A comparative study of ANI- and ARL-unbiased geometric and CCC_G 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 CCC_G chart where a group of samples is inspected instead of individual items.

Keywords:

• Average number of inspected items
• average run length
• geometric chart
• high-yield processes
• unbiased chart

SUBJECT CLASSIFICATIONS:

• 62F03
• 62P30

ACKNOWLEDGMENTS

The authors thank the anonymous reviewers, an associate editor, and Editor-in-Chief Professor Nitis Mukhopadhyay for their suggestions, which significantly improved the article.

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

The first author’s work was supported by the Science and Engineering Research Board (SERB), Government of India, under grant number EMR/2017/002281. The second author’s work was supported by a Senior Research Fellowship (SRF) from University Grant Commission (UGC), India, for doctoral program in the Department of Statistics, Banaras Hindu University, Varanasi.