Series machines, i.e., machines (which are usually unreliable) arranged in series with no buffering, are pervasive in production systems. In the analysis, design, and optimization of the series-machine system, the efficiency analysis is one of the most fundamental issues. There are not a lot of researches analyzing the efficiency of the series-machine system, and almost all of them assume that the system operates under type-I failure mechanisms (i.e., the breakdown of a machine could make all other series machines forced down) rather than under type-II mechanisms (i.e., the breakdown of a machine does not make any other series machines forced down). The reason that the type-I failure mechanisms are usually assumed in the literature is that the analysis of the series-machine system under type-II mechanisms is much more complex than under type-I mechanisms, although type-II mechanisms are more common in practice. To thoroughly and systematically estimate the efficiency of the series-machine system, in this paper, we propose a unified analytical approach to investigate the efficiency under both type-I and type-II failure mechanisms. Both cases of deterministic and random cycle times are considered. Different from under type-I failure mechanisms, analytical expressions of the efficiency of series-machine systems under type-II failure mechanisms are extremely hard to obtain, and thus, limit bounds of the efficiency are derived and algorithms are developed to calculate its exact value. Results show that the series-machine system under type-II failure mechanisms is more efficient than under type-I mechanisms, which, intuitively making sense, is the reason that type-II mechanisms are more common in the industry.

中文翻译：

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估算生产线中系列机器效率的分析方法


串联机器，即无缓冲串联排列的机器（通常不可靠），在生产系统中普遍存在。在串机系统的分析、设计和优化中，效率分析是最基本的问题之一。分析串机系统效率的研究并不多，几乎所有的研究都假设系统在I类故障机制下运行（即一台机器的故障可能导致所有其他串机被迫停机）而不是在II型机制下（即，一台机器的故障不会使任何其他系列的机器被迫停机）。文献中通常假设 I 类故障机制的原因是，II 类机制下的串机系统的分析比 I 类机制下的分析要复杂得多，尽管 II 类机制在实践。为了彻底、系统地估计串联机器系统的效率，在本文中，我们提出了一种统一的分析方法来研究 I 类和 II 类故障机制下的效率。考虑确定性和随机循环时间两种情况。与I类故障机制下不同，II类故障机制下串机系统效率的解析表达式极难获得，因此推导了效率的极限值并开发了算法来计算其精确值。结果表明，II 类故障机制下的串机系统比 I 类机制下的效率更高，直观上讲，这就是 II 类机制在行业中更常见的原因。