Optimal CUSUM and adaptive CUSUM charts with auxiliary information for process mean

ABSTRACT

The CUSUM chart is good enough to detect small-to-moderate shifts in the process parameter(s) as it can be optimally designed to detect a particular shift size. The adaptive CUSUM (ACUSUM) chart provides good detection over a range of shift sizes because of its ability to update the reference parameter using the estimated process shift. In this paper, we propose auxiliary-information-based (AIB) optimal CUSUM (OCUSUM) and ACUSUM charts, named AIB-OCUSUM and AIB-ACUSUM charts, using a difference estimator of the process mean. The performance comparisons between existing and proposed charts are made in terms of the average run length (ARL), extra quadratic loss and integral relative ARL measures. It is found that the AIB-OCUSUM and AIB-ACUSUM charts are more sensitive than the AIB-CUSUM and ACUSUM charts, respectively. Moreover, the AIB-ACUSUM chart surpasses the AIB-OCUSUM chart when detecting a range of mean shift sizes. Illustrative examples are given to support the theory.

KEYWORDS:

• Adaptive CUSUM
• auxiliary information
• average run length
• difference estimator
• extra quadratic loss
• integral relative average run length
• process mean
• statistical process control

Acknowledgements

The authors are thankful to the three anonymous reviewers for providing useful comments that led to an improved version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Abdul Haq http://orcid.org/0000-0002-4467-9719