# One-sided Downward Control Chart for Monitoring the Multivariate Coefficient of Variation with VSSI Strategy

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2020.52.1.8## Keywords:

average time to signal, downward shifts, expected average time to signal, multivariate coefficient of variation, variable sample size and sampling interval## Abstract

In recent years, control charts monitoring the coefficient of variation (CV), denoted as the ratio of the variance to the mean, is attracting significant attention due to its ability to monitor processes in which the process mean and process variance are not independent of each other. However, very few studies have been done on charts to monitor downward process shifts, which is important since downward process shifts show process improvement. In view of the importance of today's competitive manufacturing environment, this paper proposes a one-sided chart to monitor the downward multivariate CV (MCV) with variable sample size and sampling interval (VSSI), i.e. the VSSI_{D} MCV chart. This paper monitors the MCV as most industrial processes simultaneously monitor at least two or more quality characteristics, while the VSSI feature is incorporated, as it is shown that this feature brings about a significant improvement of the chart. A Markov chain approach was adopted for designing a performance measure of the proposed chart. The numerical comparison revealed that the proposed chart outperformed existing MCV charts. The implementation of the VSSI_{D} MCV chart is illustrated with an example.

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