Enhanced adaptive CUSUM charts for process mean

ABSTRACT

A statistical quality control chart is an important tool of the statistical process control, which is widely used to control and monitor a production process. The CUSUM chart is designed to detect a specific shift, provided that the shift size is known in advance. In practice, however, shift sizes are rarely known. It is then customary to use an adaptive CUSUM chart, which can effectively detect a range of shift sizes. In this paper, we enhance the sensitivities of the improved adaptive CUSUM mean charts using an auxiliary-information-based (AIB) mean estimator. The run length performances of the proposed charts are compared with those of the AIB adaptive and non-adaptive CUSUM charts in terms of the average run length (ARL), extra quadratic loss, and integral relative ARL. These run length comparisons reveal that the proposed charts are more sensitive than the existing charts when detecting different kinds of shift in the process mean. An example is given to demonstrate the implementation of existing and proposed charts.

Keywords:

• Auxiliary information
• average run length
• control chart
• difference estimator
• extra quadratic loss
• integral relative average run length
• process mean

2010 Mathematics Subject Classification:

• 62N10

Acknowledgments

The authors are thankful to the Associate Editor and the anonymous reviewer 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