Lead Time Distribution of Three-Machine Two-Buffer Lines with Unreliable Machines and Finite Buffers
Lead Time Distribution of Three-Machine Two-Buffer Lines with Unreliable Machines and Finite Buffers
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机器不可靠和缓冲区有限的三机两缓冲区生产线的交货时间分布
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Gershwin
中科院分区：
文献类型：
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作者：
Chuan Shi;S. Gershwin
制造系统的提前期是指一个零件在系统中所花费的时间。这一数量很重要，因为客户需要短而可靠的提前期，而且许多产品在储存中会失去价值。它是随机的，因为在生产过程中发生的一些事件，包括不可预测的机器故障，不确定的加工时间和质量变化。提前期的概率分布的知识可以在决定如何设计或操作系统，并在交货日期的承诺是有用的。本文描述了一种确定三台机器、两个缓冲区的生产线的稳态提前期概率分布的解析方法，其中缓冲区是有限的。该方法是最近的工作由作者的概率分布的逗留时间的两个机器线上的扩展。我们考虑参考部分从到达到离开的运动。我们首先计算提前期T = τ的条件概率，给定零件到达时生产线的状态。这是通过求解一组递归方程来完成的，该递归方程是根据对参考部件通过第一缓冲器、从第一缓冲器到第二缓冲器以及通过第二缓冲器的运动的详细分析而开发的。利用三机生产线的稳态概率分布，消除了条件作用。我们提供了两种数值证据，这种方法的准确性。首先，我们证明它满足利特尔定律。然后，我们比较了几种情况下，由新方法计算的分布与模拟提前期分布，并显示非常接近的协议。几个数值例子，然后检查观察的概率分布的形状，以及它们是如何影响的机器的参数和缓冲区的大小。其他数值实验证明了瓶颈的存在和位置的影响。最后，我们提出了未来的研究方向。
The lead time of a manufacturing system is the amount of time a part spends in it. This quantity is important because customers demand short and reliable lead times, and because many products lose value in storage. It is random because of some of the events that occur during the production process, including unpredictable machine failures, uncertain processing times, and quality variations. Knowledge of the probability distribution of lead time can be useful in deciding how to design or operate a system, and in making delivery date commitments. We describe an analytic method for determining the steady-state probability distribution of the lead time of a three-machine, two-buffer production line in which the buffers are finite. The method is an extension of recent work by the authors on the probability distribution of the sojourn time of a two-machine line. We consider the movement of a reference part from its arrival until its departure. We first compute the conditional probability that the lead time T = τ , given the state of the line when the part arrives. This is done by solving a set of recurrence equations which are developed from a detailed analysis of the reference part’s movement through the first buffer, from the first to the second buffer, and through the second buffer. The conditioning is removed by using the steady-state probability distribution of the three-machine line. We provide two kinds of numerical evidence for the accuracy of this method. First, we show that it satisfies Little’s Law. Then we compare the distribution calculated by the new method with the simulated lead time distribution for several cases and show very close agreement. Several numerical examples then are examined to observe the shapes of the probability distributions and how they are influenced by the parameters of the machines and the sizes of the buffers. Other numerical experiments demonstrate the effect of the existence and location of a bottleneck. Finally, we suggest future research directions.