Variable sample size and sampling interval (VSSI) and variable parameters (VP) run sum charts for the coefficient of variation

ABSTRACT

This paper improves the sensitivity of the existing run sum chart for shifts in the coefficient of variation $\left(\gamma \right)$ by proposing two types of adaptive schemes, i.e. the variable sample size and sampling interval (VSSI) and variable parameter (VP) schemes. The VSSI run sum $\gamma$ chart varies the sample size $\left(n\right)$ and sampling interval $\left(h\right)$, while the VP run sum $\gamma$ chart varies not only n and h but also the size of each region of the run sum chart. The operations, as well as formulae and algorithms to optimize the charts’ performance, are developed. Subsequently, tables of optimal charting parameters are obtained. The VP run sum $\gamma$ chart is shown to outperform the VSSI run sum $\gamma$ chart. The proposed charts are also shown to outperform the variable sampling interval (VSI) run sum, variable sample size (VSS) run sum, and the VSSI, VSS and VSI $\gamma$ charts, as well as the VSS and VSI EWMA ${\gamma }^2$ charts for moderate and large shift sizes. Implementation on an actual industrial example shows the sensitivity of the proposed charts towards small shifts.

KEYWORDS:

• Average time to signal
• coefficient of variation
• run sum
• variable parameters
• variable sample size and sampling interval

Acknowledgements

This research was supported by Ministry of Higher Education Malaysia, Fundamental Research Grant Scheme (FRGS), project code FRGS/1/2018/STG06/UM/02/3 (FP052-2018A) and Sunway University Internal Grant Scheme, under grant GRTIN-IGS(02)-DAPS-07-2022.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Ministry of Higher Education Malaysia, Fundamental Research Grant Scheme (FRGS), project code FRGS/1/2018/STG06/UM/02/3 (FP052-2018A) and Sunway University Internal Grant Scheme, under grant GRTIN-IGS(02)-DAPS-07-2022.

Notes on contributors

Wai Chung Yeong

Wai Chung Yeong is an associate professor in the School of Mathematical Sciences, Sunway University, Malaysia. He received his PhD from the School of Mathematical Sciences, University Sains Malaysia. He specializes in Statistical Quality Control.

Yen Yoon Tan

Yen Yoon Tan is a lecturer in A Levels, Sunway College Kuala Lumpur, Malaysia. She is pursuing her Phd from the School of Mathematical Sciences, Sunway University, Malaysia. Her research interrest is in Statistical Process Control.

Sok Li Lim

Sok Li Lim is an associate professor in the School of Accounting and Finance, Faculty of Business and Law, Taylors’s University. Her research interest is on Statistical Process Control.

Khai Wah Khaw

Khai Wah Khaw is a senior lecturer in the School of Management, University Sains Malaysia. He received his Phd from the School of Mathematical Sciences, University Sains Malaysia. His research interest is in Statistical Process Control and advanced analytics.

Michael Boon Chong Khoo

Michael Boon Chong Khoo is a professor in the School of Mathematical Sciences, University Sains Malaysia. He received his Phd in Applied Statistics in 2001 from University Sains Malaysia. His research interest is in Statistical Process Control. He is a member of the American Society for Quality.