Monitoring Mortality Caused by COVID-19 Using Gamma-Distributed Variables Based on Generalized Multiple Dependent...

Area of Science:

• Statistical Quality Control
• Industrial Statistics
• Process Monitoring

Background:

• Traditional control charts assume normal distributions, limiting their application for non-normal quality characteristics.
• Non-normal data, particularly gamma distributions, are common in various industrial and healthcare settings.
• Advanced sampling techniques are needed to enhance the sensitivity of control charts for non-normal processes.

Purpose of the Study:

• To propose a novel generalized multiple dependent state (GMDS) sampling control chart for gamma distributed quality characteristics.
• To transform gamma data into a normal distribution for effective process monitoring.
• To evaluate the performance of the proposed control chart against existing methods.

Main Methods:

• Development of a GMDS sampling control chart for gamma distributions.
• Parameter estimation using in-control average run length (ARL) at specified shape parameters.
• Simulation studies to assess out-of-control ARL for various scale parameter shifts.
• Application of a case study using COVID-19 ICU data.

Main Results:

• The proposed gamma control chart with GMDS sampling demonstrates superior performance in terms of average run lengths compared to existing MDS and Shewhart charts.
• The control chart effectively detects shifts in the scale parameter of gamma distributed data.
• The simulation results confirm the enhanced sensitivity and efficiency of the proposed method.

Conclusions:

• The proposed GMDS sampling gamma control chart offers a robust and effective solution for monitoring non-normal quality characteristics.
• This method provides improved statistical power for process control in industries dealing with skewed data.
• The practical application using COVID-19 data highlights its real-world utility and adaptability.