Abstract The Phase-I analysis is necessary for verification of process stability based on the collected data and for establishing a reference sample for Phase-II monitoring. A large number of schemes designed for this purpose assume normality. In various practical applications, however, process distributions do not always meet the assumption of normality. Therefore, distribution-free schemes are appealing in practice for Phase-I analysis. Only a few distribution-free procedures, to our knowledge, can determine the stability of process location or scale parameters simultaneously via Phase-I analysis. The present research focuses on a new distribution-free Phase-I procedure for dual monitoring of two aspects of a process, namely, location and scale, using a single chart. To this end, we propose a distribution-free Phase-I scheme for bi-aspect monitoring using the multi-sample Cucconi statistic. In-control and out-of-control properties of the new Phase-I Cucconi scheme are studied. The proposed scheme appears to be as good or better than its competitors in terms of various performance metrics in a large number of situations. We demonstrate the design and implementation of the proposed scheme with a practical example.

中文翻译：

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基于多样本 Cucconi 统计的双向监测的新的无分布阶段 I 程序

摘要 第一阶段分析对于基于收集的数据验证过程稳定性和建立第二阶段监测的参考样本是必要的。为此目的而设计的大量方案都假定为常态。然而，在各种实际应用中，过程分布并不总是满足正态性假设。因此，无分配方案在实践中对阶段 I 分析很有吸引力。据我们所知，只有少数免分配程序可以通过阶段 I 分析同时确定过程位置或规模参数的稳定性。目前的研究重点是一种新的无分布的第一阶段程序，用于使用单个图表对过程的两个方面（即位置和规模）进行双重监测。为此，我们提出了一种使用多样本 Cucconi 统计量进行双方面监测的无分布阶段 I 方案。研究了新的 Phase-I Cucconi 方案的控制和失控特性。在许多情况下，就各种性能指标而言，所提议的方案似乎与其竞争对手一样好或更好。我们通过一个实际例子来展示所提出方案的设计和实现。