Weighted adaptive multivariate CUSUM charts with variable sampling intervals

ABSTRACT

The adaptive multivariate CUSUM (AMCUSUM) chart has received considerable attention because of its superior sensitivity against a range of mean shift sizes than that of the conventional non-adaptive multivariate CUSUM (MCUSUM) chart. Recently, weighted AMCUSUM (WAMCUSUM) charts with a fixed sampling interval (FSI) have been proposed, called the WAMCUSUM-FSI charts, which provide more sensitivity than the AMCUSUM-FSI charts. In this paper, we extend this work and propose WAMCUSUM charts with variable sampling interval (VSI), named the WAMCUSUM-VSI charts, for efficiently monitoring the mean of a multivariate normally distributed process. The Monte Carlo simulation method is used to compute the average time to signal (ATS) and the adjusted ATS (AATS) profiles of the existing and proposed charts. It is found that the WAMCUSUM-VSI charts perform substantially and nearly uniformly better than the WAMCUSUM-FSI charts in terms of the ATS and AATS performance criterion. An example is given to explain the implementation of the WAMCUSUM charts with fixed and VSIs.

KEYWORDS:

• Average time to signal
• fixed and variable sampling intervals
• multivariate CUSUM chart
• process mean
• statistical process control

Acknowledgements

The author is 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 author.

ORCID

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