A maximum dual CUSUM chart for joint monitoring of process mean and variance

ABSTRACT

A dual chart provides more sensitivity than the conventional chart when it is known that a shift size varies within a given interval. In this paper, we propose a maximum dual CUSUM (MDC) chart for monitoring the joint shifts (that lie in different intervals) in the mean and variance of a normally distributed process. The Monte Carlo simulation method is used to estimate the zero-state and steady-state run-length properties of the MDC chart, which include the average run-length (ARL), expected weighted run-length (EWRL) and expected relative ARL (ERARL). Based on detailed run-length comparisons in terms of the EWRL and ERARL, it is found that the MDC chart outperforms the maximum adaptive EWMA (MAE) and maximum weighted adaptive CUSUM (MWAC) charts when detecting a range of the joint shift sizes. Moreover, the diagnostic abilities of the MDC chart are also studied. Real and simulated datasets are considered to demonstrate the implementation of the MAE, MWAC and MDC charts.

KEYWORDS:

• Control chart
• maximum dual CUSUM
• Monte carlo simulation
• process mean and variance
• run length properties
• statistical process control

Acknowledgements

The authors are thankful to the associate editor and two 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 author(s).

Additional information

Notes on contributors

Abdul Haq

Abdul Haq is an Associate Professor at the Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan. His research interest is in Statistical Process Control.

Qamar Ali

Qamar Ali is an MPhil Student at the Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan. His research interest is in Statistical Process Control.