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Sequential Window Problems

机译：顺序窗口问题

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Window problems have an important application when there is concern about the clustering of nonconforming units or when there is an early surge of information that allows us to terminate an experiment sooner than usual. Motivated by these ideas, in this paper we use probability generating functions to study the stopping rules and their effects related to waiting time random variables. The use of windows introduces many new challenging probability questions, but it also requires basic tables that are not now available; some of these tables are included in the present paper. Since waiting-time random variables and scan statistics are closely related, the exact results and the computational method in this paper could also be useful in scan statistics. In the final section we apply the sequential-window concept to the possibility of changing the usual rules for a chess tournament and show that they could lead to a smaller expected number of games and to a higher chance of finding the better player.
机译：当担心不合格单元的聚类或信息的激增使我们比平时更早终止实验时，窗口问题将成为重要的应用。受这些想法的激励，本文中我们使用概率生成函数来研究停止规则及其与等待时间随机变量相关的影响。 Windows的使用引入了许多新的具有挑战性的概率问题，但是它也需要基本的表格，这些表格现在不可用。其中一些表包含在本白皮书中。由于等待时间随机变量和扫描统计信息密切相关，因此本文的准确结果和计算方法也可能对扫描统计信息有用。在最后一节中，我们将顺序窗口概念应用于更改国际象棋锦标赛的常规规则的可能性，并表明它们可能导致预期的比赛次数减少，并有更高的机会找到更好的球员。

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