A side-sensitive synthetic chart for the multivariate coefficient of variation.

Area of Science:

• Statistical Process Control
• Quality Engineering
• Multivariate Data Analysis

Background:

• Conventional control charts monitor process mean (μ) or standard deviation (σ) separately.
• Coefficient of variation (γ = σ/μ) charts offer a more comprehensive stability measure.
• A side-sensitive synthetic (SS) chart enhances univariate γ monitoring but lacks multivariate application.

Purpose of the Study:

• To propose and evaluate a side-sensitive synthetic (SS) control chart for monitoring the coefficient of variation (γ) in multivariate processes.
• To address the need for monitoring correlated quality characteristics in practical industrial scenarios.

Main Methods:

• Development of a multivariate SS chart for the coefficient of variation (γ).
• Performance evaluation using run length analysis based on numerical examples.
• Comparison with existing methods like the Shewhart γ chart and Multivariate Exponentially Weighted Moving Average (MEWMA) γ chart.

Main Results:

• The multivariate SS chart demonstrates significantly improved sensitivity, especially for small shifts (τ), small sample sizes (n), and high dimensionality (p).
• The side-sensitivity feature enhances detection capabilities compared to non-side-sensitive approaches.
• The proposed chart outperforms the Shewhart γ chart and shows marginal advantages over the MEWMA γ chart for moderate to large shifts.

Conclusions:

• The multivariate SS chart is a highly effective tool for monitoring process stability using the coefficient of variation (γ) in complex, correlated quality characteristics.
• Its superior performance in detecting small shifts makes it valuable for maintaining process quality.
• The chart's practical implementation is demonstrated through monitoring investment risks.