Abstract Geometric charts have an important role in monitoring fraction nonconforming in high-yield processes where the rate of nonconforming is very low, say, parts per million. Currently, the average number of inspected items (ANI) to give an out-of-control (OOC) signal is preferred to the average run length (ARL) in designing and evaluating geometric charts. The ANI carries more information than the ARL because the former considers the number of inspected units contained in each charting point until a signal occurs. Like ARL, the ANI function possesses bias, which results that the chart requiring more items to be inspected to detect an OOC signal rather than a false alarm. In this article, an ANI-unbiased geometric chart is proposed and its performance is compared with the existing ARL-unbiased chart. The study shows that neither is better than the other for all shifts in the process parameter. The study is also extended to the CCCG chart where a group of samples is inspected instead of individual items.

中文翻译：

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ANI 和 ARL 无偏几何和 CCCG 控制图的比较研究

摘要 在不合格率非常低（例如，百万分之几）的高产量过程中，几何图表在监控不合格率方面具有重要作用。目前，在设计和评估几何图表时，给出失控 (OOC) 信号的平均检查项目数 (ANI) 优于平均游程长度 (ARL)。ANI 比 ARL 携带更多信息，因为前者会考虑每个图表点中包含的检查单元数量，直到出现信号。与 ARL 一样，ANI 函数具有偏差，这导致图表需要检查更多项目以检测 OOC 信号而不是误报。在本文中，提出了一种 ANI 无偏几何图，并将其性能与现有的 ARL 无偏图进行了比较。研究表明，对于过程参数的所有变化，两者都不优于另一个。该研究还扩展到 CCCG 图表，其中检查一组样本而不是单个项目。