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摘要: 装配系统是生产系统的基本结构之一, 广泛应用于汽车、电器、电子产品等实际生产环境中.与传统的串行生产线取得的研究成果相比, 装配系统的研究, 特别是对系统暂态过程的实时性能分析的研究仍然未得到深入探讨.本文针对具有三台几何可靠性机器模型和有限缓冲区容量框架下的装配系统, 首先建立了用于此类系统暂态性能分析的数学模型, 通过马尔科夫方法导出了系统性能分析的解析公式.然后, 提出了一种基于分解的性能评估算法来近似系统的实时性能.具体来说, 本文推导出了用于计算具有三台几何可靠性机器模型的装配系统的实时生产率、消耗率、在制品数量, 以及完成一个生产批次所需时间的解析表达式.最后, 通过数值实验对所提出算法的准确性进行验证.Abstract: Assembly system is one of the most fundamental production system structures. It can be widely seen in practical manufacturing environments (e.g., automomobile, appliance, consumer electronics). Compared to the extensive investigations of serial lines in the existing literature, investigations on assembly systems, especially transient-based realtime performance analysis, are still largely unexplored. In the framework of assembly systems with three geometric machines and finite buffers, a mathematical model for real time performance analysis of such systems is developed in this paper. The formulas for exact performance analysis are derived by using the Markovian approach first. Then, a decomposition-based computationally efficient algorithm for real-time performance evaluation is proposed. Specifically, closed-form formulas are derived for calculating real-time production rate, consumption rates, as well as work-in-process, completion time on completing a production run, of assembly systems with three geometric machines. Finally, the accuracy of the algorithm is justified by numerical experiments.
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Key words:
- Assembly systems /
- performance evaluation /
- geometric reliability machine model /
- production system
1) 本文责任编委 段书凯 -
图 5 三台几何可靠型机器装配系统的数值实例
Fig. 5 Example of an assembly system with three geometric machines
图 6 基于分解的近似方法与仿真分析的三台几何可靠型机器装配系统实时性能评估对比
Fig. 6 Comparison of decomposition-based approximation and simulation analysis for real-time performance evaluation in assembly system with three geometric machines
表 1 系统状态排序
Table 1 Arrangement of the system states
State $ h_1 $ $ h_2 $ $ f_0 $ $ s_0 $ $ s_1 $ $ s_2 $ $1$ 0 0 0 0 0 0 $2$ 0 0 0 0 0 1 $3$ 0 0 0 0 1 0 $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $9$ 0 0 1 0 0 0 $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ 8 $B+1$ 0 0 $B$ 0 0 0 8 $B+2$ 0 0 $B$ 0 0 1 $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $Q-1$ $N_1$ $N_2$ $B$ 1 1 0 $Q$ $N_1$ $N_2$ $B$ 1 1 1 
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表 2 系统状态排序($k = 0, 1, \cdots, N_1$)
Table 2 Arrangement of the system states ($k = 0, 1, \cdots, N_1$)
State $ h_1$ $ s_1$ $ s_0^u$ $4k+1$ $k$ 0 0 $4k+2$ $k$ 0 1 $4k+3$ $k$ 1 0 $4k+4$ $k$ 1 1
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