A variable sampling interval run sum chart for monitoring multivariate coefficient of variation

Area of Science:

• Statistical Process Control
• Quality Engineering
• Multivariate Data Analysis

Background:

• The coefficient of variation (CV) measures relative data dispersion.
• Multivariate coefficient of variation (MCV) charts monitor CV in Phase-II studies.
• Existing MCV and run sum MCV (RS MCV) charts have limitations in shift detection.

Purpose of the Study:

• To develop novel upward and downward variable sampling interval run sum multivariate coefficient of variation (VSI RS MCV) charts.
• To enhance the detection of shifts in MCV.
• To evaluate and compare the performance of VSI RS MCV charts against existing MCV and RS MCV charts.

Main Methods:

• Development of VSI RS MCV charts for Phase-II monitoring.
• Performance evaluation using Average Time To Signal (ATS), Standard Deviation of Time To Signal (SDTS), and Expected Average Time To Signal (EATS).
• Optimization using Markov chain methodology in MATLAB to determine optimal chart parameters.

Main Results:

• The developed VSI RS MCV charts demonstrate superior performance across all shift sizes.
• VSI RS MCV charts show improved ATS, SDTS, and EATS compared to MCV and RS MCV charts.
• Optimization programs successfully identified parameters minimizing out-of-control values.

Conclusions:

• VSI RS MCV charts are highly effective for detecting MCV shifts in multivariate quality control.
• The proposed charts offer significant improvements over existing methods in terms of detection efficiency.
• An illustrative example confirms the practical implementation and benefits of VSI RS MCV charts.