Multi-chart schemes for detecting a range of variance changes

ABSTRACT

This article considers how CUmulative SUM (CUSUM) and Exponentially Weighted Moving Average (EWMA) multi-charts were used to monitor the variance (variability). Multi-chart schemes are a combination of several single charts that detect changes in a process quickly. We give a theoretical equation to arrive at the optimality of the CUSUM multi-chart for the variance. Simulation studies and asymptotic analyses show that the CUSUM multi-chart has better performance than the EWMA multi-chart in detecting variance shifts in an $i.i.d.$ normal observations. The variance change problem has diverse and attractive application areas; we give a real example in the field of agriculture that monitors the price variability of maize to demonstrate the practicality of the schemes.

KEYWORDS:

• Multi-charts
• variance change
• optimality
• CUSUM and EWMA
• maize prices

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data used to support the findings of this study are available from (https://www.indexmundi.com/commodities/?commodity=corn months = 360).

Additional information

Funding

The work was supported by the National Basic Research Program of China (973 Program, 2015CB856004), National Natural Science Foundation of China (11531001) National Basic Research Program of China (973 Program, 2015CB856004), National Natural Science Foundation of China (11531001) .This research was supported by National Basic Research Program of China (973 Program, 2015CB856004) and the National Natural Science Foundation of China (11531001).

Notes on contributors

Gideon Mensah Engmann

Gideon Mensah Engmann obtained his Master’s degree in Statistics (Biostatistics) in 2009 from the Center for Statistics, University of Hasselt, Belgium. He earned his PhD in Statistics from the School of Mathematical Sciences, Shanghai Jiao Tong University, People’s Republic of China in 2021. He is a Senior Lecturer at the Department of Biometry, C. K. Tedam University of Technology and Applied Sciences, Ghana. His current research interest includes Statistical Process Control and its Applications.

Dong Han

Dong Han obtained his Master’s degree in Probability and Statistics in 1985 from Central South University, People’s Republic of China. He earned his PhD in Probability and Statistics from Beijing Normal University, People’s Republic of China in 1989. He taught in the Department of Mathematics at the Xinjiang University, People’s Republic of China from 1989 to 2000. He joined School of Mathematical Sciences, Shanghai Jiao Tong University, People’s Republic of China in 2000 and currently working as a Professor. His research interest includes Statistical Process Control, Mathematical Models in Finance, Random Graphs and Complex Networks.

Muhammad Ali Raza

Muhammad Ali Raza obtained his MSc and MPhil in Statistics from the University of the Punjab Lahore, Pakistan. He earned his PhD in Statistics from the School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China in 2019. He has been working as an Assistant Professor in the Department of Statistics, Government College University Faisalabad, Pakistan since 2011. He has more than 30 publications in various research journals. His research interests include Statistical Process Control and Monitoring and Applied Statistics.