On a Correlated Variance Ratio Distribution and Its Industrial Application

Abstract

The distribution of correlated variance ratio arises if variables in the parent population are correlated. One such case arises if sample observations follow independent bivariate normal distributions. We study its cumulative distribution function, raw moments, mean centered moments, coefficient of skewness and kurtosis, median and reliability. The density function is also graphed. We address the issue of the invariance of the distribution of correlated variance ratio, and testing equality of variances under correlation. Finally we exhibit an application of the said distribution in quality control problems for monitoring process outputs using control charts.

Keywords:

• Correlated chi-square variables
• Cumulative distribution function
• Equality of variances
• Invariance
• Moments
• Quality control
• Testing of hypotheses
• Variance ratio

Mathematics Subject Classification:

• Primary 62E
• Scondary 62P