A control chart for bivariate discrete data monitoring

Area of Science:

• Statistical Process Control
• Quality Management
• Industrial Statistics

Background:

• Control charts are essential for detecting process variations.
• Existing methods like Hotelling's T^2 chart have limitations in monitoring complex data.
• Continuous improvement relies on advanced process monitoring tools.

Purpose of the Study:

• To introduce a bivariate exponentially weighted moving average (MEWMA) control chart.
• To monitor the mean vector of Gumbel's bivariate geometric (GBG) data.
• To compare the proposed MEWMA (GBG) chart's performance against Hotelling's T^2 chart.

Main Methods:

• Development of a MEWMA control chart tailored for GBG distributions.
• Comparative analysis using simulated and real-life datasets.
• Performance evaluation based on statistical metrics and detection capabilities.

Main Results:

• The proposed MEWMA (GBG) chart demonstrates superior performance over Hotelling's T^2 chart.
• The MEWMA (GBG) chart uniformly and substantially outperforms existing methods.
• Validation through real-world industrial examples and simulated data.

Conclusions:

• The MEWMA (GBG) chart is a more effective tool for joint monitoring of GBG data.
• This advancement offers improved process stability and performance monitoring.
• The study recommends the adoption of the MEWMA (GBG) chart for enhanced quality control.