Efficient signed-rank based EWMA and HWMA repetitive control charts for monitoring process mean with and without auxiliary information

Ambreen Shafqat; Huang Zhensheng; Muhammad Aslam

doi:10.1038/s41598-023-42632-x

Efficient signed-rank based EWMA and HWMA repetitive control charts for monitoring process mean with and without auxiliary information

Sci Rep. 2023 Sep 30;13(1):16459. doi: 10.1038/s41598-023-42632-x.

Authors

Ambreen Shafqat^{1

2}, Huang Zhensheng³, Muhammad Aslam⁴

Affiliations

¹ Department of Financial Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, China.
² Department of Urology, Roswell Park Cancer Research Institute, Buffalo, NY, 14263, USA.
³ Department of Financial Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, China. stahzs@126.com.
⁴ Department of Statistics, Faculty of Science, King Abdulaziz University, 21551, Jeddah, Saudi Arabia.

Abstract

Control charts are powerful tools to observe the presentation of the manufacturing process. Mostly, when the data in industries come from the process may follow non-normal or unknown distributions. So, the distribution-free control charts are useful in practice when the possibility model of the process productivity is unknown. In such situations, the correct selection of the sampling mechanism is beneficial for process examination. This paper proposes a nonparametric exponentially weighted moving average signed-rank (EWMA-SR) and also proposed a homogeneously weighted moving average Signed-Rank (HWMA-SR) control charts for examining the small shift in process with the help of an auxiliary variable (in the form of a regression estimator) by using an efficient plan, namely, a repetitive sampling plan. The proposal's presentation is evaluated and matched with its complements for different symmetric distributions by using some famous run length properties including average run length, median run length, and standard deviation of run length.