准确性分析结果
Table 1 Accuracy analysis results of production rate (Ppr)
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
0.786 2 | 0.747 4 | 0.727 4 | 0.717 3 | 0.710 3 | 0.705 9 | |
0.784 4 | 0.746 4 | 0.724 7 | 0.712 9 | 0.704 3 | 0.698 6 | |
0.27 | 0.92 | 1.26 | 1.50 | 1.70 | 1.82 |
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
3.204 9 | 3.325 8 | 3.334 4 | 3.334 6 | 3.350 0 | 3.359 7 | |
3.201 0 | 3.324 7 | 3.332 1 | 3.329 4 | 3.334 8 | 3.330 2 | |
1.08 | 2.35 | 3.37 | 4.12 | 4.43 | 4.81 |
表2 在制品水平(Wb)准确性分析结果
Table 2 Accuracy analysis results of work in process level (Wb)
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
3.204 9 | 3.325 8 | 3.334 4 | 3.334 6 | 3.350 0 | 3.359 7 | |
3.201 0 | 3.324 7 | 3.332 1 | 3.329 4 | 3.334 8 | 3.330 2 | |
1.08 | 2.35 | 3.37 | 4.12 | 4.43 | 4.81 |
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
4.944 2 | 4.595 7 | 4.550 4 | 4.571 7 | 4.550 0 | 4.560 8 | |
4.943 1 | 4.637 2 | 4.592 0 | 4.614 0 | 4.592 6 | 4.603 7 | |
0.02 | 0.84 | 0.86 | 0.88 | 0.89 | 0.89 |
表3 线边零件库存水平(Wl)准确性分析结果
Table 3 Accuracy analysis results of inventory level in the line-side buffers (Wl)
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
4.944 2 | 4.595 7 | 4.550 4 | 4.571 7 | 4.550 0 | 4.560 8 | |
4.943 1 | 4.637 2 | 4.592 0 | 4.614 0 | 4.592 6 | 4.603 7 | |
0.02 | 0.84 | 0.86 | 0.88 | 0.89 | 0.89 |
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
0.062 2 | 0.050 6 | 0.060 8 | 0.065 8 | 0.069 8 | 0.072 5 | |
0.064 3 | 0.052 7 | 0.063 6 | 0.069 2 | 0.073 6 | 0.076 5 | |
0.002 1 | 0.006 3 | 0.009 6 | 0.012 1 | 0.013 4 | 0.014 6 |
表4 阻塞率(Pbl)准确性分析结果
Table 4 Accuracy analysis results of blockage probability (Pbl)
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
0.062 2 | 0.050 6 | 0.060 8 | 0.065 8 | 0.069 8 | 0.072 5 | |
0.064 3 | 0.052 7 | 0.063 6 | 0.069 2 | 0.073 6 | 0.076 5 | |
0.002 1 | 0.006 3 | 0.009 6 | 0.012 1 | 0.013 4 | 0.014 6 |
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
0.058 4 | 0.051 3 | 0.060 2 | 0.065 2 | 0.069 1 | 0.071 0 | |
0.060 5 | 0.053 2 | 0.063 2 | 0.069 2 | 0.073 8 | 0.076 7 | |
0.002 1 | 0.006 5 | 0.009 6 | 0.011 9 | 0.013 3 | 0.014 5 |
表5 饥饿率(Pst)准确性分析结果
Table 5 Accuracy analysis results of starvation probability (Pst)
指标 | ||||||
---|---|---|---|---|---|---|
2 | 4 | 6 | 8 | 10 | 12 | |
0.058 4 | 0.051 3 | 0.060 2 | 0.065 2 | 0.069 1 | 0.071 0 | |
0.060 5 | 0.053 2 | 0.063 2 | 0.069 2 | 0.073 8 | 0.076 7 | |
0.002 1 | 0.006 5 | 0.009 6 | 0.011 9 | 0.013 3 | 0.014 5 |
编号 | 概率参数 | 线边零件库存控制参数 |
---|---|---|
表6 三阶段装配线具体参数
Table 6 Parameters of three-stage assembly lines
编号 | 概率参数 | 线边零件库存控制参数 |
---|---|---|
编号 | 概率参数 | 线边零件库存控制参数 |
---|---|---|
表7 七阶段装配线具体参数
Table 7 Parameters of seven-stage assembly lines
编号 | 概率参数 | 线边零件库存控制参数 |
---|---|---|
编号 | ||||||
---|---|---|---|---|---|---|
1 | [0.45,0.51] | 0.50 | 0.48 | 0.53 | 0.60 | 0.54 |
2 | 0.45 | [0.50,0.59] | 0.48 | 0.53 | 0.60 | 0.54 |
3 | 0.45 | 0.50 | [0.48,0.53] | 0.53 | 0.60 | 0.54 |
4 | 0.45 | 0.50 | 0.48 | [0.53,0.63] | 0.60 | 0.54 |
5 | 0.45 | 0.50 | 0.48 | 0.53 | [0.60,0.70] | 0.54 |
6 | 0.45 | 0.50 | 0.48 | 0.53 | 0.60 | [0.54,0.67] |
表8 三阶段装配线概率参数取值范围及组合情况
Table 8 Efficiency parameters ranges and combination of three-stage assembly lines
编号 | ||||||
---|---|---|---|---|---|---|
1 | [0.45,0.51] | 0.50 | 0.48 | 0.53 | 0.60 | 0.54 |
2 | 0.45 | [0.50,0.59] | 0.48 | 0.53 | 0.60 | 0.54 |
3 | 0.45 | 0.50 | [0.48,0.53] | 0.53 | 0.60 | 0.54 |
4 | 0.45 | 0.50 | 0.48 | [0.53,0.63] | 0.60 | 0.54 |
5 | 0.45 | 0.50 | 0.48 | 0.53 | [0.60,0.70] | 0.54 |
6 | 0.45 | 0.50 | 0.48 | 0.53 | 0.60 | [0.54,0.67] |
编号 | ||||||
---|---|---|---|---|---|---|
7 | [ | 7 | 6 | 2 | 1 | 1 |
8 | 8 | [ | 6 | 2 | 1 | 1 |
9 | 8 | 7 | [ | 2 | 1 | 1 |
10 | 8 | 7 | 6 | [ | 1 | 1 |
11 | 8 | 7 | 6 | 2 | [ | 1 |
12 | 8 | 7 | 6 | 2 | 1 | [ |
表9 三阶段装配线线边零件库存控制参数取值范围及组合情况
Table 9 Value range and combination of threshold parameters for line-side buffers of three-stage assembly lines
编号 | ||||||
---|---|---|---|---|---|---|
7 | [ | 7 | 6 | 2 | 1 | 1 |
8 | 8 | [ | 6 | 2 | 1 | 1 |
9 | 8 | 7 | [ | 2 | 1 | 1 |
10 | 8 | 7 | 6 | [ | 1 | 1 |
11 | 8 | 7 | 6 | 2 | [ | 1 |
12 | 8 | 7 | 6 | 2 | 1 | [ |
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