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The effects of constructed bivariate copulas on multivariate control charts effectiveness
Author(s) -
Sukparungsee Saowanit,
Sasiwannapong Sirasak,
Busababodhin Piyapatr,
Areepong Yupaporn
Publication year - 2021
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2850
Subject(s) - control chart , bivariate analysis , multivariate statistics , statistics , chart , multivariate normal distribution , \bar x and r chart , statistical process control , mathematics , control limits , shewhart individuals control chart , econometrics , ewma chart , computer science , process (computing) , operating system
The average control chart monitors the shifts in the process. The familiar multivariate control charts are used to detect the mean vector of the process such as multivariate cumulative sum (MCUSUM) and Hotelling's T 2 control charts. In this paper, the effects of constructing bivariate copulas on multivariate control charts, that is, MCUSUM and Hotelling's T 2 control charts are intensively investigated when observations are drawn from the exponential distribution. Moreover, the dependence levels of observations are classified to be weak, moderate, and strong in both positive and negative values by Kendall's tau. The numerical results were obtained by Monte Carlo simulation to explore the average run length (ARL). The simulation results show that the performance of Hotelling's T 2 control chart is superior to the MCUSUM control chart for all shifts in the mean vector of process. Furthermore, from applying the presented control chart to two sets of real data, data set of the strength of 1.5 cm glass fibers measured at the National Physical Laboratory, England and data set of the strength of glass of the aircraft window, it was found that for a small shift ( δ ≤ 0.1 ), the MCUSUM control chart is better than Hotelling's T 2 control chart.