A comparative study of ANI- and ARL-unbiased geometric and CCCG control charts

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.